* [?????](#?????) * [???????](#???????) * [??????](#??????) * [????](#????) * [????](#????) * [???????](#???????) * [??????](#??????) * [?????](#?????) * [????](#????) * [BFS](#bfs) * [DFS](#dfs) * [Backtracking](#backtracking) * [????](#????) * [???](#???) * [????œý](#????œý) * [???????](#???????) * [????¡¤??](#????¡¤??) * [??????????](#??????????) * [????????????](#????????????) * [???????????](#???????????) * [0-1 ????](#0-1-????) * [????????](#????????) * [???????](#???????) * [????????](#????????) * [???](#???) * [????](#????) * [??????](#??????) * [???????](#???????) * [???](#???) * [????????????](#????????????) * [????????](#????????) * [??????????](#??????????) * [????](#????) * [????????](#????????) * [??????](#??????) * [?????](#?????) * [?????](#?????) * [?????????](#?????????) * [???????](#???????) * [????](#????) * [??](#??) * [???](#???) * [??¦Á???](#??¦Á???) * [??§Ü??????](#??§Ü??????) * [BST](#bst) * [Trie](#trie) * [?](#?) * [¦Ë????](#¦Ë????) * [?¦Ï?????](#?¦Ï?????) # ????? ## ??????? ?????????????????????????§»??????????? 1. ????? mid ???????? mid = (l + h) / 2 ??????????? l + h ???????????????????? mid = l + (h - l) / 2 ?? 2. ?? h ??????????????§Û???????????? l <= h ???h = mid - 1???????????? l < h ???h = mid?? ??????????????????? l <= h ?????? h = mid??????????????????????????? l = 1??h = 1????? mid ????? 1??????????????? h = mid ??????????????????????????? l < h ????? h = mid - 1??????????????????????????????? 1,2,3 ??????? 1 ????? l = 0??h = 2??mid = 1???§Ø? key < arr[mid] ??? h = mid - 1 = 0?????????????????????????????? 3. l ???????? l = mid + 1?? ```java public int search(int key, int[] arr) { int l = 0, h = arr.length - 1; while (l <= h) { int mid = l + (h - l) / 2; if (key == arr[mid]) return mid; if (key < arr[mid]) h = mid - 1; else l = mid + 1; } return -1; } ``` **???** [Leetcode : 69. Sqrt(x) (Easy)](https://leetcode.com/problems/sqrtx/description/) ????? x ????? sqrt ????? 0 \~ x ??????????? sqrt == x / sqrt ?????????????????? 0 \~ x ?????? sqrt?? ```java public int mySqrt(int x) { if(x <= 1) return x; int l = 1, h = x; while(l <= h){ int mid = l + (h - l) / 2; int sqrt = x / mid; if(sqrt == mid) return mid; else if(sqrt < mid) h = mid - 1; else l = mid + 1; } return h; } ``` **?????** [Leetcode : 441. Arranging Coins (Easy)](https://leetcode.com/problems/arranging-coins/description/) ```html n = 8 The coins can form the following rows: ?? ?? ?? ?? ?? ?? ?? ?? Because the 4th row is incomplete, we return 3. ``` ??????????? i ?§Ñ? i ?????????????§Ö??????? ???? h ?????? l????????????????§Ó????????? ```java public int arrangeCoins(int n) { int l = 0, h = n; while(l <= h){ int m = l + (h - l) / 2; long x = m * (m + 1L) / 2; if(x == n) return m; else if(x < n) l = m + 1; else h = m - 1; } return h; } ``` ?????????????????????????? ```java public int arrangeCoins(int n) { int level = 1; while (n > 0) { n -= level; level++; } return n == 0 ? level - 1 : level - 2; } ``` **????????? Single Element** [Leetcode : 540. Single Element in a Sorted Array (Medium)](https://leetcode.com/problems/single-element-in-a-sorted-array/description/) ?????????????????????????????????????¦²??????????? ```java public int singleNonDuplicate(int[] nums) { int l = 0, h = nums.length - 1; while(l < h) { int m = l + (h - l) / 2; if(m % 2 == 1) m--; // ??? l/h/m ???????¦Ë????¨°????????§³?????? ???? if(nums[m] == nums[m + 1]) l = m + 2; else h = m; } return nums[l]; } ``` ## ?????? ?????????¦Â??????????????????????????????????????? **???????** [Leetcode : 455. Assign Cookies (Easy)](https://leetcode.com/problems/assign-cookies/description/) ???????????????????????????????????????????§³????§Ò?????§³???????????????????¨²???????????????????????????????????? ?????§³????????????????????????????§³?????????????????????????§³????????¨²??????????????????????????????????? ??????????????????§µ????????????? i ?????????? m ???????????? i ?????????????§³???? m ???????????????? i ?????????§³?????????????????????????? k ???????????????????????????§Ú? i ?????????? n ?????????????????????? m ??????????????????????????????? k ?????????????????? m ???????????? n ???????????????????????????????????????????????????????????? ```java public int findContentChildren(int[] g, int[] s) { Arrays.sort(g); Arrays.sort(s); int i = 0, j = 0; while(i < g.length && j < s.length){ if(g[i] <= s[j]) i++; j++; } return i; } ``` **??????????** [Leetcode : 452. Minimum Number of Arrows to Burst Balloons (Medium)](https://leetcode.com/problems/minimum-number-of-arrows-to-burst-balloons/description/) ``` Input: [[10,16], [2,8], [1,6], [7,12]] Output: 2 ``` ?????????????????????????????????????????????????????????¡¤???????????????????§³???????????? ```java public int findMinArrowShots(int[][] points) { if(points.length == 0) return 0; Arrays.sort(points,(a,b) -> (a[1] - b[1])); int curPos = points[0][1]; int ret = 1; for (int i = 1; i < points.length; i++) { if(points[i][0] <= curPos) { continue; } curPos = points[i][1]; ret++; } return ret; } ``` **????????????** [Leetcode : 122. Best Time to Buy and Sell Stock II (Easy)](https://leetcode.com/problems/best-time-to-buy-and-sell-stock-ii/description/) ?????????????????????????¨°??????????µµ ??????????? [a, b, c, d]??????? a <= b <= c <= d ????????????? d - a = (d - c) + (c - b) + (b - a) ???????????? prices[i] ?? prices[i] - prices[i-1] ???????? prices[i] - prices[i-1] ????????§µ?????????????????????????????? ```java public int maxProfit(int[] prices) { int profit = 0; for(int i = 1; i < prices.length; i++){ if(prices[i] > prices[i-1]) profit += (prices[i] - prices[i-1]); } return profit; } ``` **???????** [Leetcode : 605. Can Place Flowers (Easy)](https://leetcode.com/problems/can-place-flowers/description/) ```html Input: flowerbed = [1,0,0,0,1], n = 1 Output: True ``` ????????????????????????????¦Ë?????? ```java public boolean canPlaceFlowers(int[] flowerbed, int n) { int cnt = 0; for(int i = 0; i < flowerbed.length; i++){ if(flowerbed[i] == 1) continue; int pre = i == 0 ? 0 : flowerbed[i - 1]; int next = i == flowerbed.length - 1 ? 0 : flowerbed[i + 1]; if(pre == 0 && next == 0) { cnt++; flowerbed[i] = 1; } } return cnt >= n; } ``` **???????????????????** [Leetcode : 665. Non-decreasing Array (Easy)](https://leetcode.com/problems/non-decreasing-array/description/) ??????????§Ø?????????????????????????????????î• ?? nums[i] < nums[i - 1] ??????????????????? nums[i - 1] = nums[i]??????????? nums[i] = nums[i - 1] ???????? nums[i] ???????????????§á???? nums[i + 1] ???????????? nums[i] ??§³?? ?????? nums[i] < nums[i - 2] ???????????? nums[i - 1] ??????????????????????????? nums[i] = nums[i - 1] ???§³? ```java public boolean checkPossibility(int[] nums) { int cnt = 0; for(int i = 1; i < nums.length; i++){ if(nums[i] < nums[i - 1]){ cnt++; if(i - 2 >= 0 && nums[i - 2] > nums[i]) nums[i] = nums[i-1]; else nums[i - 1] = nums[i]; } } return cnt <= 1; } ``` **?§Ø????????** [Leetcode : 392. Is Subsequence (Medium)](https://leetcode.com/problems/is-subsequence/description/) ```html s = "abc", t = "ahbgdc" Return true. ``` ```java public boolean isSubsequence(String s, String t) { for (int i = 0, pos = 0; i < s.length(); i++, pos++) { pos = t.indexOf(s.charAt(i), pos); if(pos == -1) return false; } return true; } ``` **????????????????????????** [Leetcode : 763. Partition Labels (Medium)](https://leetcode.com/problems/partition-labels/description/) ```java public List partitionLabels(String S) { List ret = new ArrayList<>(); int[] lastIdxs = new int[26]; for(int i = 0; i < S.length(); i++) lastIdxs[S.charAt(i) - 'a'] = i; int startIdx = 0; while(startIdx < S.length()) { int endIdx = startIdx; for(int i = startIdx; i < S.length() && i <= endIdx; i++) { int lastIdx = lastIdxs[S.charAt(i) - 'a']; if(lastIdx == i) continue; if(lastIdx > endIdx) endIdx = lastIdx; } ret.add(endIdx - startIdx + 1); startIdx = endIdx + 1; } return ret; } ``` **??????????????????** ```html Input: [[7,0], [4,4], [7,1], [5,0], [6,1], [5,2]] Output: [[5,0], [7,0], [5,2], [6,1], [4,4], [7,1]] ``` ???????????????? (h, k) ??????h ???????k ????????????? k ??????????????????????????? ????????????k ??????????????????????§Ö?? k ??¦Ë???§³? ```java public int[][] reconstructQueue(int[][] people) { if(people == null || people.length == 0 || people[0].length == 0) return new int[0][0]; Arrays.sort(people, new Comparator() { public int compare(int[] a, int[] b) { if(a[0] == b[0]) return a[1] - b[1]; return b[0] - a[0]; } }); int n = people.length; List tmp = new ArrayList<>(); for(int i = 0; i < n; i++) { tmp.add(people[i][1], new int[]{people[i][0], people[i][1]}); } int[][] ret = new int[n][2]; for(int i = 0; i < n; i++) { ret[i][0] = tmp.get(i)[0]; ret[i][1] = tmp.get(i)[1]; } return ret; } ``` ## ???? ?????????????????ï…????????????????????§¿???????? **??????????????????§Ó???????????????????? 0** [Leetcode ??167. Two Sum II - Input array is sorted (Easy)](https://leetcode.com/problems/two-sum-ii-input-array-is-sorted/description/) ????????????????????§³???????????????????????????§³???????????¦Â???????????????????¦Â????????? ?????????????????? sum == target??????????????????? sum > target?????????????? sum ??§³?§»????? sum < target???????§³??????? sum ????§»?? ```java public int[] twoSum(int[] numbers, int target) { int i = 0, j = numbers.length - 1; while (i < j) { int sum = numbers[i] + numbers[j]; if (sum == target) return new int[]{i + 1, j + 1}; else if (sum < target) i++; else j--; } return null; } ``` ????????????????????? 0 ??????[???????????????? P351](#) **?????????????????????????øA??** [???????????????? P354/P355/P358](#) **???§Ü??§Ø???????????§Ó??????** [???????????????? P347](#) **?????????§Ö???????** [Leetcode : 345. Reverse Vowels of a String (Easy)](https://leetcode.com/problems/reverse-vowels-of-a-string/description/) ??????????????????????????????????????¦Â?????????????¦Â????????? ```java private HashSet vowels = new HashSet<>(Arrays.asList('a','e','i','o','u','A','E','I','O','U')); public String reverseVowels(String s) { if(s.length() == 0) return s; int i = 0, j = s.length() - 1; char[] result = new char[s.length()]; while(i <= j){ char ci = s.charAt(i); char cj = s.charAt(j); if(!vowels.contains(ci)){ result[i] = ci; i++; } else if(!vowels.contains(cj)){ result[j] = cj; j--; } else{ result[i] = cj; result[j] = ci; i++; j--; } } return new String(result); } ``` **?????????** [Leetcode : 633. Sum of Square Numbers (Easy)](https://leetcode.com/problems/sum-of-square-numbers/description/) ?§Ø???????????????????????????? 5 = 1² + 2²?? ```java public boolean judgeSquareSum(int c) { int left = 0, right = (int) Math.sqrt(c); while(left <= right){ int powSum = left * left + right * right; if(powSum == c) return true; else if(powSum > c) right--; else left++; } return false; } ``` **??????????????????????????** [Leetcode : 680. Valid Palindrome II (Easy)](https://leetcode.com/problems/valid-palindrome-ii/description/) ```java public boolean validPalindrome(String s) { int i = 0, j = s.length() -1; while(i < j){ if(s.charAt(i) != s.charAt(j)){ return isPalindrome(s, i, j - 1) || isPalindrome(s, i + 1, j); } i++; j--; } return true; } private boolean isPalindrome(String s, int l, int r){ while(l < r){ if(s.charAt(l) != s.charAt(r)) return false; l++; r--; } return true; } ``` **?öã????????????** [Leetcode : 88. Merge Sorted Array (Easy)](https://leetcode.com/problems/merge-sorted-array/description/) ??öã????›Ô???????????? ```java public void merge(int[] nums1, int m, int[] nums2, int n) { int i = m - 1, j = n - 1; // ?????¦Â??????????????? nums1 ??öã???????????¦Ä???§Ûöã????? int idx = m + n - 1; while(i >= 0 || j >= 0){ if(i < 0) nums1[idx] = nums2[j--]; else if(j < 0) nums1[idx] = nums1[i--]; else if(nums1[i] > nums2[j]) nums1[idx] = nums1[i--]; else nums1[idx] = nums2[j--]; idx--; } } ``` **?§Ø????????????** [Leetcode : 141. Linked List Cycle (Easy)](https://leetcode.com/problems/linked-list-cycle/description/) ????????????????????????????????????????????????????????????????????????????? ```java public boolean hasCycle(ListNode head) { if(head == null) return false; ListNode l1 = head, l2 = head.next; while(l1 != null && l2 != null){ if(l1 == l2) return true; l1 = l1.next; if(l2.next == null) break; l2 = l2.next.next; } return false; } ``` **????????** [Leetcode : 524. Longest Word in Dictionary through Deleting (Medium)](https://leetcode.com/problems/longest-word-in-dictionary-through-deleting/description/) ``` Input: s = "abpcplea", d = ["ale","apple","monkey","plea"] Output: "apple" ``` ```java public String findLongestWord(String s, List d) { String ret = ""; for (String str : d) { for (int i = 0, j = 0; i < s.length() && j < str.length(); i++) { if (s.charAt(i) == str.charAt(j)) j++; if (j == str.length()) { if (ret.length() < str.length() || (ret.length() == str.length() && ret.compareTo(str) > 0)) { ret = str; } } } } return ret; } ``` ## ???? ### ??????? ?????????? **Kth Element** ?????????? O(n) ??ÁÙ????O(1) ??ÁÙ????????????? ???????????????????????????????????ï…?????????????ÁÙ???? O(n²)?? ### ?????? ????????????? **TopK Elements** ???????????????§³? K ???????§Ö??????? TopK Elements??????????????????? Kth Element ??????????????????????? Kth Element????????????????? TopK Elements ?????????? Kth Element ??????????????ï…????§³????? Kth Element ???????? TopK Elements?????????????????????????????? Kth Element ?? TopK Elements ????????§á???????????? **Kth Element** [Leetocde : 215. Kth Largest Element in an Array (Medium)](https://leetcode.com/problems/kth-largest-element-in-an-array/description/) ????¦Ï???[Solution explained](https://leetcode.com/problems/kth-largest-element-in-an-array/discuss/60294/Solution-explained) - ??ÁÙ??? O(nlgn)????ÁÙ??? O(1) ???????? - ??ÁÙ??? O(nlgk)????ÁÙ??? O(k) ?????????? - ??ÁÙ??? O(n)????ÁÙ??? O(1) ????QuickSelect **ToK Elements** [???????????????? P336](#) ### ????? **?????????????? k ????** [Leetcode : 347. Top K Frequent Elements (Medium)](https://leetcode.com/problems/top-k-frequent-elements/description/) ????? ```java public List topKFrequent(int[] nums, int k) { List ret = new ArrayList<>(); Map map = new HashMap<>(); for(int num : nums) { map.put(num, map.getOrDefault(num, 0) + 1); } List[] bucket = new List[nums.length + 1]; for(int key : map.keySet()) { int frequency = map.get(key); if(bucket[frequency] == null) { bucket[frequency] = new ArrayList<>(); } bucket[frequency].add(key); } for(int i = bucket.length - 1; i >= 0 && ret.size() < k; i--) { if(bucket[i] != null) { ret.addAll(bucket[i]); } } return ret; } ``` ## ???? ?????????????????????????????????????§µ?????????????????????? ### BFS  ??????????????????????§Ö????????????§Ò????????? 0 ???????????? 6??2??1 ?? 5 ????????? ?????? 6 ??????????????? 4 ???? 2 ?????????????????????? 1 ?????????????????????? 5 ???????????? 3 ?? 4 ??????????????????????4 ?? 3 ?? ???????????????????????????????? ??????????????????????????¡¤????????????? d_i ????? i ????????????¡¤????????????????????????????????? i ?????????? j???? d_i<=d_j????????????????????????¡¤?? **?????** ????????¦Á????????????????????¡¤??????¡¤????????????????????????????????????????¡¤??????????¡¤???? ???????? BFS ???????????????? - ???§µ??????›¥??????????? - ??????????????????????????????????????? **???????????§Õ?????????????¡¤??????** ```html [[1,1,0,1], [1,0,1,0], [1,1,1,1], [1,0,1,1]] ``` ```java public int minPathLength(int[][] grids, int tr, int tc) { int[][] next = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}}; int m = grids.length, n = grids[0].length; Queue queue = new LinkedList<>(); queue.add(new Position(0, 0, 1)); while (!queue.isEmpty()) { Position pos = queue.poll(); for (int i = 0; i < 4; i++) { Position nextPos = new Position(pos.r + next[i][0], pos.c + next[i][1], pos.length + 1); if (nextPos.r < 0 || nextPos.r >= m || nextPos.c < 0 || nextPos.c >= n) continue; if (grids[nextPos.r][nextPos.c] != 1) continue; grids[nextPos.r][nextPos.c] = 0; if (nextPos.r == tr && nextPos.c == tc) return nextPos.length; queue.add(nextPos); } } return -1; } private class Position { int r, c, length; public Position(int r, int c, int length) { this.r = r; this.c = c; this.length = length; } } ``` ### DFS  ?????????????????????????????????????????????????›¥??????????????????????????????????????????????????????????????????§Ò????????? 0 ?????????????????????? 6 ???????????? 6 ???§Ò???????????? 4??????????????????????????????????????????????????????? 0 ?????????????????? 0 ???§Ò???????????? 2??????????????Ò ???????????????? DFS ?????????§Ò???????????????????????????????DFS ????????????? **?????** ???? ???????? DFS ???????????????? - ???????????›Ì???????????????????????????????????????????????????? - ?????? BFS ??????????????????????????§Ò??? **??????????????** [Leetcode : 695. Max Area of Island (Easy)](https://leetcode.com/problems/max-area-of-island/description/) ```html [[0,0,1,0,0,0,0,1,0,0,0,0,0], [0,0,0,0,0,0,0,1,1,1,0,0,0], [0,1,1,0,1,0,0,0,0,0,0,0,0], [0,1,0,0,1,1,0,0,1,0,1,0,0], [0,1,0,0,1,1,0,0,1,1,1,0,0], [0,0,0,0,0,0,0,0,0,0,1,0,0], [0,0,0,0,0,0,0,1,1,1,0,0,0], [0,0,0,0,0,0,0,1,1,0,0,0,0]] ``` ```java public int maxAreaOfIsland(int[][] grid) { int m = grid.length, n = grid[0].length; int max = 0; for(int i = 0; i < m; i++){ for(int j = 0; j < n; j++){ if(grid[i][j] == 1) max = Math.max(max, dfs(grid, i, j)); } } return max; } private int dfs(int[][] grid, int i, int j){ int m = grid.length, n = grid[0].length; if(i < 0 || i >= m || j < 0 || j >= n) return 0; if(grid[i][j] == 0) return 0; grid[i][j] = 0; return dfs(grid, i + 1, j) + dfs(grid, i - 1, j) + dfs(grid, i, j + 1) + dfs(grid, i, j - 1) + 1; } ``` **??????????** [Leetcode : 547. Friend Circles (Medium)](https://leetcode.com/problems/friend-circles/description/) ```html Input: [[1,1,0], [1,1,0], [0,0,1]] Output: 2 Explanation:The 0th and 1st students are direct friends, so they are in a friend circle. The 2nd student himself is in a friend circle. So return 2. ``` ```java public int findCircleNum(int[][] M) { int n = M.length; int ret = 0; boolean[] hasFind = new boolean[n]; for(int i = 0; i < n; i++) { if(!hasFind[i]) { dfs(M, i, hasFind); ret++; } } return ret; } private void dfs(int[][] M, int i, boolean[] hasFind) { hasFind[i] = true; int n = M.length; for(int k = 0; k < n; k++) { if(M[i][k] == 1 && !hasFind[k]) { dfs(M, k, hasFind); } } } ``` **?????§Ö????????????** [Leetcode : 200. Number of Islands (Medium)](https://leetcode.com/problems/number-of-islands/description/) ```html 11110 11010 11000 00000 Answer: 1 ``` ```java private int m, n; private int[][] direction = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}}; public int numIslands(char[][] grid) { if (grid == null || grid.length == 0) return 0; m = grid.length; n = grid[0].length; int ret = 0; for (int i = 0; i < m; i++) { for (int j = 0; j < n; j++) { if (grid[i][j] == '1') { dfs(grid, i, j); ret++; } } } return ret; } private void dfs(char[][] grid, int i, int j) { if (i < 0 || i >= m || j < 0 || j >= n || grid[i][j] == '0') return; grid[i][j] = '0'; for (int k = 0; k < direction.length; k++) { dfs(grid, i + direction[k][0], j + direction[k][1]); } } ``` **??????????????§Õ????????¡¤??** [Leetcode : 257. Binary Tree Paths (Easy)](https://leetcode.com/problems/binary-tree-paths/description/) ```html 1 / \ 2 3 \ 5 ``` ```html ["1->2->5", "1->3"] ``` ```java public List binaryTreePaths(TreeNode root) { List ret = new ArrayList(); if(root == null) return ret; dfs(root, "", ret); return ret; } private void dfs(TreeNode root, String prefix, List ret){ if(root == null) return; if(root.left == null && root.right == null){ ret.add(prefix + root.val); return; } prefix += (root.val + "->"); dfs(root.left, prefix, ret); dfs(root.right, prefix, ret); } ``` **?????????** [Leetcode : 130. Surrounded Regions (Medium)](https://leetcode.com/problems/surrounded-regions/description/) ```html For example, X X X X X O O X X X O X X O X X After running your function, the board should be: X X X X X X X X X X X X X O X X ``` ????????????? 'X' ?? 'O' ???? 'X'?? ?????????????????????????????? ```java private int[][] direction = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}}; private int m, n; public void solve(char[][] board) { if (board == null || board.length == 0) return; m = board.length; n = board[0].length; for (int i = 0; i < m; i++) { dfs(board, i, 0); dfs(board, i, n - 1); } for (int i = 0; i < n; i++) { dfs(board, 0, i); dfs(board, m - 1, i); } for (int i = 0; i < m; i++) { for (int j = 0; j < n; j++) { if (board[i][j] == 'T') board[i][j] = 'O'; else if (board[i][j] == 'O') board[i][j] = 'X'; } } } private void dfs(char[][] board, int r, int c) { if (r < 0 || r >= m || c < 0 || c >= n || board[r][c] != 'O') return; board[r][c] = 'T'; for (int i = 0; i < direction.length; i++) { dfs(board, r + direction[i][0], c + direction[i][1]); } } ``` **????????????????????** [Leetcode : 417. Pacific Atlantic Water Flow (Medium)](https://leetcode.com/problems/pacific-atlantic-water-flow/description/) ```html Given the following 5x5 matrix: Pacific \~ \~ \~ \~ \~ \~ 1 2 2 3 (5) * \~ 3 2 3 (4) (4) * \~ 2 4 (5) 3 1 * \~ (6) (7) 1 4 5 * \~ (5) 1 1 2 4 * * * * * * Atlantic Return: [[0, 4], [1, 3], [1, 4], [2, 2], [3, 0], [3, 1], [4, 0]] (positions with parentheses in above matrix). ``` ???????????????????????????¡À?????????????????????¦²????¦È??????????????????????????????????????????????§Ö???? ```java private int m, n; private int[][] matrix; private int[][] direction = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}}; public List pacificAtlantic(int[][] matrix) { List ret = new ArrayList<>(); if (matrix == null || matrix.length == 0) return ret; this.m = matrix.length; this.n = matrix[0].length; this.matrix = matrix; boolean[][] canReachP = new boolean[m][n]; boolean[][] canReachA = new boolean[m][n]; for (int i = 0; i < m; i++) { dfs(i, 0, canReachP); dfs(i, n - 1, canReachA); } for (int i = 0; i < n; i++) { dfs(0, i, canReachP); dfs(m - 1, i, canReachA); } for (int i = 0; i < m; i++) { for (int j = 0; j < n; j++) { if (canReachP[i][j] && canReachA[i][j]) { ret.add(new int[]{i, j}); } } } return ret; } private void dfs(int r, int c, boolean[][] canReach) { if(canReach[r][c]) return; canReach[r][c] = true; for (int i = 0; i < direction.length; i++) { int nextR = direction[i][0] + r; int nextC = direction[i][1] + c; if (nextR < 0 || nextR >= m || nextC < 0 || nextC >= n || matrix[r][c] > matrix[nextR][nextC]) continue; dfs(nextR, nextC, canReach); } } ``` **N ???** [Leetcode : 51. N-Queens (Hard)](https://leetcode.com/problems/n-queens/description/)  ??????????? n\*n ??????§Ñ?? n ?????????????????????§µ????§µ??????????????????§Ö? n ???? ?????§Ö?????????????§Ö????????????????????????????????????????????????????????????????????????§Ò?????î”45 ????????????? 135 ???????????î• 45 ????????????????? 2\*n - 1??????????????? (r,c) ??¦Ë????????????¡À?? r + c??  135 ??????????????????? 2\*n - 1??(r,c) ??¦Ë????????????¡À?? n - 1 - (r - c)??  ```java private List> ret; private char[][] nQueens; private boolean[] colUsed; private boolean[] diagonals45Used; private boolean[] diagonals135Used; private int n; public List> solveNQueens(int n) { ret = new ArrayList<>(); nQueens = new char[n][n]; Arrays.fill(nQueens, '.'); colUsed = new boolean[n]; diagonals45Used = new boolean[2 * n - 1]; diagonals135Used = new boolean[2 * n - 1]; this.n = n; backstracking(0); return ret; } private void backstracking(int row) { if (row == n) { List list = new ArrayList<>(); for (char[] chars : nQueens) { list.add(new String(chars)); } ret.add(list); return; } for (int col = 0; col < n; col++) { int diagonals45Idx = row + col; int diagonals135Idx = n - 1 - (row - col); if (colUsed[col] || diagonals45Used[diagonals45Idx] || diagonals135Used[diagonals135Idx]) { continue; } nQueens[row][col] = 'Q'; colUsed[col] = diagonals45Used[diagonals45Idx] = diagonals135Used[diagonals135Idx] = true; backstracking(row + 1); colUsed[col] = diagonals45Used[diagonals45Idx] = diagonals135Used[diagonals135Idx] = false; nQueens[row][col] = '.'; } } ``` ### Backtracking ?????? DFS ?????????????????????????????????????? **???????** ?????????? { 'a','b','c' } ??????????????????????????????§Ö??????????? ???????????????????????????§Ò????????????????????????????????????????????????????????????????????????????????????????????????????????????????ú“??????????????????¦Ä??????????????????????????§Ó?????????????????????????????????????????????????????????§Ö????? **??????????** [Leetcode : 17. Letter Combinations of a Phone Number (Medium)](https://leetcode.com/problems/letter-combinations-of-a-phone-number/description/)  ```html Input:Digit string "23" Output: ["ad", "ae", "af", "bd", "be", "bf", "cd", "ce", "cf"]. ``` ```java private static final String[] KEYS = {"", "", "abc", "def", "ghi", "jkl", "mno", "pqrs", "tuv", "wxyz"}; public List letterCombinations(String digits) { List ret = new ArrayList<>(); if (digits != null && digits.length() != 0) { combination("", digits, 0, ret); } return ret; } private void combination(String prefix, String digits, int offset, List ret) { if (offset == digits.length()) { ret.add(prefix); return; } String letters = KEYS[digits.charAt(offset) - '0']; for (char c : letters.toCharArray()) { combination(prefix + c, digits, offset + 1, ret); } } ``` **???????????????** [Leetcode : 79. Word Search (Medium)](https://leetcode.com/problems/word-search/description/) ```html For example, Given board = [ ['A','B','C','E'], ['S','F','C','S'], ['A','D','E','E'] ] word = "ABCCED", -> returns true, word = "SEE", -> returns true, word = "ABCB", -> returns false. ``` ```java private static int[][] shift = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}}; private static boolean[][] visited; private int m; private int n; public boolean exist(char[][] board, String word) { if (word == null || word.length() == 0) return true; if (board == null || board.length == 0 || board[0].length == 0) return false; m = board.length; n = board[0].length; visited = new boolean[m][n]; for (int i = 0; i < m; i++) { for (int j = 0; j < n; j++) { if (dfs(board, word, 0, i, j)) return true; } } return false; } private boolean dfs(char[][] board, String word, int start, int r, int c) { if (start == word.length()) { return true; } if (r < 0 || r >= m || c < 0 || c >= n || board[r][c] != word.charAt(start) || visited[r][c] ) { return false; } visited[r][c] = true; for (int i = 0; i < shift.length; i++) { int nextR = r + shift[i][0]; int nextC = c + shift[i][1]; if (dfs(board, word, start + 1, nextR, nextC)) return true; } visited[r][c] = false; return false; } ``` **IP ???????** [Leetcode : 93. Restore IP Addresses(Medium)](https://leetcode.com/problems/restore-ip-addresses/description/) ```html Given "25525511135", return ["255.255.11.135", "255.255.111.35"]. ``` ```java private List ret; public List restoreIpAddresses(String s) { ret = new ArrayList<>(); doRestore(0, "", s); return ret; } private void doRestore(int k, String path, String s) { if (k == 4 || s.length() == 0) { if (k == 4 && s.length() == 0) { ret.add(path); } return; } for (int i = 0; i < s.length() && i <= 2; i++) { if (i != 0 && s.charAt(0) == '0') break; String part = s.substring(0, i + 1); if (Integer.valueOf(part) <= 255) { doRestore(k + 1, path.length() != 0 ? path + "." + part : part, s.substring(i + 1)); } } } ``` **????** [Leetcode : 46. Permutations (Medium)](https://leetcode.com/problems/permutations/description/) ??????????????????????????§³? ```java public List> permute(int[] nums) { List> ret = new ArrayList<>(); List permuteList = new ArrayList<>(); boolean[] visited = new boolean[nums.length]; backtracking(permuteList, visited, nums, ret); return ret; } private void backtracking(List permuteList, boolean[] visited, int[] nums, List> ret){ if(permuteList.size() == nums.length){ ret.add(new ArrayList(permuteList)); return; } for(int i = 0; i < visited.length; i++){ if(visited[i]) continue; visited[i] = true; permuteList.add(nums[i]); backtracking(permuteList, visited, nums, ret); permuteList.remove(permuteList.size() - 1); visited[i] = false; } } ``` **?????????????** [Leetcode : 47. Permutations II (Medium)](https://leetcode.com/problems/permutations-ii/description/) ```html [1,1,2] have the following unique permutations: [[1,1,2], [1,2,1], [2,1,1]] ``` ?????????? Permutations ????????????????????????????????§Ø?????????????????????????????????????????¦Ä????????????????????? ```java public List> permuteUnique(int[] nums) { List> ret = new ArrayList<>(); List permuteList = new ArrayList<>(); Arrays.sort(nums); boolean[] visited = new boolean[nums.length]; backtracking(permuteList, visited, nums, ret); return ret; } private void backtracking(List permuteList, boolean[] visited, int[] nums, List> ret) { if (permuteList.size() == nums.length) { ret.add(new ArrayList(permuteList)); return; } for (int i = 0; i < visited.length; i++) { if (i != 0 && nums[i] == nums[i - 1] && !visited[i - 1]) continue; if (visited[i]) continue; visited[i] = true; permuteList.add(nums[i]); backtracking(permuteList, visited, nums, ret); permuteList.remove(permuteList.size() - 1); visited[i] = false; } } ``` **???** [Leetcode : 77. Combinations (Medium)](https://leetcode.com/problems/combinations/description/) ?????????????? 1 \~ n ????? k ?????????§á???????? ```java public List> combine(int n, int k) { List> ret = new ArrayList<>(); List combineList = new ArrayList<>(); backtracking(1, n, k, combineList, ret); return ret; } private void backtracking(int start, int n, int k, List combineList, List> ret){ if(k == 0){ ret.add(new ArrayList(combineList)); // ??????????????? List return; } for(int i = start; i <= n - k + 1; i++){ // ??? combineList.add(i); // ?? i ????????? backtracking(i + 1, n, k - 1, combineList, ret); combineList.remove(combineList.size() - 1); // ?? i ????¦Ä???? } } ``` **??????** [Leetcode : 39. Combination Sum (Medium)](https://leetcode.com/problems/combination-sum/description/) ```html given candidate set [2, 3, 6, 7] and target 7, A solution set is: [[7],[2, 2, 3]] ``` ```java private List> ret; public List> combinationSum(int[] candidates, int target) { ret = new ArrayList<>(); doCombination(candidates, target, 0, new ArrayList<>()); return ret; } private void doCombination(int[] candidates, int target, int start, List list) { if (target == 0) { ret.add(new ArrayList<>(list)); return; } for (int i = start; i < candidates.length; i++) { if (candidates[i] <= target) { list.add(candidates[i]); doCombination(candidates, target - candidates[i], i, list); list.remove(list.size() - 1); } } } ``` **???????????????** [Leetcode : 40. Combination Sum II (Medium)](https://leetcode.com/problems/combination-sum-ii/description/) ```html For example, given candidate set [10, 1, 2, 7, 6, 1, 5] and target 8, A solution set is: [ [1, 7], [1, 2, 5], [2, 6], [1, 1, 6] ] ``` ```java private List> ret; public List> combinationSum2(int[] candidates, int target) { ret = new ArrayList<>(); Arrays.sort(candidates); doCombination(candidates, target, 0, new ArrayList<>(), new boolean[candidates.length]); return ret; } private void doCombination(int[] candidates, int target, int start, List list, boolean[] visited) { if (target == 0) { ret.add(new ArrayList<>(list)); return; } for (int i = start; i < candidates.length; i++) { if (i != 0 && candidates[i] == candidates[i - 1] && !visited[i - 1]) continue; if (candidates[i] <= target) { list.add(candidates[i]); visited[i] = true; doCombination(candidates, target - candidates[i], i + 1, list, visited); visited[i] = false; list.remove(list.size() - 1); } } } ``` **???** [Leetcode : 78. Subsets (Medium)](https://leetcode.com/problems/subsets/description/) ??????????????????????????????????????[1, 2] ?? [2, 1] ???????????? ```java private List> ret; private List subsetList; public List> subsets(int[] nums) { ret = new ArrayList<>(); subsetList = new ArrayList<>(); for (int i = 0; i <= nums.length; i++) { backtracking(0, i, nums); } return ret; } private void backtracking(int startIdx, int size, int[] nums) { if (subsetList.size() == size) { ret.add(new ArrayList(subsetList)); return; } for (int i = startIdx; i < nums.length; i++) { subsetList.add(nums[i]); backtracking(i + 1, size, nums); // startIdx ????????????? subset ?§Ö????????????? subsetList.remove(subsetList.size() - 1); } } ``` **????????????** [Leetcode : 90. Subsets II (Medium)](https://leetcode.com/problems/subsets-ii/description/) ```html For example, If nums = [1,2,2], a solution is: [ [2], [1], [1,2,2], [2,2], [1,2], [] ] ``` ```java private List> ret; private List subsetList; private boolean[] visited; public List> subsetsWithDup(int[] nums) { ret = new ArrayList<>(); subsetList = new ArrayList<>(); visited = new boolean[nums.length]; Arrays.sort(nums); for (int i = 0; i <= nums.length; i++) { backtracking(0, i, nums); } return ret; } private void backtracking(int startIdx, int size, int[] nums) { if (subsetList.size() == size) { ret.add(new ArrayList(subsetList)); return; } for (int i = startIdx; i < nums.length; i++) { if (i != 0 && nums[i] == nums[i - 1] && !visited[i - 1]) continue; subsetList.add(nums[i]); visited[i] = true; backtracking(i + 1, size, nums); visited[i] = false; subsetList.remove(subsetList.size() - 1); } } ``` **????????????????????????** [Leetcode : 131. Palindrome Partitioning (Medium)](https://leetcode.com/problems/palindrome-partitioning/description/) ```java private List> ret; public List> partition(String s) { ret = new ArrayList<>(); doPartion(new ArrayList<>(), s); return ret; } private void doPartion(List list, String s) { if (s.length() == 0) { ret.add(new ArrayList<>(list)); return; } for (int i = 0; i < s.length(); i++) { if (isPalindrome(s, 0, i)) { list.add(s.substring(0, i + 1)); doPartion(list, s.substring(i + 1)); list.remove(list.size() - 1); } } } private boolean isPalindrome(String s, int begin, int end) { while (begin < end) { if (s.charAt(begin++) != s.charAt(end--)) return false; } return true; } ``` **????** [Leetcode : 37. Sudoku Solver (Hard)](https://leetcode.com/problems/sudoku-solver/description/)  ```java private boolean[][] rowsUsed = new boolean[9][10]; private boolean[][] colsUsed = new boolean[9][10]; private boolean[][] cubesUsed = new boolean[9][10]; private char[][] board; public void solveSudoku(char[][] board) { this.board = board; for (int i = 0; i < 9; i++) { for (int j = 0; j < 9; j++) { if (board[i][j] == '.') continue; int num = board[i][j] - '0'; rowsUsed[i][num] = true; colsUsed[j][num] = true; cubesUsed[cubeNum(i, j)][num] = true; } } for (int i = 0; i < 9; i++) { for (int j = 0; j < 9; j++) { backtracking(i, j); } } } private boolean backtracking(int row, int col) { while (row < 9 && board[row][col] != '.') { row = col == 8 ? row + 1 : row; col = col == 8 ? 0 : col + 1; } if (row == 9) { return true; } for (int num = 1; num <= 9; num++) { if (rowsUsed[row][num] || colsUsed[col][num] || cubesUsed[cubeNum(row, col)][num]) continue; rowsUsed[row][num] = colsUsed[col][num] = cubesUsed[cubeNum(row, col)][num] = true; board[row][col] = (char) (num + '0'); if (backtracking(row, col)) return true; board[row][col] = '.'; rowsUsed[row][num] = colsUsed[col][num] = cubesUsed[cubeNum(row, col)][num] = false; } return false; } private int cubeNum(int i, int j) { int r = i / 3; int c = j / 3; return r * 3 + c; } ``` ## ???? **????????????** [Leetcode : 241. Different Ways to Add Parentheses (Medium)](https://leetcode.com/problems/different-ways-to-add-parentheses/description/) ```html Input: "2-1-1". ((2-1)-1) = 0 (2-(1-1)) = 2 Output : [0, 2] ``` ```java public List diffWaysToCompute(String input) { int n = input.length(); List ret = new ArrayList<>(); for (int i = 0; i < n; i++) { char c = input.charAt(i); if (c == '+' || c == '-' || c == '*') { List left = diffWaysToCompute(input.substring(0, i)); List right = diffWaysToCompute(input.substring(i + 1)); for (int l : left) { for (int r : right) { switch (c) { case '+': ret.add(l + r); break; case '-': ret.add(l - r); break; case '*': ret.add(l * r); break; } } } } } if (ret.size() == 0) ret.add(Integer.valueOf(input)); return ret; } ``` ## ??? ????????????§³??????????? ## ????œý ?????????????????????????????????????????????????????????¦±? ### ??????? **??????????????** [Leetcode : 343. Integer Break (Medim)](https://leetcode.com/problems/integer-break/description/) ?????????For example, given n = 2, return 1 (2 = 1 + 1); given n = 10, return 36 (10 = 3 + 3 + 4). ```java public int integerBreak(int n) { int[] dp = new int[n + 1]; dp[1] = 1; for(int i = 2; i <= n; i++) { for(int j = 1; j <= i - 1; j++) { dp[i] = Math.max(dp[i], Math.max(j * dp[i - j], j * (i - j))); } } return dp[n]; } ``` **????????????????** [Leetcode : 279. Perfect Squares(Medium)](https://leetcode.com/problems/perfect-squares/description/) ?????????For example, given n = 12, return 3 because 12 = 4 + 4 + 4; given n = 13, return 2 because 13 = 4 + 9. ```java public int numSquares(int n) { List squares = new ArrayList<>(); // ?›¥§³?? n ??????? int diff = 3; while(square <= n) { squares.add(square); square += diff; diff += 2; } int[] dp = new int[n + 1]; for(int i = 1; i <= n; i++) { int max = Integer.MAX_VALUE; for(int s : squares) { if(s > i) break; max = Math.min(max, dp[i - s] + 1); } dp[i] = max; } return dp[n]; } ``` **???????????????????** [Leetcode : 91. Decode Ways (Medium)](https://leetcode.com/problems/decode-ways/description/) ?????????Given encoded message "12", it could be decoded as "AB" (1 2) or "L" (12). ```java public int numDecodings(String s) { if(s == null || s.length() == 0) return 0; int n = s.length(); int[] dp = new int[n + 1]; dp[0] = 1; dp[1] = s.charAt(0) == '0' ? 0 : 1; for(int i = 2; i <= n; i++) { int one = Integer.valueOf(s.substring(i - 1, i)); if(one != 0) dp[i] += dp[i - 1]; if(s.charAt(i - 2) == '0') continue; int two = Integer.valueOf(s.substring(i - 2, i)); if(two <= 26) dp[i] += dp[i - 2]; } return dp[n]; } ``` ### ????¡¤?? **???????¡¤????** [Leetcode : 62. Unique Paths (Medium)](https://leetcode.com/problems/unique-paths/description/) ????????????????????????????¡¤???????????????????????????? ```java public int uniquePaths(int m, int n) { int[] dp = new int[n]; for (int i = 0; i < m; i++) { for (int j = 0; j < n; j++) { if(i == 0) dp[j] = 1; else if(j != 0) dp[j] = dp[j] + dp[j - 1]; } } return dp[n - 1]; } ``` **???????§³¡¤????** [Leetcode : 64. Minimum Path Sum (Medium)](https://leetcode.com/problems/minimum-path-sum/description/) ??????????????????????????????§³¡¤????????????????????????? ```java public int minPathSum(int[][] grid) { if(grid.length == 0 || grid[0].length == 0) return 0; int m = grid.length, n = grid[0].length; int[] dp = new int[n]; for(int i = 0; i < m; i++) { for(int j = 0; j < n; j++) { if(j == 0) dp[0] = dp[0] + grid[i][0]; else if(i == 0) dp[j] = dp[j - 1] + grid[0][j]; else dp[j] = Math.min(dp[j - 1], dp[j]) + grid[i][j]; } } return dp[n - 1]; } ``` ### ?????????? ????????????????? 4 ?????????????????? N ???????????????????????????ÁÙ?????§³? O(lgN)?? **?????** [Leetcode : 70. Climbing Stairs (Easy)](https://leetcode.com/problems/climbing-stairs/description/) ??????????? N ????????¦Ï???????????????????§Ø???????????????? ??????????? dp ?›¥?????????????????????????????¡À?? 1 ???????dp[i] ???????? i ???????????????? i ?????????? i-1 ?? i-2 ????????????????????? i ????????????????? i-1 ??? i-2 ??????????????? dp[i] = dp[i-1] + dp[i-2] dp[N] ??????? ????? dp[i] ??? dp[i - 1] ?? dp[i - 2] ?§Û??????????????????????›¥ dp[i - 1] ?? dp[i - 2] ????????????? O(n) ??ÁÙ??????? O(1) ?????? ```java public int climbStairs(int n) { if(n == 1) return 1; if(n == 2) return 2; // ???????????????? int pre1 = 2, pre2 = 1; for(int i = 2; i < n; i++){ int cur = pre1 + pre2; pre2 = pre1; pre1 = cur; } return pre1; } ``` **??????** [????????????????-P181](#) ?????????????????§Ô????????????? 1 ?§³?????????????????????????? 1 ?§³????????????????????§³??????§³?? 3 ???????????????§³???????????? N???? N ???????????? ?? i ???????????????? dp[i] = dp[i-1] + dp[i-3] **???????** [Leetcode : 198. House Robber (Easy)](https://leetcode.com/problems/house-robber/description/) ????????????????????????????????????????????????????? ???? dp ?????????›¥???????????????? dp[i] ????????? i ??????????????????????????????????????????????????? i ??????????????? i - 2 ?? i - 3 ??????????? +nums[i]) O(n) ??ÁÙ??????????? ```java public int rob(int[] nums) { int n = nums.length; if(n == 0) return 0; if(n == 1) return nums[0]; if(n == 2) return Math.max(nums[0], nums[1]); int[] dp = new int[n]; dp[0] = nums[0]; dp[1] = nums[1]; dp[2] = nums[0] + nums[2]; for(int i = 3; i < n; i++){ dp[i] = Math.max(dp[i -2], dp[i - 3]) + nums[i]; } return Math.max(dp[n - 1], dp[n - 2]); } ``` O(1) ??ÁÙ??????????? ```java public int rob(int[] nums) { int n = nums.length; if(n == 0) return 0; if(n == 1) return nums[0]; if(n == 2) return Math.max(nums[0], nums[1]); int pre3 = nums[0], pre2 = nums[1], pre1 = nums[2] + nums[0]; for(int i = 3; i < n; i++){ int cur = Math.max(pre2, pre3) + nums[i]; pre3 = pre2; pre2 = pre1; pre1 = cur; } return Math.max(pre1, pre2); } ``` **???????¦Í???????** [Leetcode : 213. House Robber II (Medium)](https://leetcode.com/problems/house-robber-ii/description/) ```java public int rob(int[] nums) { if(nums == null || nums.length == 0) return 0; int n = nums.length; if(n == 1) return nums[0]; return Math.max(rob(nums, 0, n - 2), rob(nums, 1, n - 1)); } private int rob(int[] nums, int s, int e) { int n = nums.length; if(e - s == 0) return nums[s]; if(e - s == 1) return Math.max(nums[s], nums[s + 1]); int[] dp = new int[n]; dp[s] = nums[s]; dp[s + 1] = nums[s + 1]; dp[s + 2] = nums[s] + nums[s + 2]; for (int i = s + 3; i <= e; i++) { dp[i] = Math.max(dp[i - 2], dp[i - 3]) + nums[i]; } return Math.max(dp[e], dp[e - 1]); } ``` **???????** ??????????? N ?? ?? ?? ?????????????????????????????? ??????????? dp ?›¥???????????dp[i] ???? i ???????????????????????? i ????????? j ????????—¨???? j ????????? k ????????µµ???? i ?? k ?????????????????? ?? i==k?????? i ?? k ???????????????????????¦Ë??????????? i-2 ?????? dp[i-2] ????????????????? j ?? i-1 ???????????? (i-1)\*dp[i-2] ???????????? ?? i != k?????? i ?? j ?????? i ???????????????¦Ë??????? i-1 ?????? dp[i-1] ???????????????? j ?? i-1 ???????????? (n-1)\*dp[i-1] ???????????? ??????????????????????????????? dp[i] = (i-1) \* dp[i-2] + (i-1) \* dp[i-1] dp[N] ??????? ????????????????dp[i] ??? dp[i-1] ?? dp[i-2] ?§Û????????????????????????›¥ dp[i-1] ?? dp[i-2]?? ### ???????????? ?????????? {S₁, S₂,...,S_n} ????????????????????? {S_i1, S_i2,..., S_im}?????? i1??i2 ... im ??????????????????§Ú??????????????????§Ö???????????????????§Ö????**??????**?? ????????????§µ????¡À? ix > iy ???S_ix > S_iy???????????????§Ö????**??????????**?? ??????????? dp ?›¥???????????§Ö?????dp[n] ????? S_n ??¦Â?????§Ö????????????§Ô????????????????????? {S_i1, S_i2,...,S_im}????? im < n ???? S_im < S_n ????? {S_i1, S_i2,..., S_im, S_n} ?????????????§µ??????????§Ö???????? 1??????????????????????????§µ?????????????????????§à??????????????????????????????? S_n ????????? S_n ???¦Â?????????????§³???? dp[n] = max{ dp[i]+1 | S_i < S_n && i < n} ?? ??????? dp[n] ????????????????????????????????§µ???? {S_n} ???????????????§µ?????????????????????????? dp[n] ??§³? 1?????? ](https://leetcode.com/problems/longest-increasing-subsequence/description/) ```java public int lengthOfLIS(int[] nums) { int n = nums.length; int[] dp = new int[n]; for(int i = 0; i < n; i++){ int max = 1; for(int j = 0; j < i; j++){ if(nums[i] > nums[j]) max = Math.max(max, dp[j] + 1); } dp[i] = max; } int ret = 0; for(int i = 0; i < n; i++){ ret = Math.max(ret, dp[i]); } return ret; } ``` ?????????ÁÙ???? O(n²) ????????????????????ÁÙ??????? O(nlog_n)????????? tails ???ï…???? tails[i] ?›¥????? i + 1 ?????????????§Ö?????????????????????? [4,5,6,3]???? ```html len = 1 : [4], [5], [6], [3] => tails[0] = 3 len = 2 : [4, 5], [5, 6] => tails[1] = 5 len = 3 : [4, 5, 6] => tails[2] = 6 ``` ?????????? x??????????? tails ???????§Ö??????????????? tails ???—±??? tails[i-1] < x <= tails[i]????????? tails[i] = x ?? ??????? tails ???÷g?????????????? S_i ¦Ë?? tails ?????¦Ë?????????????????? ```java public int lengthOfLIS(int[] nums) { int n = nums.length; int[] tails = new int[n]; int size = 0; for(int i = 0; i < n; i++){ int idx = binarySearch(tails, 0, size, nums[i]); tails[idx] = nums[i]; if(idx == size) size++; } return size; } private int binarySearch(int[] nums, int sIdx, int eIdx, int key){ while(sIdx < eIdx){ int mIdx = sIdx + (eIdx - sIdx) / 2; if(nums[mIdx] == key) return mIdx; else if(nums[mIdx] > key) eIdx = mIdx; else sIdx = mIdx + 1; } return sIdx; } ``` **???????????** [Leetcode : 376. Wiggle Subsequence (Medium)](https://leetcode.com/problems/wiggle-subsequence/description/) ?????? O(n) ??ÁÙ?????? ????????? up ?? down?? ```java public int wiggleMaxLength(int[] nums) { int len = nums.length; if (len == 0) return 0; int up = 1, down = 1; for (int i = 1; i < len; i++) { if (nums[i] > nums[i - 1]) up = down + 1; else if (nums[i] < nums[i - 1]) down = up + 1; } return Math.max(up, down); } ``` ### ??????????? ?????????????? S1 ?? S2?????????????????????§³? ?????????????? dp ?????›¥???????????§Ö????????? dp[i][j] ??? S1 ??? i ??????? S2 ??? j ????????????????§Ö????????? S1_i ?? S2_j ???????????????????? ?? ?? S1_i==S2_j ???????????? S1 ??? i-1 ??????? S2 ??? j-1 ????????????????§Ö??????????? S1_i ?????????????????§Ô???? 1 ???? dp[i][j] = dp[i-1][j-1] + 1?? ?? ?? S1_i != S2_j ??????????????????? S1 ??? i-1 ??????? S2 ??? j ????????????????§µ??? S1 ??? i ??????? S2 ??? j-1 ????????????????§µ?????????????? dp[i][j] = max{ dp[i-1][j], dp[i][j-1] }?? ???????????????§Ö???????????? &&{S1_i<>S2_j} \end{array}\right. ) ???????? N ?????? S₁ ?? ????? M ?????? S₂??dp[N][M] ???????? S₁ ?????? S₂ ?????????????§Ô???? ???????????????????????????????????????? ?? ?????????????§µ???????????????????§³? ?? ???????????????§µ?dp[i] ????? S_i ???¦Â?????????????§Ô?????????§Ò?????? S_i ?????????????????§µ?dp[i][j] ??? S1 ??? i ??????? S2 ??? j ??????????????????§Ô????????????? S1_i ?? S2_j ?? ?? ???? 2 ???????????????????????????? dp[N][M] ????????????????????????? dp[N] ?????????????? S_N ???¦Â?????????????§Ó?????????????????????????§µ??????????? dp ????????????? ```java public int lengthOfLCS(int[] nums1, int[] nums2) { int n1 = nums1.length, n2 = nums2.length; int[][] dp = new int[n1 + 1][n2 + 1]; for (int i = 1; i <= n1; i++) { for (int j = 1; j <= n2; j++) { if (nums1[i - 1] == nums2[j - 1]) dp[i][j] = dp[i - 1][j - 1] + 1; else dp[i][j] = Math.max(dp[i - 1][j], dp[i][j - 1]); } } return dp[n1][n2]; } ``` ### 0-1 ???? ?????????? N ????????????????????????????????§»????????????????? w ???? v?? ?????????????? dp ?›¥??????????? dp[i][j] ???????????? j ????????? i ???????????????????? i ????????? w?????? v??????? i ?????????????????§µ?????????????????? ?? ?? i ??????????????????????????? j ??? i ??????????????????????????? j ??? i-1 ??????????????dp[i][j] = dp[i-1][j]?? ?? ?? i ??????????????§µ?dp[i][j] = dp[i-1][j-w] + v?? ?? i ??????????????????????????????????????????? ?????0-1 ????????????????? ) ```java public int knapsack(int W, int N, int[] weights, int[] values) { int[][] dp = new int[N][W]; for (int i = W - 1; i >= 0; i--) { dp[0][i] = i > weights[0] ? values[0] : 0; } for (int i = 1; i < N; i++) { for (int j = W - 1; j >= weights[i]; j--) { dp[i][j] = Math.max(dp[i - 1][j], dp[i - 1][j - weights[i]] + values[i]); } for (int j = weights[i - 1] - 1; j >= 0; j--) { dp[i][j] = dp[i - 1][j]; } } return dp[N - 1][W - 1]; } ``` **??????** ?????????????? 0-1 ??????????????????????????????? i ?????????????? i-1 ??????????§Û????????? dp ??????????ï…???? dp[j] ??????? dp[i-1][j] ??????? dp[i][j]??????? ) ??? dp[j-w] ??? dp[i-1][j-w]???????????? dp[i][j-w] ????? dp[i-1][j-w] ????????????????? dp[i][j] ????? dp[i][j-w]???????????????????????????? **????????????????** 0-1 ???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 5 ?????????????????? 0 ???????? 1?????????????? 16????????§³? 2 ?????????????????? 1 ????? 2?????? 22. | id | w | v | v/w | | --- | --- | --- | --- | | 0 | 1 | 6 | 6 | | 1 | 2 | 10 | 5 | | 2 | 3 | 12 | 4 | **????** ??????????????????????????????? 0-1 ?????????????????????????? 1/2/4... ????????????????????????????????????????????¦±? ?????????????????????????????????? 0-1 ?????? ????????????????????????????????????????????????????? ??????????????????????????? **?????????????????????** [Leetcode : 416. Partition Equal Subset Sum (Medium)](https://leetcode.com/problems/partition-equal-subset-sum/description/) ????????????????§³? sum/2 ?? 0-1 ??????????????§Ó??????????????§Þ???????????????????????? ??????????????????? ```java public boolean canPartition(int[] nums) { int sum = 0; for (int num : nums) { sum += num; } if (sum % 2 != 0) { return false; } int W = sum / 2; boolean[] dp = new boolean[W + 1]; int n = nums.length; for(int i = 0; i <= W; i++) { if(nums[0] == i) dp[i] = true; } for(int i = 1; i < n; i++) { for(int j = W; j >= nums[i]; j--) { dp[j] = dp[j] || dp[j - nums[i]]; } } return dp[W]; } ``` **????????????§Ò???** [Leetcode : 139. Word Break (Medium)](https://leetcode.com/problems/word-break/description/) ```html s = "leetcode", dict = ["leet", "code"]. Return true because "leetcode" can be segmented as "leet code". ``` ```java public boolean wordBreak(String s, List wordDict) { int n = s.length(); boolean[] dp = new boolean[n + 1]; dp[0] = true; for (int i = 1; i <= n; i++) { for (String word : wordDict) { if (word.length() <= i && word.equals(s.substring(i - word.length(), i))) { dp[i] = dp[i] || dp[i - word.length()]; } } } return dp[n]; } ``` **?????????????????????????????????** [Leetcode : 494. Target Sum (Medium)](https://leetcode.com/problems/target-sum/description/) ```html Input: nums is [1, 1, 1, 1, 1], S is 3. Output: 5 Explanation: -1+1+1+1+1 = 3 +1-1+1+1+1 = 3 +1+1-1+1+1 = 3 +1+1+1-1+1 = 3 +1+1+1+1-1 = 3 There are 5 ways to assign symbols to make the sum of nums be target 3. ``` ????????????? subset sum ?????????? 0-1 ????????????????????????????????????P ?? N?????? P ????????N ?????????????????? ```html sum(P) - sum(N) = target sum(P) + sum(N) + sum(P) - sum(N) = target + sum(P) + sum(N) 2 * sum(P) = target + sum(nums) ``` ????????????????????????????????????? (target + sum(nums))/2???????????? ```java public int findTargetSumWays(int[] nums, int S) { int sum = 0; for (int num : nums) { sum += num; } if (sum < S || (sum + S) % 2 == 1) { return 0; } return subsetSum(nums, (sum + S) >>> 1); } private int subsetSum(int[] nums, int targetSum) { Arrays.sort(nums); int[] dp = new int[targetSum + 1]; dp[0] = 1; for (int i = 0; i < nums.length; i++) { int num = nums[i]; for (int j = targetSum; j >= num; j--) { dp[j] = dp[j] + dp[j - num]; } } return dp[targetSum]; } ``` **01????????????????** [Leetcode : 474. Ones and Zeroes (Medium)](https://leetcode.com/problems/ones-and-zeroes/description/) ```html Input: Array = {"10", "0001", "111001", "1", "0"}, m = 5, n = 3 Output: 4 Explanation: This are totally 4 strings can be formed by the using of 5 0s and 3 1s, which are ??10,??0001??,??1??,??0?? ``` ??????????????? 0-1 ????????????????????§³??0 ???????? 1 ???????? ```java public int findMaxForm(String[] strs, int m, int n) { if (strs == null || strs.length == 0) return 0; int l = strs.length; int[][] dp = new int[m + 1][n + 1]; for (int i = 0; i < l; i++) { String s = strs[i]; int ones = 0, zeros = 0; for (char c : s.toCharArray()) { if (c == '0') zeros++; else if (c == '1') ones++; } for (int j = m; j >= zeros; j--) { for (int k = n; k >= ones; k--) { if (zeros <= j && ones <= k) { dp[j][k] = Math.max(dp[j][k], dp[j - zeros][k - ones] + 1); } } } } return dp[m][n]; } ``` **?????** [Leetcode : 322. Coin Change (Medium)](https://leetcode.com/problems/coin-change/description/) ????????????§»???????????????§»??????????????????????????????????????????????????¨¢? ?????????????????????????????? 0-1???????????????¦·??????????????????? 0 ?????????????¦Â??????? ```java public int coinChange(int[] coins, int amount) { int[] dp = new int[amount + 1]; Arrays.fill(dp, amount + 1); dp[0] = 0; for (int i = 1; i <= amount; i++) { for (int j = 0; j < coins.length; j++) { if (coins[j] <= i) { dp[i] = Math.min(dp[i], dp[i - coins[j]] + 1); } } } return dp[amount] > amount ? -1 : dp[amount]; } ``` **??????** [Leetcode : 377. Combination Sum IV (Medium)](https://leetcode.com/problems/combination-sum-iv/description/) ```html nums = [1, 2, 3] target = 4 The possible combination ways are: (1, 1, 1, 1) (1, 1, 2) (1, 2, 1) (1, 3) (2, 1, 1) (2, 2) (3, 1) Note that different sequences are counted as different combinations. Therefore the output is 7. ``` ```java public int combinationSum4(int[] nums, int target) { int[] dp = new int[target + 1]; dp[0] = 1; for (int i = 1; i <= target; i++) { for (int j = 0; j < nums.length; j++) { if(nums[j] <= i) { dp[i] += dp[i - nums[j]]; } } } return dp[target]; } ``` **?????????¦Å???????** [Leetcode : 123. Best Time to Buy and Sell Stock III (Hard)](https://leetcode.com/problems/best-time-to-buy-and-sell-stock-iii/description/) ```java public int maxProfit(int[] prices) { int firstBuy = Integer.MIN_VALUE, firstSell = 0; int secondBuy = Integer.MIN_VALUE, secondSell = 0; for (int curPrice : prices) { if (firstBuy < -curPrice) firstBuy = -curPrice; if (firstSell < firstBuy + curPrice) firstSell = firstBuy + curPrice; if (secondBuy < firstSell - curPrice) secondBuy = firstSell - curPrice; if (secondSell < secondBuy + curPrice) secondSell = secondBuy + curPrice; } return secondSell; } ``` **?????? k ?¦Å???????** [Leetcode : 188. Best Time to Buy and Sell Stock IV (Hard)](https://leetcode.com/problems/best-time-to-buy-and-sell-stock-iv/description/) ```html dp[i, j] = max(dp[i, j-1], prices[j] - prices[jj] + dp[i-1, jj]) { jj in range of [0, j-1] } = max(dp[i, j-1], prices[j] + max(dp[i-1, jj] - prices[jj])) ``` ```java public int maxProfit(int k, int[] prices) { int n = prices.length; if (k >= n/2) { int maxPro = 0; for (int i = 1; i < n; i++) { if (prices[i] > prices[i-1]) maxPro += prices[i] - prices[i-1]; } return maxPro; } int[][] dp = new int[k + 1][n]; for (int i = 1; i <= k; i++) { int localMax = dp[i - 1][0] - prices[0]; for (int j = 1; j < n; j++) { dp[i][j] = Math.max(dp[i][j - 1], prices[j] + localMax); localMax = Math.max(localMax, dp[i - 1][j] - prices[j]); } } return dp[k][n - 1]; } ``` ### ???????? **?????????** [Leetcode : 303. Range Sum Query - Immutable (Easy)](https://leetcode.com/problems/range-sum-query-immutable/description/) ?????? i \~ j ???????????? sum[j] - sum[i-1]?????? sum[i] ? 0 \~ j ???? ```java class NumArray { int[] nums; public NumArray(int[] nums) { for(int i = 1; i < nums.length; i++) nums[i] += nums[i - 1]; this.nums = nums; } public int sumRange(int i, int j) { return i == 0 ? nums[j] : nums[j] - nums[i - 1]; } } ``` **???????????** [Leetcode : 53. Maximum Subarray (Easy)](https://leetcode.com/problems/maximum-subarray/description/) ?? sum[i] ??? num[i] ???¦Â???????????????????? sum[i-1] ??? sum[i] ???????? sum[i-1] §³?? 0??????? num[i] ???¦Â???????öö???????????????????????????????????????? num[i] ??§³?? ```java public int maxSubArray(int[] nums) { int n = nums.length; int[] sum = new int[n]; sum[0] = nums[0]; int max = sum[0]; for(int i = 1; i < n; i++){ sum[i] = (sum[i-1] > 0 ? sum[i-1] : 0) + nums[i]; max = Math.max(max, sum[i]); } return max; } ``` **?????§Ö???????????????** [Leetcode : 413. Arithmetic Slices (Medium)](https://leetcode.com/problems/arithmetic-slices/description/) ```html A = [1, 2, 3, 4] return: 3, for 3 arithmetic slices in A: [1, 2, 3], [2, 3, 4] and [1, 2, 3, 4] itself. ``` ???? (1,2,3,4)????????????????????????????????? (1,2,3,4,5)??????????????????????? (1,2,3,4) ?????????????????? (1,2,3,4,5)????? dp[i] = dp[i - 1] + 1?? ```java public int numberOfArithmeticSlices(int[] A) { int n = A.length; int[] dp = new int[n]; for(int i = 2; i < n; i++) { if(A[i] - A[i - 1] == A[i - 1] - A[i - 2]) { dp[i] = dp[i - 1] + 1; } } int ret = 0; for(int cnt : dp) { ret += cnt; } return ret; } ``` ### ??????? **?????????????????????????** [Leetcode : 583. Delete Operation for Two Strings (Medium)](https://leetcode.com/problems/delete-operation-for-two-strings/description/) ????????????????????????????????????? ```java public int minDistance(String word1, String word2) { int m = word1.length(), n = word2.length(); int[][] dp = new int[m + 1][n + 1]; for (int i = 0; i <= m; i++) { for (int j = 0; j <= n; j++) { if (i == 0 || j == 0) continue; dp[i][j] = word1.charAt(i - 1) == word2.charAt(j - 1) ? dp[i - 1][j - 1] + 1 : Math.max(dp[i][j - 1], dp[i - 1][j]); } } return m + n - 2 * dp[m][n]; } ``` **????????????????????????** // TODO [Leetcode : 72. Edit Distance (Hard)](https://leetcode.com/problems/edit-distance/description/) **??????????????????????????**// TODO [????????????????-?????](#) ### ???????? **???????????????** [Leetcode : 309. Best Time to Buy and Sell Stock with Cooldown(Medium)](https://leetcode.com/problems/best-time-to-buy-and-sell-stock-with-cooldown/description/) ???????????????????????????????  ```html s0[i] = max(s0[i - 1], s2[i - 1]); // Stay at s0, or rest from s2 s1[i] = max(s1[i - 1], s0[i - 1] - prices[i]); // Stay at s1, or buy from s0 s2[i] = s1[i - 1] + prices[i]; // Only one way from s1 ``` ```java public int maxProfit(int[] prices) { if (prices == null || prices.length == 0) return 0; int n = prices.length; int[] s0 = new int[n]; int[] s1 = new int[n]; int[] s2 = new int[n]; s0[0] = 0; s1[0] = -prices[0]; s2[0] = Integer.MIN_VALUE; for (int i = 1; i < n; i++) { s0[i] = Math.max(s0[i - 1], s2[i - 1]); s1[i] = Math.max(s1[i - 1], s0[i - 1] - prices[i]); s2[i] = Math.max(s2[i - 1], s1[i - 1] + prices[i]); } return Math.max(s0[n - 1], s2[n - 1]); } ``` **???? 0 \~ n ???????????????? 1 ?????** [Leetcode : 338. Counting Bits (Medium)](https://leetcode.com/problems/counting-bits/description/) ???????? 6(110)????????????????? 2(10) ????????? 1 ????? dp[i] = dp[i&(i-1)] + 1; ```java public int[] countBits(int num) { int[] ret = new int[num + 1]; for(int i = 1; i <= num; i++){ ret[i] = ret[i&(i-1)] + 1; } return ret; } ``` **?????????????????????** [Leetcode : 646. Maximum Length of Pair Chain (Medium)](https://leetcode.com/problems/maximum-length-of-pair-chain/description/) ???? (a, b) ?? (c, d) ????? b < c????????????????????? ```java public int findLongestChain(int[][] pairs) { if(pairs == null || pairs.length == 0) { return 0; } Arrays.sort(pairs, (a, b) -> (a[0] - b[0])); int n = pairs.length; int[] dp = new int[n]; Arrays.fill(dp, 1); for(int i = 0; i < n; i++) { for(int j = 0; j < i; j++) { if(pairs[i][0] > pairs[j][1]){ dp[i] = Math.max(dp[i], dp[j] + 1); } } } int ret = 0; for(int num : dp) { ret = Math.max(ret, num); } return ret; } ``` **???????????????????** [Leetcode : 121. Best Time to Buy and Sell Stock (Easy)](https://leetcode.com/problems/best-time-to-buy-and-sell-stock/description/) ???????¦Í???? ???????????§³?????????§³??????????????????????????????????????????????????? ```java public int maxProfit(int[] prices) { int n = prices.length; if(n == 0) return 0; int soFarMin = prices[0]; int max = 0; for(int i = 1; i < n; i++){ if(soFarMin > prices[i]) soFarMin = prices[i]; else max = Math.max(max, prices[i] - soFarMin); } return max; } ``` **??????????** [Leetcode : 650. 2 Keys Keyboard (Medium)](https://leetcode.com/problems/2-keys-keyboard/description/) ```java public int minSteps(int n) { int[] dp = new int[n + 1]; for (int i = 2; i <= n; i++) { dp[i] = i; for (int j = i - 1; j >= 0; j--) { if (i % j == 0) { dp[i] = dp[j] + dp[i / j]; break; } } } return dp[n]; } ``` ```java public int minSteps(int n) { if (n == 1) return 0; for (int i = 2; i <= Math.sqrt(n); i++) { if (n % i == 0) return i + minSteps(n / i); } return n; } ``` ## ??? ### ???? **???????** ????????????????????????????? 84 = 2² \* 3¹ \* 5⁰ \* 7¹ \* 11⁰ \* 13⁰ \* 17⁰ \* ?? **????** ?? x = 2^m0 \* 3^m1 \* 5^m2 \* 7^m3 \* 11^m4 \* ?? ?? y = 2ⁿ⁰ \* 3ⁿ¹ \* 5ⁿ² \* 7ⁿ³ \* 11ⁿ⁴ \* ?? ??? x ???? y??y mod x == 0????????????? i??mi <= ni?? x ?? y ?? **??????** ???gcd(x,y) = 2^min(m0,n0) \* 3^min(m1,n1) \* 5^min(m2,n2) \* ... x ?? y ?? **??§³??????** ???lcm(x,y) = 2^max(m0,n0) \* 3^max(m1,n1) \* 5^max(m2,n2) \* ... **????????????** [Leetcode : 204. Count Primes (Easy)](https://leetcode.com/problems/count-primes/description/) ???????????????????????????????????????????????????????? ```java public int countPrimes(int n) { boolean[] notPrimes = new boolean[n + 1]; int cnt = 0; for(int i = 2; i < n; i++){ if(notPrimes[i]) continue; cnt++; // ?? i * i ??????????? k < i????? k * i ?????????????????? for(long j = (long) i * i; j < n; j += i){ notPrimes[(int) j] = true; } } return cnt; } ``` ### ?????? ```java int gcd(int a, int b) { if (b == 0) return a; return gcd(b, a % b); } ``` ??????????????????????????? ```java int lcm(int a, int b){ return a * b / gcd(a, b); } ``` ???????????????????????? a % b ??????????????????????????? [ ????????2.7]() ??????????¨¹???????¦Ë???????�I???? ???? a ?? b ???????? f(a, b)???§µ? 1\. ??? a ?? b ????????f(a, b) = 2\*f(a/2, b/2); 2\. ??? a ????? b ????????f(a, b) = f(a/2, b); 3\. ??? b ????? a ????????f(a, b) = f(a, b/2); 4\. ??? a ?? b ?????????f(a, b) = f(a, a-b); ?? 2 ??? 2 ????????????¦Ë?????? ### ??????? Java ?? static String toString(int num, int radix) ???????????????? redix ??????????????? **7 ????** [Leetcode : 504. Base 7 (Easy)](https://leetcode.com/problems/base-7/description/) ```java public String convertToBase7(int num) { if (num < 0) { return '-' + convertToBase7(-num); } if (num < 7) { return num + ""; } return convertToBase7(num / 7) + num % 7; } ``` **16 ????** [Leetcode : 405. Convert a Number to Hexadecimal (Easy)](https://leetcode.com/problems/convert-a-number-to-hexadecimal/description/) ```java public String toHex(int num) { char[] map = {'0','1','2','3','4','5','6','7','8','9','a','b','c','d','e','f'}; if(num == 0) return "0"; String ret = ""; while(num != 0){ ret = map[(num & 0b1111)] + ret; num >>>= 4; } return ret; } ``` ### ??? **?????¦Â???§Ø???? 0** [Leetcode : 172. Factorial Trailing Zeroes (Easy)](https://leetcode.com/problems/factorial-trailing-zeroes/description/) ¦Â???? 0 ?? 2 * 5 ??????2 ????????????? 5 ?????????????????§Ø???? 5 ???¨À? ????????? N?????????? 5 ????????N/5 + N/5² + N/5³ + ...?????? N/5 ????????? N ?????? 5 ???????????? 5??N/5² ????????? N ?????? 5² ????????????? 5 ...?? ```java public int trailingZeroes(int n) { return n == 0 ? 0 : n / 5 + trailingZeroes(n / 5); } ``` ????????? N! ??????????????¦Ë 1 ??¦Ë?????????§Ø???? 2 ?????????????? [ ????????2.2](#) ????????§Ø???? 5 ?????2 ?????? N/2 + N/2² + N/2³ + ... ### ???????????? **????????** [Leetcode : 67. Add Binary (Easy)](https://leetcode.com/problems/add-binary/description/) ```java public String addBinary(String a, String b) { int i = a.length() - 1, j = b.length() - 1, carry = 0; String str = ""; while(i >= 0 || j >= 0){ if(i >= 0 && a.charAt(i--) == '1') carry++; if(j >= 0 && b.charAt(j--) == '1') carry++; str = (carry % 2) + str; carry /= 2; } if(carry == 1) str = "1" + str; return str; } ``` **????????** [Leetcode : 415. Add Strings (Easy)](https://leetcode.com/problems/add-strings/description/) ????????????????????????? ```java public String addStrings(String num1, String num2) { StringBuilder sb = new StringBuilder(); int carry = 0; for(int i = num1.length() - 1, j = num2.length() - 1; i >= 0 || j >= 0 || carry == 1; i--, j--){ int x = i < 0 ? 0 : num1.charAt(i) - '0'; int y = j < 0 ? 0 : num2.charAt(j) - '0'; sb.append((x + y + carry) % 10); carry = (x + y + carry) / 10; } return sb.reverse().toString(); } ``` ### ???????? **??????????????§Ö????????????** [Leetcode : 462. Minimum Moves to Equal Array Elements II (Medium)](https://leetcode.com/problems/minimum-moves-to-equal-array-elements-ii/description/) ???????????¦Ï????????????????????????????§³????????? ???????????????????????????§³?????????????????????¦Ë????????????? ?? m ???¦Ë????a ?? b ?? m ??????????????? b > a???? a ?? b ???????????????????? b - a?????????? (b - m) + (m - a)???????????????????????¦Ë????????????? ?????øA??? N?????????? N/2 ?? a ?? b ????????????????? m ??¦Ë?¨¢? **?? 1** ????????ÁÙ????O(NlgN) ```java public int minMoves2(int[] nums) { Arrays.sort(nums); int ret = 0; int l = 0, h = nums.length - 1; while(l <= h) { ret += nums[h] - nums[l]; l++; h--; } return ret; } ``` **?? 2** ???????????????¦Ë??????ÁÙ??? O(N) ```java public int minMoves2(int[] nums) { int ret = 0; int n = nums.length; int median = quickSelect(nums, 0, n - 1, n / 2 + 1); for(int num : nums) ret += Math.abs(num - median); return ret; } private int quickSelect(int[] nums, int start, int end, int k) { int l = start, r = end, privot = nums[(l + r) / 2]; while(l <= r) { while(nums[l] < privot) l++; while(nums[r] > privot) r--; if(l >= r) break; swap(nums, l, r); l++; r--; } int left = l - start + 1; if(left > k) return quickSelect(nums, start, l - 1, k); if(left == k && l == r) return nums[l]; int right = r - start + 1; return quickSelect(nums, r + 1, end, k - right); } private void swap(int[] nums, int i, int j) { int tmp = nums[i]; nums[i] = nums[j]; nums[j] = tmp; } ``` ### ?????????? **?????§Ô?????????? n / 2 ?????** [Leetcode : 169. Majority Element (Easy)](https://leetcode.com/problems/majority-element/description/) ??????????????§Þ???????????????????? n / 2 ```java public int majorityElement(int[] nums) { Arrays.sort(nums); return nums[nums.length / 2]; } ``` ???????? Boyer-Moore Majority Vote Algorithm ?????????????????ÁÙ???? O(n)???????????????????? cnt ????????????????????????????????????????????????? cnt--????????????? i ???????? cnt == 0 ?????? i ???????? majority???????? majority????????????????? i / 2 ???????????? i / 2 ??? cnt ?????????? 0 ????????? n - i ??????§µ?majority ????????? (n - i) / 2?????????????????? majority?? ```java public int majorityElement(int[] nums) { int cnt = 0, majority = 0; for(int i = 0; i < nums.length; i++){ if(cnt == 0) { majority = nums[i]; cnt++; } else if(majority == nums[i]) cnt++; else cnt--; } return majority; } ``` **?????§Ô?????????? n / k ?????** [???????????????? P343](#) ? k - 1 ????? ### ???? **?????** [Leetcode : 367. Valid Perfect Square (Easy)](https://leetcode.com/problems/valid-perfect-square/description/) ??????§µ?1,4,9,16,.. ?????3,5,7,... ??????????§µ?????????????????? 1 ???????????§³? ```java public boolean isPerfectSquare(int num) { int subNum = 1; while (num > 0) { num -= subNum; subNum += 2; } return num == 0; } ``` **3 ?? n ?¦Ç?** [Leetcode : 326. Power of Three (Easy)](https://leetcode.com/problems/power-of-three/description/) ```java public boolean isPowerOfThree(int n) { return n > 0 && (1162261467 % n == 0); } ``` **????????§Ö?????????????** [Leetcode : 628. Maximum Product of Three Numbers (Easy)](https://leetcode.com/problems/maximum-product-of-three-numbers/description/) ```java public int maximumProduct(int[] nums) { int max1 = Integer.MIN_VALUE, max2 = Integer.MIN_VALUE, max3 = Integer.MIN_VALUE, min1 = Integer.MAX_VALUE, min2 = Integer.MAX_VALUE; for (int n : nums) { if (n > max1) { max3 = max2; max2 = max1; max1 = n; } else if (n > max2) { max3 = max2; max2 = n; } else if (n > max3) { max3 = n; } if (n < min1) { min2 = min1; min1 = n; } else if (n < min2) { min2 = n; } } return Math.max(max1*max2*max3, max1*min1*min2); } ``` **???????** [Leetcode : 238. Product of Array Except Self (Medium)](https://leetcode.com/problems/product-of-array-except-self/description/) ???????????????????ï…????????????ï…?????????????????????§Ô????¦Ë??????????????????????? ????????ÁÙ???? O(n)???????????¨®????? ```java public int[] productExceptSelf(int[] nums) { int n = nums.length; int[] ret = new int[n]; ret[0] = 1; for(int i = 1; i < n; i++) { ret[i] = ret[i - 1] * nums[i - 1]; } int right = 1; for(int i = n - 1; i >= 0; i--) { ret[i] *= right; right *= nums[i]; } return ret; } ``` # ???????? ## ?????? **?????????** ???????? ```java class MyQueue { private Stack st = new Stack(); public void push(int x) { Stack temp = new Stack(); while(!st.isEmpty()){ temp.push(st.pop()); } st.push(x); while(!temp.isEmpty()){ st.push(temp.pop()); } } public int pop() { return st.pop(); } public int peek() { return st.peek(); } public boolean empty() { return st.isEmpty(); } } ``` ????????? ```java class MyQueue { private Stack in = new Stack(); private Stack out = new Stack(); public void push(int x) { in.push(x); } public int pop() { in2out(); return out.pop(); } public int peek() { in2out(); return out.peek(); } private void in2out(){ if(out.isEmpty()){ while(!in.isEmpty()){ out.push(in.pop()); } } } public boolean empty() { return in.isEmpty() && out.isEmpty(); } } ``` **?????????** [Leetcode : 225. Implement Stack using Queues (Easy)](https://leetcode.com/problems/implement-stack-using-queues/description/) ```java class MyStack { private Queue queue; public MyStack() { queue = new LinkedList<>(); } public void push(int x) { queue.add(x); for(int i = 1; i < queue.size(); i++){ // ??? queue.add(queue.remove()); } } public int pop() { return queue.remove(); } public int top() { return queue.peek(); } public boolean empty() { return queue.isEmpty(); } } ``` **??§³??** [Leetcode : 155. Min Stack (Easy)](https://leetcode.com/problems/min-stack/description/) ???????????????›¥?????????›¥??§³??? ```java class MinStack { private Stack dataStack; private Stack minStack; private int min; public MinStack() { dataStack = new Stack<>(); minStack = new Stack<>(); min = Integer.MAX_VALUE; } public void push(int x) { dataStack.add(x); if(x < min) { min = x; } minStack.add(min); } public void pop() { dataStack.pop(); minStack.pop(); if(!minStack.isEmpty()) { min = minStack.peek(); } else{ min = Integer.MAX_VALUE; } } public int top() { return dataStack.peek(); } public int getMin() { return min; } } ``` ?????????§³?????????????????????????????????????????????§³???????????????? ????????3.7?? **?????????????** [Leetcode : 20. Valid Parentheses (Easy)](https://leetcode.com/problems/valid-parentheses/description/) ```html "()[]{}" Output : true ``` ```java public boolean isValid(String s) { Stack stack = new Stack<>(); for(int i = 0; i < s.length(); i++){ char c = s.charAt(i); if(c == '(' || c == '{' || c == '[') stack.push(c); else{ if(stack.isEmpty()) return false; char cStack = stack.pop(); if(c == ')' && cStack != '(' || c == ']' && cStack != '[' || c == '}' && cStack != '{' ) { return false; } } } return stack.isEmpty(); } ``` **?????§Ò????????????????????????** ```html Input: [73, 74, 75, 71, 69, 72, 76, 73] Output: [1, 1, 4, 2, 1, 1, 0, 0] ``` [Leetcode : 739. Daily Temperatures (Medium)](https://leetcode.com/problems/daily-temperatures/description/) ???????›¥??¦Ä???????????????????????????????????????????????????????????????????§µ???????????????????????????????????? ```java public int[] dailyTemperatures(int[] temperatures) { int n = temperatures.length; int[] ret = new int[n]; Stack stack = new Stack<>(); for(int i = 0; i < n; i++) { while(!stack.isEmpty() && temperatures[i] > temperatures[stack.peek()]) { int idx = stack.pop(); ret[idx] = i - idx; } stack.add(i); } return ret; } ``` **??????????????????????** [Leetcode : 496. Next Greater Element I (Easy)](https://leetcode.com/problems/next-greater-element-i/description/) ```html Input: nums1 = [4,1,2], nums2 = [1,3,4,2]. Output: [-1,3,-1] ``` ???????????? Stack ???????§Ö???????????????????????????????????????????????????????????????????????? ```java public int[] nextGreaterElement(int[] nums1, int[] nums2) { Map map = new HashMap<>(); Stack stack = new Stack<>(); for(int num : nums2){ while(!stack.isEmpty() && num > stack.peek()){ map.put(stack.pop(), num); } stack.add(num); } int[] ret = new int[nums1.length]; for(int i = 0; i < nums1.length; i++){ if(map.containsKey(nums1[i])) ret[i] = map.get(nums1[i]); else ret[i] = -1; } return ret; } ``` **?????????????????????????** [Leetcode : 503. Next Greater Element II (Medium)](https://leetcode.com/problems/next-greater-element-ii/description/) ```java public int[] nextGreaterElements(int[] nums) { int n = nums.length, next[] = new int[n]; Arrays.fill(next, -1); Stack stack = new Stack<>(); for (int i = 0; i < n * 2; i++) { int num = nums[i % n]; while (!stack.isEmpty() && nums[stack.peek()] < num) next[stack.pop()] = num; if (i < n) stack.push(i); } return next; } ``` ## ????? ???? Hash Table ????????????????????????????????????????????›¥?????????????ÁÙ?????????????????? Hash Table ?????ÈÎ??????????? Java ?§Ö? **HashSet** ????›¥???????????? O(1) ????ÁÙ??????????????????§³? ???????????????¦¶???????????????????????????›¥???????????????????????§³§Õ???????????????????????? 26 ????????????›¥???????????????ÁÙ??????? O(1)?? Java ?§Ö? **HashMap** ??????????????????????????????????? ?????????????????????????????????? HashMap ?????????????????????????????????????????? url ?????§µ?[Leetcdoe : 535. Encode and Decode TinyURL (Medium)](https://leetcode.com/problems/encode-and-decode-tinyurl/description/)???????? HashMap ?????›¥?????? url ???? url ???????¨°????????????? url???????????? url ????? url ?????¦Ë???????????? HashMap ????????????????§Þ??????????????????????????? HashSet ??????????????????¦¶??????????????????????????? **?????§Ö???????????????** [Leetcode : 1. Two Sum (Easy)](https://leetcode.com/problems/two-sum/description/) ???????????????????????????????????????????????????????ÁÙ???? O(nlg_n)????ÁÙ???? O(1)?? ?? HashMap ?›¥??????????????????????? nums[i] ????§Ø? HashMap ???????? target - nums[i] ???????????? target - nums[i] ??????????? i ?????????????????¡Â???????ÁÙ???? O(n)????ÁÙ???? O(n)??????????????? ```java public int[] twoSum(int[] nums, int target) { HashMap map = new HashMap<>(); for(int i = 0; i < nums.length; i++){ if(map.containsKey(target - nums[i])) return new int[]{map.get(target - nums[i]), i}; else map.put(nums[i], i); } return null; } ``` **????§Ô????** ??§Ô???????????????§³?????????? 1 [Leetcode : 594. Longest Harmonious Subsequence (Easy)](https://leetcode.com/problems/longest-harmonious-subsequence/description/) ```java public int findLHS(int[] nums) { Map map = new HashMap<>(); for (long num : nums) { map.put(num, map.getOrDefault(num, 0) + 1); } int result = 0; for (long key : map.keySet()) { if (map.containsKey(key + 1)) { result = Math.max(result, map.get(key + 1) + map.get(key)); } } return result; } ``` ## ????? **????????????????????????????** [Leetcode : 242. Valid Anagram (Easy)](https://leetcode.com/problems/valid-anagram/description/) ??????????§³§Õ?????????? 26 ??§³§Õ??????????? Hash Table ??????????????????????????¦¶??§³??????????????????????? ??¨®???? 26 ???????????????????????????????????????????????????????????????? ```java public boolean isAnagram(String s, String t) { int[] cnts = new int[26]; for(int i = 0; i < s.length(); i++) cnts[s.charAt(i) - 'a'] ++; for(int i = 0; i < t.length(); i++) cnts[t.charAt(i) - 'a'] --; for(int i = 0; i < 26; i++) if(cnts[i] != 0) return false; return true; } ``` **????????** [Leetcode : 205. Isomorphic Strings (Easy)](https://leetcode.com/problems/isomorphic-strings/description/) ???? "egg" ?? "add" ???????????????? ???????????¦Ã????¦Ë?????????????????????????¦Ã????¦Ë????????????????????? ```java public boolean isIsomorphic(String s, String t) { int[] m1 = new int[256]; int[] m2 = new int[256]; for(int i = 0; i < s.length(); i++){ if(m1[s.charAt(i)] != m2[t.charAt(i)]) { return false; } m1[s.charAt(i)] = i + 1; m2[t.charAt(i)] = i + 1; } return true; } ``` **???????????????????????????????????** [Leetcode : 409. Longest Palindrome](https://leetcode.com/problems/longest-palindrome/description/) ??¨®???? 128 ?????????????????????????????????????????????????????????????????????????????????§Þ????????????????????????????§Ö???????????????????§Þ? ```java public int longestPalindrome(String s) { int[] cnts = new int[128]; // ascii ????? 128 ?? for(char c : s.toCharArray()) cnts[c]++; int ret = 0; for(int cnt : cnts) ret += (cnt / 2) * 2; if(ret < s.length()) ret ++; // ????????? s ??????§Ö???¦Ä??????????????????????????????????§Þ? return ret; } ``` **?§Ø??????????????????** [Leetcode : 9. Palindrome Number (Easy)](https://leetcode.com/problems/palindrome-number/description/) ??????????????????????????????????????§Ø?? ???????????????????????????????????????§Ø???????????????? ```java public boolean isPalindrome(int x) { if(x == 0) return true; if(x < 0) return false; if(x % 10 == 0) return false; int right = 0; while(x > right){ right = right * 10 + x % 10; x /= 10; } return x == right || x == right / 10; } ``` **???????????** [Leetcode : 647. Palindromic Substrings (Medium)](https://leetcode.com/problems/palindromic-substrings/description/) ???????????????????¦Ë???????????????????????? ```java private int cnt = 0; public int countSubstrings(String s) { for(int i = 0; i < s.length(); i++) { extendSubstrings(s, i, i); // ???????? extendSubstrings(s, i, i + 1); // ??????? } return cnt; } private void extendSubstrings(String s, int start, int end) { while(start >= 0 && end < s.length() && s.charAt(start) == s.charAt(end)) { start--; end++; cnt++; } } ``` **??????????????????? 1 ?? ???? 0 ????????????????????** ```html Input: "00110011" Output: 6 Explanation: There are 6 substrings that have equal number of consecutive 1's and 0's: "0011", "01", "1100", "10", "0011", and "01". ``` [Leetcode : 696. Count Binary Substrings (Easy)](https://leetcode.com/problems/count-binary-substrings/description/) ```java public int countBinarySubstrings(String s) { int preLen = 0, curLen = 1, ret = 0; for(int i = 1; i < s.length(); i++){ if(s.charAt(i) == s.charAt(i-1)) curLen++; else{ preLen = curLen; curLen = 1; } if(preLen >= curLen) ret++; } return ret; } ``` **??????????¦Ë????** [ ????????3.1](#) ????????????? s1 ?? s2 ??????§Ø? s2 ???????? s1 ???????¦Ë???????????????? ```html s1 = AABCD, s2 = CDAA Return : true ``` s1 ?????????¦Ë?????? s1s1 ?????????????????§Ø? s2 ????? s1s1 ????????????¨À? **??????????¦Ë** [ ????????2.17](#) ????????????????? k ¦Ë?? ???? abcd123 ??????? 3 ¦Ë ??? 123abcd ?? abcd123 ?§Ö? abcd ?? 123 ?????????? dcba321?????????????????????????123abcd?? **??????§Ö??????** [????????????????](#) ???ÁL "I am a student" ????? "student a am I" ????????????????????????????? ## ????????? **???????** // TODO [??????????? P114](#) **???????** //TODO [???????????????? P335](#) **???????§Ö? 0 ????¦Â** [Leetcode : 283. Move Zeroes (Easy)](https://leetcode.com/problems/move-zeroes/description/) ```java public void moveZeroes(int[] nums) { int n = nums.length; int idx = 0; for(int i = 0; i < n; i++){ if(nums[i] != 0) nums[idx++] = nums[i]; } while(idx < n){ nums[idx++] = 0; } } ``` **???????????? [1, n] ???????????????�I?????????????????????????????** [Leetcode : 645. Set Mismatch (Easy)](https://leetcode.com/problems/set-mismatch/description/) ??????????????????????????????????ÁÙ???? O(nlog_n)??????????? O(n) ????ÁÙ????O(1) ??ÁÙ???????? ?????????????????????????????????????????????¦Ë????? ???????ï…????? i ¦Ë????????? i + 1 ???????????? i ¦Ë ?? nums[i] - 1 ¦Ë?????????? num[i] - 1 ?????? nums[i] ????????¦Ë??????????????????????????????§µ??????¦Í?????????? i ¦Ë???????????????????????????????????????????????????????????????????????????????????? nums[i] != nums[nums[i] - 1 ?????? ????????? - [Leetcode :448. Find All Numbers Disappeared in an Array (Easy)](https://leetcode.com/problems/find-all-numbers-disappeared-in-an-array/description/)????????§Ø??????? - [Leetcode : 442. Find All Duplicates in an Array (Medium)](https://leetcode.com/problems/find-all-duplicates-in-an-array/description/)?????????????????? ```java public int[] findErrorNums(int[] nums) { for(int i = 0; i < nums.length; i++){ while(nums[i] != i + 1 && nums[i] != nums[nums[i] - 1]) swap(nums, i, nums[i] - 1); } for(int i = 0; i < nums.length; i++){ if(i + 1 != nums[i]) return new int[]{nums[i], i + 1}; } return null; } private void swap(int[] nums, int i, int j){ int tmp = nums[i]; nums[i] = nums[j]; nums[j] = tmp; } ``` **????????????????????????? [0, n-1] ???** [Leetcode : 287. Find the Duplicate Number (Medium)](https://leetcode.com/problems/find-the-duplicate-number/description/) ?????????? ```java public int findDuplicate(int[] nums) { int l = 1, h = nums.length - 1; while (l <= h) { int mid = l + (h - l) / 2; int cnt = 0; for (int i = 0; i < nums.length; i++) { if (nums[i] <= mid) cnt++; } if (cnt > mid) h = mid - 1; else l = mid + 1; } return l; } ``` ??????????????§Ý?????????????????? ```java public int findDuplicate(int[] nums) { int slow = nums[0], fast = nums[nums[0]]; while (slow != fast) { slow = nums[slow]; fast = nums[nums[fast]]; } fast = 0; while (slow != fast) { slow = nums[slow]; fast = nums[fast]; } return slow; } ``` ### ??????? ?????????????§Ü??§Ù?????????? ?????????????????????????????? ```html [ [ 1, 5, 9], [10, 11, 13], [12, 13, 15] ] ``` **??????????** [Leetocde : 240. Search a 2D Matrix II (Medium)](https://leetcode.com/problems/search-a-2d-matrix-ii/description/) ```java public boolean searchMatrix(int[][] matrix, int target) { if (matrix == null || matrix.length == 0 || matrix[0].length == 0) return false; int m = matrix.length, n = matrix[0].length; int row = 0, col = n - 1; while (row < m && col >= 0) { if (target == matrix[row][col]) return true; else if (target < matrix[row][col]) col--; else row++; } return false; } ``` **???????? Kth Element** [Leetcode : 378. Kth Smallest Element in a Sorted Matrix ((Medium))](https://leetcode.com/problems/kth-smallest-element-in-a-sorted-matrix/description/) ```html matrix = [ [ 1, 5, 9], [10, 11, 13], [12, 13, 15] ], k = 8, return 13. ``` ????¦Ï???[Share my thoughts and Clean Java Code](https://leetcode.com/problems/kth-smallest-element-in-a-sorted-matrix/discuss/85173) ?????????? ```java public int kthSmallest(int[][] matrix, int k) { int m = matrix.length, n = matrix[0].length; int lo = matrix[0][0], hi = matrix[m - 1][n - 1]; while(lo <= hi) { int mid = lo + (hi - lo) / 2; int cnt = 0; for(int i = 0; i < m; i++) { for(int j = 0; j < n && matrix[i][j] <= mid; j++) { cnt++; } } if(cnt < k) lo = mid + 1; else hi = mid - 1; } return lo; } ``` ????? ```java public int kthSmallest(int[][] matrix, int k) { int m = matrix.length, n = matrix[0].length; PriorityQueue pq = new PriorityQueue(); for(int j = 0; j < n; j++) pq.offer(new Tuple(0, j, matrix[0][j])); for(int i = 0; i < k - 1; i++) { // §³???????? k - 1 ?????????????????????? k ???? Tuple t = pq.poll(); if(t.x == m - 1) continue; pq.offer(new Tuple(t.x + 1, t.y, matrix[t.x + 1][t.y])); } return pq.poll().val; } class Tuple implements Comparable { int x, y, val; public Tuple(int x, int y, int val) { this.x = x; this.y = y; this.val = val; } @Override public int compareTo(Tuple that) { return this.val - that.val; } } ``` ## ???? **?§Ø?????????????** [Leetcode : 160. Intersection of Two Linked Lists](https://leetcode.com/problems/intersection-of-two-linked-lists/description/) ```html A: a1 ?? a2 ?K c1 ?? c2 ?? c3 ?J B: b1 ?? b2 ?? b3 ``` ?????ÁÙ???? O(n) ??ÁÙ???? O(1) ?? A ?????? a + c??B ?????? b + c?????? c ?¦Â????????????????? a + c + b = b + c + a?? ?????? A ????????????????¦Â??????????????? B ???????????????? B?????????????? B ????????????????¦Â??????????????? A ???????????????? A???????????????? A ?? B ????????????????????????? ```java public ListNode getIntersectionNode(ListNode headA, ListNode headB) { if(headA == null || headB == null) return null; ListNode l1 = headA, l2 = headB; while(l1 != l2){ l1 = (l1 == null) ? headB : l1.next; l2 = (l2 == null) ? headA : l2.next; } return l1; } ``` ???????§Ø???????????????????????????? ????????3.6 ???????????????????????????¦Â??????????????????????????????????????????????????????????????????????????????????????????? **?????** [Leetcode : 206. Reverse Linked List](https://leetcode.com/problems/reverse-linked-list/description/) ??¾Þ?????????????? ```java public ListNode reverseList(ListNode head) { ListNode newHead = null; // ??? null ?????????????¦Â while(head != null){ ListNode nextNode = head.next; head.next = newHead; newHead = head; head = nextNode; } return newHead; } ``` **?öã?????????????** [Leetcode : 21. Merge Two Sorted Lists](https://leetcode.com/problems/merge-two-sorted-lists/description/) ???????????????????ú›??????‰Ø?????????????????????????????????????????????????????????????????? ```java public ListNode mergeTwoLists(ListNode l1, ListNode l2) { if(l1 == null) return l2; if(l2 == null) return l1; ListNode newHead = null; if(l1.val < l2.val){ newHead = l1; newHead.next = mergeTwoLists(l1.next, l2); } else{ newHead = l2; newHead.next = mergeTwoLists(l1, l2.next); } return newHead; } ``` **?????????????????????** [Leetcode : 83. Remove Duplicates from Sorted List (Easy)](https://leetcode.com/problems/remove-duplicates-from-sorted-list/description/) ```java public ListNode deleteDuplicates(ListNode head) { if(head == null || head.next == null) return head; head.next = deleteDuplicates(head.next); return head.next != null && head.val == head.next.val ? head.next : head; } ``` **????????** [Leetcode : 234. Palindrome Linked List (Easy)](https://leetcode.com/problems/palindrome-linked-list/description/) ?§Ô?????????¦Ç???????????????????? ```java public boolean isPalindrome(ListNode head) { if(head == null || head.next == null) return true; ListNode slow = head, fast = head.next; while(fast != null && fast.next != null){ slow = slow.next; fast = fast.next.next; } if(fast != null){ // ???????? slow ??????????? slow = slow.next; } cut(head, slow); // ?§Ô????????? ListNode l1 = head, l2 = slow; l2 = reverse(l2); return isEqual(l1, l2); } private void cut(ListNode head, ListNode cutNode){ while( head.next != cutNode ) head = head.next; head.next = null; } private ListNode reverse(ListNode head){ ListNode newHead = null; while(head != null){ ListNode nextNode = head.next; head.next = newHead; newHead = head; head = nextNode; } return newHead; } private boolean isEqual(ListNode l1, ListNode l2){ while(l1 != null && l2 != null){ if(l1.val != l2.val) return false; l1 = l1.next; l2 = l2.next; } return true; } ``` **??????????????** [????????3.4]()  ```java B.val = C.val; B.next = C.next; ``` **??????????????** [Leetcode : 328. Odd Even Linked List (Medium)](https://leetcode.com/problems/odd-even-linked-list/description/) ```java public ListNode oddEvenList(ListNode head) { if (head == null) { return head; } ListNode odd = head, even = head.next, evenHead = even; while (even != null && even.next != null) { odd.next = odd.next.next; odd = odd.next; even.next = even.next.next; even = even.next; } odd.next = evenHead; return head; } ``` ## ?? ### ??? ?????????????????????????????????????????????????????????????????????????????? **??????** [Leetcode : 104. Maximum Depth of Binary Tree (Easy)](https://leetcode.com/problems/maximum-depth-of-binary-tree/description/) ```java public int maxDepth(TreeNode root) { if(root == null) return 0; return Math.max(maxDepth(root.left), maxDepth(root.right)) + 1; } ``` **?????** [Leetcode : 226. Invert Binary Tree (Easy)](https://leetcode.com/problems/invert-binary-tree/description/) ```java public TreeNode invertTree(TreeNode root) { if(root == null) return null; TreeNode left = root.left; // ???????????? left ??????????????? root.left = invertTree(root.right); root.right = invertTree(left); return root; } ``` **?öã??????** [Leetcode : 617. Merge Two Binary Trees (Easy)](https://leetcode.com/problems/merge-two-binary-trees/description/) ```java public TreeNode mergeTrees(TreeNode t1, TreeNode t2) { if(t1 == null && t2 == null) return null; if(t1 == null) return t2; if(t2 == null) return t1; TreeNode root = new TreeNode(t1.val + t2.val); root.left = mergeTrees(t1.left, t2.left); root.right = mergeTrees(t1.right, t2.right); return root; } ``` **?§Ø?¡¤???????????????** [Leetcdoe : 112. Path Sum (Easy)](https://leetcode.com/problems/path-sum/description/) ?????????¡¤?????????? root ?? leaf ?????§ß???? ```java public boolean hasPathSum(TreeNode root, int sum) { if(root == null) return false; if(root.left == null && root.right == null && root.val == sum) return true; return hasPathSum(root.left, sum - root.val) || hasPathSum(root.right, sum - root.val); } ``` **???¡¤??????????????¡¤??????** [Leetcode : 437. Path Sum III (Easy)](https://leetcode.com/problems/path-sum-iii/description/) ?????????¡¤????????? root ??????? leaf ??¦Â????????????? pathSumStartWithRoot() ??????????????????¡¤???????? ```java public int pathSum(TreeNode root, int sum) { if(root == null) return 0; int ret = pathSumStartWithRoot(root, sum) + pathSum(root.left, sum) + pathSum(root.right, sum); return ret; } private int pathSumStartWithRoot(TreeNode root, int sum){ if(root == null) return 0; int ret = 0; if(root.val == sum) ret++; ret += pathSumStartWithRoot(root.left, sum - root.val) + pathSumStartWithRoot(root.right, sum - root.val); return ret; } ``` **??????** [Leetcode : 101. Symmetric Tree (Easy)](https://leetcode.com/problems/symmetric-tree/description/) ```java public boolean isSymmetric(TreeNode root) { if(root == null) return true; return isSymmetric(root.left, root.right); } private boolean isSymmetric(TreeNode t1, TreeNode t2){ if(t1 == null && t2 == null) return true; if(t1 == null || t2 == null) return false; if(t1.val != t2.val) return false; return isSymmetric(t1.left, t2.right) && isSymmetric(t1.right, t2.left); } ``` **?????** [Leetcode : 110. Balanced Binary Tree (Easy)](https://leetcode.com/problems/balanced-binary-tree/description/) ????????????????????????§³????? 1 ```java private boolean result = true; public boolean isBalanced(TreeNode root) { maxDepth(root); return result; } public int maxDepth(TreeNode root) { if (root == null) return 0; int l = maxDepth(root.left); int r = maxDepth(root.right); if (Math.abs(l - r) > 1) result = false; return 1 + Math.max(l, r); } ``` **??§³¡¤??** [Leetcode : 111. Minimum Depth of Binary Tree (Easy)](https://leetcode.com/problems/minimum-depth-of-binary-tree/description/) ?????????????????????????§³???? ```java public int minDepth(TreeNode root) { if(root == null) return 0; int left = minDepth(root.left); int right = minDepth(root.right); if(left == 0 || right == 0) return left + right + 1; return Math.min(left, right) + 1; } ``` **????????????** [Leetcode : 404. Sum of Left Leaves (Easy)](https://leetcode.com/problems/sum-of-left-leaves/description/) ```java public int sumOfLeftLeaves(TreeNode root) { if(root == null) return 0; if(isLeaf(root.left)) return root.left.val + sumOfLeftLeaves(root.right); return sumOfLeftLeaves(root.left) + sumOfLeftLeaves(root.right); } private boolean isLeaf(TreeNode node){ if(node == null) return false; return node.left == null && node.right == null; } ``` **????????** [Leetcode : 669. Trim a Binary Search Tree (Easy)](https://leetcode.com/problems/trim-a-binary-search-tree/description/) ????????????????? L \~ R ?????? ```java public TreeNode trimBST(TreeNode root, int L, int R) { if(root == null) return null; if(root.val > R) return trimBST(root.left, L, R); if(root.val < L) return trimBST(root.right, L, R); root.left = trimBST(root.left, L, R); root.right = trimBST(root.right, L, R); return root; } ``` **????** [Leetcode : 572. Subtree of Another Tree (Easy)](https://leetcode.com/problems/subtree-of-another-tree/description/) ```java public boolean isSubtree(TreeNode s, TreeNode t) { if(s == null && t == null) return true; if(s == null || t == null) return false; if(s.val == t.val && isSame(s, t)) return true; return isSubtree(s.left, t) || isSubtree(s.right, t); } private boolean isSame(TreeNode s, TreeNode t){ if(s == null && t == null) return true; if(s == null || t == null) return false; if(s.val != t.val) return false; return isSame(s.left, t.left) && isSame(s.right, t.right); } ``` **???????????§Û???????????** [Leetcode : 108. Convert Sorted Array to Binary Search Tree (Easy)](https://leetcode.com/problems/convert-sorted-array-to-binary-search-tree/description/) ???????????BST????????????????????????§ß??§³??????????????§ß?? ```java public TreeNode sortedArrayToBST(int[] nums) { return toBST(nums, 0, nums.length - 1); } private TreeNode toBST(int[] nums, int sIdx, int eIdx){ if(sIdx > eIdx) return null; int mIdx = (sIdx + eIdx) / 2; TreeNode root = new TreeNode(nums[mIdx]); root.left = toBST(nums, sIdx, mIdx - 1); root.right = toBST(nums, mIdx + 1, eIdx); return root; } ``` **????????¡¤??** ```html 1 / \ 2 3 / \ 4 5 Return 3, which is the length of the path [4,2,1,3] or [5,2,1,3]. ``` ```java private int max = 0; public int diameterOfBinaryTree(TreeNode root) { depth(root); return max; } private int depth(TreeNode root) { if (root == null) { return 0; } int leftDepth = depth(root.left); int rightDepth = depth(root.right); max = Math.max(max, leftDepth + rightDepth); return Math.max(leftDepth, rightDepth) + 1; } ``` **??????????§Ö??§³????** [Leetcode : 671. Second Minimum Node In a Binary Tree (Easy)](https://leetcode.com/problems/second-minimum-node-in-a-binary-tree/description/) ```html Input: 2 / \ 2 5 / \ 5 7 Output: 5 ``` ???????????? 0 ???? 2 ???????????????????????????§³???? ```java public int findSecondMinimumValue(TreeNode root) { if(root == null) return -1; if(root.left == null && root.right == null) return -1; int leftVal = root.left.val; int rightVal = root.right.val; if(leftVal == root.val) leftVal = findSecondMinimumValue(root.left); if(rightVal == root.val) rightVal = findSecondMinimumValue(root.right); if(leftVal != -1 && rightVal != -1) return Math.min(leftVal, rightVal); if(leftVal != -1) return leftVal; return rightVal; } ``` **??????????????????????** [Leetcode : 235. Lowest Common Ancestor of a Binary Search Tree (Easy)](https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-search-tree/description/) ```java public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) { if(root.val > p.val && root.val > q.val) return lowestCommonAncestor(root.left, p, q); if(root.val < p.val && root.val < q.val) return lowestCommonAncestor(root.right, p, q); return root; } ``` **???????????** [Leetcode : 236. Lowest Common Ancestor of a Binary Tree (Medium) ](https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-tree/description/) ```java public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) { if (root == null || root == p || root == q) return root; TreeNode left = lowestCommonAncestor(root.left, p, q); TreeNode right = lowestCommonAncestor(root.right, p, q); return left == null ? right : right == null ? left : root; } ``` **????????????¡¤??????** [Leetcode : 687. Longest Univalue Path (Easy)](https://pomotodo.com/app/) ```html 1 / \ 4 5 / \ \ 4 4 5 Output : 2 ``` ```java private int path = 0; public int longestUnivaluePath(TreeNode root) { dfs(root); return path; } private int dfs(TreeNode root){ if(root == null) return 0; int left = dfs(root.left); int right = dfs(root.right); int leftPath = root.left != null && root.left.val == root.val ? left + 1 : 0; int rightPath = root.right != null && root.right.val == root.val ? right + 1 : 0; path = Math.max(path, leftPath + rightPath); return Math.max(leftPath, rightPath); } ``` **???????** [Leetcode : 337. House Robber III (Medium)](https://leetcode.com/problems/house-robber-iii/description/) ```java public int rob(TreeNode root) { if (root == null) return 0; int val1 = root.val; if (root.left != null) { val1 += rob(root.left.left) + rob(root.left.right); } if (root.right != null) { val1 += rob(root.right.left) + rob(root.right.right); } int val2 = rob(root.left) + rob(root.right); return Math.max(val1, val2); } ``` ### ??¦Á??? ??? BFS???????????????????????›¥????????????????? ????????????????????????????§Ö????????????????????????????????????????????????¦Á??????????????? **????????????????????** [637. Average of Levels in Binary Tree (Easy)](https://leetcode.com/problems/average-of-levels-in-binary-tree/description/) ```java public List averageOfLevels(TreeNode root) { List ret = new ArrayList<>(); if(root == null) return ret; Queue queue = new LinkedList<>(); queue.add(root); while(!queue.isEmpty()){ int cnt = queue.size(); double sum = 0; for(int i = 0; i < cnt; i++){ TreeNode node = queue.poll(); sum += node.val; if(node.left != null) queue.add(node.left); if(node.right != null) queue.add(node.right); } ret.add(sum / cnt); } return ret; } ``` **???????????** [Leetcode : 513. Find Bottom Left Tree Value (Easy)](https://leetcode.com/problems/find-bottom-left-tree-value/description/) ```java public int findBottomLeftValue(TreeNode root) { Queue queue = new LinkedList<>(); queue.add(root); while(!queue.isEmpty()){ root = queue.poll(); if(root.right != null) queue.add(root.right); if(root.left != null) queue.add(root.left); } return root.val; } ``` ### ??§Ü?????? ```html 1 / \ 2 3 / \ \ 4 5 6 ``` ??¦Á??????[1 2 3 4 5 6] ?????????[1 2 4 5 3 6] ??????????[4 2 5 1 3 6] ??????????[4 5 2 6 3 1] ??¦Á?????? BFS ???????????? BFS ????????????????????????????????????? DFS ???? ????????????????????????????????????????????? ?? ??? ```java void dfs(TreeNode root){ visit(root); dfs(root.left); dfs(root.right); } ``` ?? ???? ```java void dfs(TreeNode root){ dfs(root.left); visit(root); dfs(root.right); } ``` ?? ???? ```java void dfs(TreeNode root){ dfs(root.left); dfs(root.right); visit(root); } ``` **????????????????????** [Leetcode : 144. Binary Tree Preorder Traversal (Medium)](https://leetcode.com/problems/binary-tree-preorder-traversal/description/) ```java public List preorderTraversal(TreeNode root) { List ret = new ArrayList<>(); if (root == null) return ret; Stack stack = new Stack<>(); stack.push(root); while (!stack.isEmpty()) { TreeNode node = stack.pop(); ret.add(node.val); if (node.right != null) stack.push(node.right); if (node.left != null) stack.push(node.left); // ?????????????????????????????????????????????? } return ret; } ``` **?????????????????????** [Leetcode : ### 145. Binary Tree Postorder Traversal (Medium)](https://leetcode.com/problems/binary-tree-postorder-traversal/description/) ??????? root -> left -> right?????????? left -> right -> root?????????????????? root -> right -> left??????????????????????????? ```java public List postorderTraversal(TreeNode root) { List ret = new ArrayList<>(); if (root == null) return ret; Stack stack = new Stack<>(); stack.push(root); while (!stack.isEmpty()) { TreeNode node = stack.pop(); ret.add(node.val); if (node.left != null) stack.push(node.left); if (node.right != null) stack.push(node.right); } Collections.reverse(ret); return ret; } ``` **?????????????????????** [Leetcode : 94. Binary Tree Inorder Traversal (Medium)](https://leetcode.com/problems/binary-tree-inorder-traversal/description/) ```java public List inorderTraversal(TreeNode root) { List ret = new ArrayList<>(); Stack stack = new Stack<>(); TreeNode cur = root; while(cur != null || !stack.isEmpty()) { while(cur != null) { // ??????????????? stack.add(cur); cur = cur.left; } TreeNode node = stack.pop(); ret.add(node.val); cur = node.right; } return ret; } ``` **???????????????????????????????** //TODO ### BST ??????? BST ??????????????? **?? BST ??????????????????????????????** [653. Two Sum IV - Input is a BST](https://leetcode.com/problems/two-sum-iv-input-is-a-bst/description/) ?????????????????????????????????????????§Ó???? ????????????????¡Â?????????????????????????????????????????????????????????????§³? ```java public boolean findTarget(TreeNode root, int k) { List nums = new ArrayList<>(); inOrder(root, nums); int i = 0, j = nums.size() - 1; while(i < j){ int sum = nums.get(i) + nums.get(j); if(sum == k) return true; if(sum < k) i++; else j--; } return false; } private void inOrder(TreeNode root, List nums){ if(root == null) return; inOrder(root.left, nums); nums.add(root.val); inOrder(root.right, nums); } ``` **?? BST ?§Ó?????§³?????????????????** [Leetcode : 530. Minimum Absolute Difference in BST (Easy)](https://leetcode.com/problems/minimum-absolute-difference-in-bst/description/) ???? BST ??????????????????????????????????????????????????????????§³??? ```java private int minDiff = Integer.MAX_VALUE; private int preVal = -1; public int getMinimumDifference(TreeNode root) { inorder(root); return minDiff; } private void inorder(TreeNode node){ if(node == null) return; inorder(node.left); if(preVal != -1) minDiff = Math.min(minDiff, Math.abs(node.val - preVal)); preVal = node.val; inorder(node.right); } ``` **?? BST ????????????????????????** [Leetcode : Convert BST to Greater Tree (Easy)](https://leetcode.com/problems/convert-bst-to-greater-tree/description/) ????????????? ```java private int sum = 0; public TreeNode convertBST(TreeNode root) { traver(root); return root; } private void traver(TreeNode root) { if (root == null) { return; } if (root.right != null) { traver(root.right); } sum += root.val; root.val = sum; if (root.left != null) { traver(root.left); } } ``` **??? BST ?§Ô????????????** ```java private int cnt = 1; private int maxCnt = 1; private TreeNode preNode = null; private List list; public int[] findMode(TreeNode root) { list = new ArrayList<>(); inorder(root); int[] ret = new int[list.size()]; int idx = 0; for(int num : list){ ret[idx++] = num; } return ret; } private void inorder(TreeNode node){ if(node == null) return; inorder(node.left); if(preNode != null){ if(preNode.val == node.val) cnt++; else cnt = 1; } if(cnt > maxCnt){ maxCnt = cnt; list.clear(); list.add(node.val); } else if(cnt == maxCnt){ list.add(node.val); } preNode = node; inorder(node.right); } ``` **??? BST ??? k ?????** [Leetcode : 230. Kth Smallest Element in a BST (Medium)](https://leetcode.com/problems/kth-smallest-element-in-a-bst/description/) ?????? ```java public int kthSmallest(TreeNode root, int k) { int leftCnt = count(root.left); if(leftCnt == k - 1) return root.val; if(leftCnt > k - 1) return kthSmallest(root.left, k); return kthSmallest(root.right, k - leftCnt - 1); } private int count(TreeNode node) { if(node == null) return 0; return 1 + count(node.left) + count(node.right); } ``` ??????????? ```java private int cnt = 0; private int val; public int kthSmallest(TreeNode root, int k) { inorder(root, k); return val; } private void inorder(TreeNode node, int k) { if(node == null) return; inorder(node.left, k); cnt++; if(cnt == k) { val = node.val; return; } inorder(node.right, k); } ``` ### Trie  Trie???????????????????????§Ø????????????????????????????????? **?????? Trie** [Leetcode : 208. Implement Trie (Prefix Tree) (Medium)](https://leetcode.com/problems/implement-trie-prefix-tree/description/) ```java class Trie { private class Node{ Node[] childs = new Node[26]; boolean isLeaf; } private Node root = new Node(); /** Initialize your data structure here. */ public Trie() { } /** Inserts a word into the trie. */ public void insert(String word) { int idx = word.charAt(0) - 'a'; insert(word, root); } private void insert(String word, Node node){ int idx = word.charAt(0) - 'a'; if(node.childs[idx] == null){ node.childs[idx] = new Node(); } if(word.length() == 1) node.childs[idx].isLeaf = true; else insert(word.substring(1), node.childs[idx]); } /** Returns if the word is in the trie. */ public boolean search(String word) { return search(word, root); } private boolean search(String word, Node node){ if(node == null) return false; int idx = word.charAt(0) - 'a'; if(node.childs[idx] == null) return false; if(word.length() == 1) return node.childs[idx].isLeaf; return search(word.substring(1), node.childs[idx]); } /** Returns if there is any word in the trie that starts with the given prefix. */ public boolean startsWith(String prefix) { return startWith(prefix, root); } private boolean startWith(String prefix, Node node){ if(node == null) return false; if(prefix.length() == 0) return true; int idx = prefix.charAt(0) - 'a'; return startWith(prefix.substring(1), node.childs[idx]); } } ``` **?????? Trie????????????** [Leetcode : 677. Map Sum Pairs (Medium)](https://leetcode.com/problems/map-sum-pairs/description/) ```java class MapSum { private class Trie { int val; Map childs; boolean isWord; Trie() { childs = new HashMap<>(); } } private Trie root; public MapSum() { root = new Trie(); } public void insert(String key, int val) { Trie cur = root; for(char c : key.toCharArray()) { if(!cur.childs.containsKey(c)) { Trie next = new Trie(); cur.childs.put(c, next); } cur = cur.childs.get(c); } cur.val = val; cur.isWord = true; } public int sum(String prefix) { Trie cur = root; for(char c : prefix.toCharArray()) { if(!cur.childs.containsKey(c)) return 0; cur = cur.childs.get(c); } return dfs(cur); } private int dfs(Trie cur) { int sum = 0; if(cur.isWord) { sum += cur.val; } for(Trie next : cur.childs.values()) { sum += dfs(next); } return sum; } } ``` ## ? ## ¦Ë???? **1. ???????** 0s ??? ??? 0 ??1s ?????? 1?? ``` x ^ 0s = x x & 0s = 0 x | 0s = x x ^ 1s = \~x x & 1s = x x | 1s = 1s x ^ x = 0 x & x = x x | x = x ``` ?? ???? x ^ 1s = \~x ??????????¦Ë?????????????? x ^ x = 0 ???????????????????????????????????????????????? ?? ???? x & 0s = 0 ?? x & 1s = x ?????????????????????????? num ?? mask ??00111100 ????¦Ë???????????? num ???? mask ?? 1 ??????????¦Ë?? ?? ???? x | 0s = x ?? x | 1s = 1s ???????????????¨°?????????? num ?? mask??00111100 ????¦Ë????????? num ???? mask ?? 1 ??????????¦Ë??????? 1 ?? \>\> n ????????????????? 2ⁿ?? \>\>\> n ????????????????? 0?? << n ????????????????? 2ⁿ?? n&(n-1) ??¦Ë????????? n ??¦Ë??????????????¦Ë???????????????? 10110**100**????? 1 ??? 10110**011**???????????????? 10110**000**?? n-n&(\~n+1) ??????????? n ??¦Ë??????????????¦Ë?? n&(-n) ???????? n ??¦Ë??????????????¦Ë??-n ??? n ?????? 1????????????? 10110**100**??-n ??? 01001**100**???????? 00000**100** **2. mask ????** ???? 111111111???? 0 ????????\~0?? ??????§Ö? i ¦Ë? 1 ?? mask???? 1 ??????? i ¦Ë?????1<<i ?????? 1<<5 ?????§Ö? 5 ¦Ë? 1 ?? mask ??00010000?? ???? 1 ?? i ¦Ë? 1 ?? mask??1<<(i+1)-1 ????????ÁL 1<<(4+1)-1 = 00010000-1 = 00001111?? ???? 1 ?? i ¦Ë? 0 ?? mask????éí 1 ?? i ¦Ë? 1 ?? mask ??????? \~(1<<(i+1)-1)?? **3. ¦Ë????????** ?? ????? i ¦Ë num & 00010000 != 0 ```java (num & (1 << i)) != 0; ``` ?? ???? i ¦Ë????? 1 num | 00010000 ```java num | (1 << i); ``` ?? ???? i ¦Ë???? 0 num & 11101111 ```java num & (\~(1 << i)) ``` ?? ?????¦Ë???? i ¦Ë???? 0 num & 00001111 ```java num & ((1 << i) - 1); ``` ?? ???? 0 ¦Ë???? i ¦Ë???? 0 num & 11110000 ```java num & (\~((1 << (i+1)) - 1)); ``` ?? ???? i ¦Ë????? 0 ???? 1 ????? i ¦Ë??????? v ???? i ¦Ë????§³?¦Ë?????? ```java (num & (1 << i)) | (v << i); ``` **4. Java ?§Ö?¦Ë????** ```html static int Integer.bitCount() // ??? 1 ?????? static int Integer.highestOneBit() // ??????¦Ë static String toBinaryString(int i) // ???¦Ë??????????????? ``` **???????????????????§Ø???¦Ë???** [Leetcode : 461. Hamming Distance (Easy)](https://leetcode.com/problems/hamming-distance/) ????????????????????????????¦Ë???? 1 ??????§Ø???? 1 ???¨À? ```java public int hammingDistance(int x, int y) { int z = x ^ y; int cnt = 0; while(z != 0){ if((z & 1) == 1) cnt++; z = z >> 1; } return cnt; } ``` ??????? Integer.bitcount() ????? 1 ????????? ```java public int hammingDistance(int x, int y) { return Integer.bitCount(x ^ y); } ``` **?????????????¦Ë** [Leetcode : 190. Reverse Bits (Easy)](https://leetcode.com/problems/reverse-bits/description/) ```java public int reverseBits(int n) { int ret = 0; for(int i = 0; i < 32; i++){ ret <<= 1; ret |= (n & 1); n >>>= 1; } return ret; } ``` **??????????????????????** [???????????????? ??P317](#) ```java a = a ^ b; b = a ^ b; a = a ^ b; ``` ?? c = a ^ b????? b ^ c = b ^ b ^ a = a??a ^ c = a ^ a ^ b = b?? **?§Ø??????????? 4 ?? n ?¦Ç?** [Leetcode : 342. Power of Four (Easy)](https://leetcode.com/problems/power-of-four/) ??????????????????????????¦Ë? 1 ????????? 0 ?????? 16 ?? 10000?????????? 1 ??????? 2 ¦Ë??????????????????????????????????????§Ø???????????? ```java public boolean isPowerOfFour(int num) { int i = 1; while(i > 0){ if(i == num) return true; i = i << 2; } return false; } ``` ??????? Java ?? Integer.toString() ?????????????? 4 ????????????????????§Ø??????????? 1 ????? ```java public boolean isPowerOfFour(int num) { return Integer.toString(num, 4).matches("10*"); } ``` **?§Ø??????????? 2 ?? n ?¦Ç?** [Leetcode : 231. Power of Two (Easy)](https://leetcode.com/problems/power-of-two/description/) ????????? Power of Four ??????????? 2 ?? n ?¦Ç???????????????????????? 1 ????? ```java public boolean isPowerOfTwo(int n) { return n > 0 && Integer.bitCount(n) == 1; } ``` ???? 1000 & 0111 == 0 ??????????????????? ```java public boolean isPowerOfTwo(int n) { return n > 0 && (n & (n - 1)) == 0; } ``` **??????¦·??????????????** [Leetcode : 136. Single Number (Easy)](https://leetcode.com/problems/single-number/description/) ?????????????????? 0??????????????????????????????????????????????? ??????§µ?[Leetcode : 389. Find the Difference (Easy)](https://leetcode.com/problems/find-the-difference/description/)??????????????????????????????????????????? O(1) ???ÁÙ?????????????????? HashSet?? ```java public int singleNumber(int[] nums) { int ret = 0; for(int n : nums) ret = ret ^ n; return ret; } ``` **?????§Ó?????????????** [Leetcode : 260. Single Number III (Medium)](https://leetcode.com/problems/single-number-iii/description/) ???????????????¦Ë??????????????¦Ë???????? ?????????????????????????????????????????????????? diff &= -diff ????? diff ?????? 0 ??¦Ë??????????????????????????¦Ë??????????????????¦Ë?????????¦Ë?????????????????????? ```java public int[] singleNumber(int[] nums) { int diff = 0; for(int num : nums) diff ^= num; // ????????¦Ë diff &= -diff; int[] ret = new int[2]; for(int num : nums) { if((num & diff) == 0) ret[0] ^= num; else ret[1] ^= num; } return ret; } ``` **?§Ø????????¦Ë?????????????????? 0 ?? 1** [Leetcode : 693. Binary Number with Alternating Bits (Easy)](https://leetcode.com/problems/binary-number-with-alternating-bits/description/) ???? 10101 ????¦Ë?????????????????????? 1 ¦Ë??? 1010 ?????????????¦Ë???????????????????? 11111?? ```java public boolean hasAlternatingBits(int n) { int a = (n ^ (n >> 1)); return (a & (a + 1)) == 0; } ``` **????????????** [Leetcode : 476. Number Complement (Easy)](https://leetcode.com/problems/number-complement/description/) ??????????????§Ö??? 0 ???? ???? 00000101??????????????? 00000111 ?????????????????????????????? 00000111?? ```java public int findComplement(int num) { if(num == 0) return 1; int mask = 1 << 30; while((num & mask) == 0) mask >>= 1; mask = (mask << 1) - 1; return num ^ mask; } ``` ???????? Java ?? Integer.highestOneBit() ????????¨²????? 1 ?????? ```java public int findComplement(int num) { if(num == 0) return 1; int mask = Integer.highestOneBit(num); mask = (mask << 1) - 1; return num ^ mask; } ``` ???? 10000000 ?????????????? 11111111?????????????¡¤????? ```html mask |= mask >> 1 11000000 mask |= mask >> 2 11110000 mask |= mask >> 4 11111111 ``` ```java public int findComplement(int num) { int mask = num; mask |= mask >> 1; mask |= mask >> 2; mask |= mask >> 4; mask |= mask >> 8; mask |= mask >> 16; return (mask ^ num); } ``` **???????????** [Leetcode : 371. Sum of Two Integers (Easy)](https://leetcode.com/problems/sum-of-two-integers/description/) a ^ b ?????§á????¦Ë???????????????(a & b) << 1 ?????¦Ë???????????????? (a & b) << 1 ?????????? 0???????????ï…??¦Ë?????? 0 ??????????????¦Ë???? 0?????????? ```java public int getSum(int a, int b) { return b == 0 ? a : getSum((a ^ b), (a & b) << 1); } ``` **??????????** [???????????????? P319](#) **??????????????** [Leetcode : 318. Maximum Product of Word Lengths (Medium)](https://leetcode.com/problems/maximum-product-of-word-lengths/description/) ?????????????????????????????§³§Õ????????????????????????????????????????????????????????????????????? ?????¡¤????????????????§Ø???????????????????????????????????§³§Õ???????? 26 ¦Ë????????????? 32 ¦Ë?????????›¥??????????????? ```java public int maxProduct(String[] words) { int n = words.length; if (n == 0) return 0; int[] val = new int[n]; for (int i = 0; i < n; i++) { for (char c : words[i].toCharArray()) { val[i] |= 1 << (c - 'a'); } } int ret = 0; for (int i = 0; i < n; i++) { for (int j = i + 1; j < n; j++) { if ((val[i] & val[j]) == 0) { ret = Math.max(ret, words[i].length() * words[j].length()); } } } return ret; } ``` # ?¦Ï????? - [Leetcode](https://leetcode.com/problemset/algorithms/?status=Todo) - ??? Offer - ??????????? - ?????? - ???????????????? - ????????????? - ?? - ???????????????§Ý??????