auto commit

notes/算法.md

@@ -83,6 +83,8 @@ public class ThreeSum {
 
 通过将数组先排序，对两个元素求和，并用二分查找方法查找是否存在该和的相反数，如果存在，就说明存在三元组的和为 0。
 
+应该注意的是，只有数组不含有相同元素才能使用这种解法，否则二分查找的结果会出错。
+
 该方法可以将 ThreeSum 算法增长数量级降低为 O(N<sup>2</sup>logN)。
 
 ```java
@@ -94,18 +96,19 @@ public class ThreeSumFast {
         for (int i = 0; i < N; i++)
             for (int j = i + 1; j < N; j++) {
                 int target = -nums[i] - nums[j];
-                int index = binarySearch(nums, target);
+                int index = BinarySearch.search(nums, target);
                 // 应该注意这里的下标必须大于 j，否则会重复统计。
-                if (index <= j)
+                if (index > j)
-                    continue;
-                while (index < N && nums[index++] == target)
                     cnt++;
             }
-
         return cnt;
     }
+}
+```
 
-    private static int binarySearch(int[] nums, int target) {
+```java
+public class BinarySearch {
+    public static int search(int[] nums, int target) {
         int l = 0, h = nums.length - 1;
         while (l <= h) {
             int m = l + (h - l) / 2;
@@ -142,23 +145,38 @@ public class ThreeSumFast {
 public class RatioTest {
     public static void main(String[] args) {
         int N = 500;
-        int K = 7;
+        int loopTimes = 7;
-        long preTime = -1;
+        double preTime = -1;
-        while (K-- > 0) {
+        while (loopTimes-- > 0) {
             int[] nums = new int[N];
-            long startTime = System.currentTimeMillis();
+            StopWatch.start();
             int cnt = ThreeSum.count(nums);
-            long endTime = System.currentTimeMillis();
+            System.out.println(cnt);
-            long time = endTime - startTime;
+            double elapsedTime = StopWatch.elapsedTime();
-            double ratio = preTime == -1 ? 0 : (double) time / preTime;
+            double ratio = preTime == -1 ? 0 : elapsedTime / preTime;
-            System.out.println(N + "  " + time + "  " + ratio);
+            System.out.println(N + "  " + elapsedTime + "  " + ratio);
-            preTime = time;
+            preTime = elapsedTime;
             N *= 2;
         }
     }
 }
 ```
 
+```java
+public class StopWatch {
+    private static long start;
+    
+    public static void start(){
+        start = System.currentTimeMillis();
+    }
+    
+    public static double elapsedTime() {
+        long now = System.currentTimeMillis();
+        return (now - start) / 1000.0;
+    }
+}
+```
+
 ## 注意事项
 
 ### 1. 大常数
@@ -187,25 +205,39 @@ public class RatioTest {
 
 First-In-Last-Out
 
+```java
+public interface MyStack<Item> extends Iterable<Item> {
+    MyStack<Item> push(Item item);
+
+    Item pop() throws Exception;
+
+    boolean isEmpty();
+
+    int size();
+}
+```
+
 ### 1. 数组实现
 
 ```java
-import java.util.Iterator;
+public class ResizingArrayStack<Item> implements MyStack<Item> {
-
-public class ResizingArrayStack<Item> implements Iterable<Item> {
     // 栈元素数组
     private Item[] a = (Item[]) new Object[1]; // 只能通过转型来创建泛型数组
     // 元素数量
     private int N = 0;
 
-    public void push(Item item) {
+    @Override
+    public MyStack<Item> push(Item item) {
         check();
         a[N++] = item;
+        return this;
     }
 
+    @Override
     public Item pop() throws Exception {
         if (isEmpty())
             throw new Exception("stack is empty");
+
         Item item = a[--N];
         check();
         a[N] = null; // 避免对象游离
@@ -229,10 +261,12 @@ public class ResizingArrayStack<Item> implements Iterable<Item> {
         a = tmp;
     }
 
+    @Override
     public boolean isEmpty() {
         return N == 0;
     }
 
+    @Override
     public int size() {
         return N;
     }
@@ -240,57 +274,29 @@ public class ResizingArrayStack<Item> implements Iterable<Item> {
     @Override
     public Iterator<Item> iterator() {
         // 返回逆序遍历的迭代器
-        return new ReverseArrayIterator();
+        return new Iterator<Item>() {
-    }
+            private int i = N;
 
-    private class ReverseArrayIterator implements Iterator<Item> {
+            @Override
-        private int i = N;
+            public boolean hasNext() {
+                return i > 0;
+            }
 
-        @Override
+            @Override
-        public boolean hasNext() {
+            public Item next() {
-            return i > 0;
+                return a[--i];
-        }
+            }
-
+        };
-        @Override
-        public Item next() {
-            return a[--i];
-        }
     }
 }
 ```
 
-```java
-public static void main(String[] args) throws Exception {
-    ResizingArrayStack<Integer> stack = new ResizingArrayStack();
-    stack.push(1);
-    stack.push(2);
-    stack.push(3);
-    stack.push(4);
-    System.out.println(stack.isEmpty());
-    System.out.println(stack.size());
-    System.out.println(stack.pop());
-    System.out.println(stack.pop());
-    for (Integer item : stack)
-        System.out.println(item);
-}
-```
-
-```html
-false
-4
-4
-3
-2
-1
-```
-
 ### 2. 链表实现
 
 需要使用链表的头插法来实现，因为头插法中最后压入栈的元素在链表的开头，它的 next 指针指向前一个压入栈的元素，在弹出元素使就可以通过 next 指针遍历到前一个压入栈的元素从而让这个元素称为新的栈顶元素。
 
 ```java
-public class ListStack<Item> {
+public class ListStack<Item> implements MyStack<Item> {
-
     private Node top = null;
     private int N = 0;
 
@@ -299,22 +305,17 @@ public class ListStack<Item> {
         Node next;
     }
 
-    public boolean isEmpty() {
+    @Override
-        return N == 0;
+    public MyStack<Item> push(Item item) {
-    }
-
-    public int size() {
-        return N;
-    }
-
-    public void push(Item item) {
         Node newTop = new Node();
         newTop.item = item;
         newTop.next = top;
         top = newTop;
         N++;
+        return this;
     }
 
+    @Override
     public Item pop() throws Exception {
         if (isEmpty())
             throw new Exception("stack is empty");
@@ -323,28 +324,36 @@ public class ListStack<Item> {
         N--;
         return item;
     }
-}
-```
 
-```java
+    @Override
-public static void main(String[] args) throws Exception {
+    public boolean isEmpty() {
-    ListStack<Integer> stack = new ListStack();
+        return N == 0;
-    stack.push(1);
+    }
-    stack.push(2);
-    stack.push(3);
-    stack.push(4);
-    System.out.println(stack.isEmpty());
-    System.out.println(stack.size());
-    System.out.println(stack.pop());
-    System.out.println(stack.pop());
-}
-```
 
-```html
+    @Override
-false
+    public int size() {
-4
+        return N;
-4
+    }
-3
+
+    @Override
+    public Iterator<Item> iterator() {
+        return new Iterator<Item>() {
+            private Node cur = top;
+
+            @Override
+            public boolean hasNext() {
+                return cur != null;
+            }
+
+            @Override
+            public Item next() {
+                Item item = cur.item;
+                cur = cur.next;
+                return item;
+            }
+        };
+    }
+}
 ```
 
 ## 队列
@@ -355,6 +364,88 @@ First-In-First-Out
 
 这里需要考虑 first 和 last 指针哪个作为链表的开头。因为出队列操作需要让队首元素的下一个元素成为队首，所以需要容易获取下一个元素，而链表的头部节点的 next 指针指向下一个元素，因此可以让 first 指针链表的开头。
 
+```java
+public interface MyQueue<Item> extends Iterable<Item> {
+    int size();
+
+    boolean isEmpty();
+
+    MyQueue<Item> add(Item item);
+
+    Item remove() throws Exception;
+}
+```
+
+```java
+public class ListQueue<Item> implements MyQueue<Item> {
+    private Node first;
+    private Node last;
+    int N = 0;
+
+    private class Node {
+        Item item;
+        Node next;
+    }
+
+    @Override
+    public boolean isEmpty() {
+        return N == 0;
+    }
+
+    @Override
+    public int size() {
+        return N;
+    }
+
+    @Override
+    public MyQueue<Item> add(Item item) {
+        Node newNode = new Node();
+        newNode.item = item;
+        newNode.next = null;
+        if (isEmpty()) {
+            last = newNode;
+            first = newNode;
+        } else {
+            last.next = newNode;
+            last = newNode;
+        }
+        N++;
+        return this;
+    }
+
+    @Override
+    public Item remove() throws Exception {
+        if (isEmpty())
+            throw new Exception("queue is empty");
+        Node node = first;
+        first = first.next;
+        N--;
+        if (isEmpty())
+            last = null;
+        return node.item;
+    }
+
+    @Override
+    public Iterator<Item> iterator() {
+        return new Iterator<Item>() {
+            Node cur = first;
+
+            @Override
+            public boolean hasNext() {
+                return cur != null;
+            }
+
+            @Override
+            public Item next() {
+                Item item = cur.item;
+                cur = cur.next;
+                return item;
+            }
+        };
+    }
+}
+```
+
 ```java
 public class Queue<Item> {
     private Node first;
@@ -401,25 +492,6 @@ public class Queue<Item> {
 }
 ```
 
-```java
-public static void main(String[] args) throws Exception {
-    Queue queue = new Queue();
-    queue.add(1);
-    queue.add(2);
-    System.out.println(queue.remove());
-    System.out.println(queue.remove());
-    queue.add(3);
-    queue.add(4);
-    System.out.println(queue.size());
-}
-```
-
-```html
-1
-2
-2
-```
-
 # 三、排序
 
 待排序的元素需要实现 Java 的 Comparable 接口，该接口有 compareTo() 方法，可以用它来判断两个元素的大小关系。