Merge pull request krahets#241 from krahets/heap-dev

Add the chapter of Heap

codes/java/chapter_hashing/array_hash_map.java

@@ -5,6 +5,7 @@
  */
 
 package chapter_hashing;
+
 import java.util.*;
 
 /* 键值对 int->String */

codes/java/chapter_hashing/hash_map.java

@@ -5,6 +5,7 @@
  */
 
 package chapter_hashing;
+
 import java.util.*;
 import include.*;
 

codes/java/chapter_heap/heap.java

@@ -0,0 +1,67 @@
+/**
+ * File: my_heap.java
+ * Created Time: 2023-01-07
+ * Author: Krahets ([email protected])
+ */
+
+package chapter_heap;
+
+import include.*;
+import java.util.*;
+
+
+public class heap {
+    public static void testPush(Queue<Integer> heap, int val) {
+        heap.add(val); // 元素入堆
+        System.out.format("\n元素 %d 入堆后\n", val);
+        PrintUtil.printHeap(heap);
+    }
+
+    public static void testPoll(Queue<Integer> heap) {
+        int val = heap.poll(); // 堆顶元素出堆
+        System.out.format("\n堆顶元素 %d 出堆后\n", val);
+        PrintUtil.printHeap(heap);
+    }
+
+    public static void main(String[] args) {
+        /* 初始化堆 */
+        // 初始化小顶堆
+        Queue<Integer> minHeap = new PriorityQueue<>();
+        // 初始化大顶堆（使用 lambda 表达式修改 Comparator 即可）
+        Queue<Integer> maxHeap = new PriorityQueue<>((a, b) -> { return b - a; });
+
+        System.out.println("\n以下测试样例为大顶堆");
+
+        /* 元素入堆 */
+        testPush(maxHeap, 1);
+        testPush(maxHeap, 3);
+        testPush(maxHeap, 2);
+        testPush(maxHeap, 5);
+        testPush(maxHeap, 4);
+
+        /* 获取堆顶元素 */
+        int peek = maxHeap.peek();
+        System.out.format("\n堆顶元素为 %d\n", peek);
+
+        /* 堆顶元素出堆 */
+        testPoll(maxHeap);
+        testPoll(maxHeap);
+        testPoll(maxHeap);
+        testPoll(maxHeap);
+        testPoll(maxHeap);
+
+        /* 获取堆大小 */
+        int size = maxHeap.size();
+        System.out.format("\n堆元素数量为 %d\n", size);
+
+        /* 判断堆是否为空 */
+        boolean isEmpty = maxHeap.isEmpty();
+        System.out.format("\n堆是否为空 %b\n", isEmpty);
+
+        /* 输入列表并建堆 */
+        // 时间复杂度为 O(n) ，而非 O(nlogn)
+        minHeap = new PriorityQueue<>(Arrays.asList(1, 3, 2, 5, 4));
+        System.out.println("\n输入列表并建立小顶堆后");
+        PrintUtil.printHeap(minHeap);
+    }
+}

codes/java/chapter_heap/my_heap.java

@@ -0,0 +1,177 @@
+/**
+ * File: my_heap.java
+ * Created Time: 2023-01-07
+ * Author: Krahets ([email protected])
+ */
+
+package chapter_heap;
+
+import include.*;
+import java.util.*;
+
+class MaxHeap {
+    // 使用列表而非数组，这样无需考虑扩容问题
+    private List<Integer> maxHeap;
+
+    /* 构造函数，建立空堆 */
+    public MaxHeap() {
+        maxHeap = new ArrayList<>();
+    }
+
+    /* 构造函数，根据输入列表建堆 */
+    public MaxHeap(List<Integer> nums) {
+        // 所有元素入堆
+        maxHeap = new ArrayList<>(nums);
+        // 堆化除叶结点以外的其他所有结点
+        for (int i = parent(size() - 1); i >= 0; i--) {
+            siftDown(i);
+        }
+    }
+
+    /* 获取左子结点索引 */
+    private int left(int i) {
+        return 2 * i + 1;
+    }
+
+    /* 获取右子结点索引 */
+    private int right(int i) {
+        return 2 * i + 2;
+    }
+
+    /* 获取父结点索引 */
+    private int parent(int i) {
+        return (i - 1) / 2; // 向下整除
+    }
+
+    /* 交换元素 */
+    private void swap(int i, int j) {
+        int a = maxHeap.get(i), 
+            b = maxHeap.get(j),
+            tmp = a;
+        maxHeap.set(i, b);
+        maxHeap.set(j, tmp);
+    }
+
+    /* 获取堆大小 */
+    public int size() {
+        return maxHeap.size();
+    }
+
+    /* 判断堆是否为空 */
+    public boolean isEmpty() {
+        return size() == 0;
+    }
+
+    /* 访问堆顶元素 */
+    public int peek() {
+        return maxHeap.get(0);
+    }
+
+    /* 元素入堆 */
+    public void push(int val) {
+        // 添加结点
+        maxHeap.add(val);
+        // 从底至顶堆化
+        siftUp(size() - 1);
+    }
+
+    /* 从结点 i 开始，从底至顶堆化 */
+    private void siftUp(int i) {
+        while (true) {
+            // 获取结点 i 的父结点
+            int p = parent(i);
+            // 当“越过根结点”或“结点无需修复”时，结束堆化
+            if (p < 0 || maxHeap.get(i) <= maxHeap.get(p))
+                break;
+            // 交换两结点
+            swap(i, p);
+            // 循环向上堆化
+            i = p;
+        }
+    }
+
+    /* 元素出堆 */
+    public int poll() {
+        // 判空处理
+        if (isEmpty())
+            throw new EmptyStackException();
+        // 交换根结点与最右叶结点（即交换首元素与尾元素）
+        swap(0, size() - 1);
+        // 删除结点
+        int val = maxHeap.remove(size() - 1);
+        // 从顶至底堆化
+        siftDown(0);
+        // 返回堆顶元素
+        return val;
+    }
+
+    /* 从结点 i 开始，从顶至底堆化 */
+    private void siftDown(int i) {
+        while (true) {
+            // 判断结点 i, l, r 中值最大的结点，记为 ma
+            int l = left(i), r = right(i), ma = i;
+            if (l < size() && maxHeap.get(l) > maxHeap.get(ma))
+                ma = l;
+            if (r < size() && maxHeap.get(r) > maxHeap.get(ma))
+                ma = r;
+            // 若结点 i 最大或索引 l, r 越界，则无需继续堆化，跳出
+            if (ma == i) break;
+            // 交换两结点
+            swap(i, ma);
+            // 循环向下堆化
+            i = ma;
+        }
+    }
+
+    /* 打印堆（二叉树） */
+    public void print() {
+        Queue<Integer> queue = new PriorityQueue<>((a, b) -> { return b - a; });
+        queue.addAll(maxHeap);
+        PrintUtil.printHeap(queue);
+    }
+}
+
+
+public class my_heap {
+    public static void testPush(MaxHeap maxHeap, int val) {
+        maxHeap.push(val);  // 元素入堆
+        System.out.format("\n添加元素 %d 后\n", val);
+        maxHeap.print();
+    }
+
+    public static void testPoll(MaxHeap maxHeap) {
+        int val = maxHeap.poll(); // 堆顶元素出堆
+        System.out.format("\n出堆元素为 %d\n", val);
+        maxHeap.print();
+    }
+
+    public static void main(String[] args) {
+        /* 初始化大顶堆 */
+        MaxHeap maxHeap = new MaxHeap(Arrays.asList(9, 8, 6, 6, 7, 5, 2, 1, 4, 3, 6, 2));
+        System.out.println("\n输入列表并建堆后");
+        maxHeap.print();
+
+        /* 获取堆顶元素 */
+        int peek = maxHeap.peek();
+        System.out.format("\n堆顶元素为 %d\n", peek);
+
+        /* 元素入堆 */
+        int val = 7;
+        maxHeap.push(val);
+        System.out.format("\n元素 %d 入堆后\n", val);
+        maxHeap.print();
+
+        /* 堆顶元素出堆 */
+        peek = maxHeap.poll();
+        System.out.format("\n堆顶元素 %d 出堆后\n", peek);
+        maxHeap.print();
+
+        /* 获取堆大小 */
+        int size = maxHeap.size();
+        System.out.format("\n堆元素数量为 %d\n", size);
+
+        /* 判断堆是否为空 */
+        boolean isEmpty = maxHeap.isEmpty();
+        System.out.format("\n堆是否为空 %b\n", isEmpty);
+    }
+}

codes/java/chapter_tree/binary_tree_bfs.java

@@ -30,7 +30,7 @@ static List<Integer> hierOrder(TreeNode root) {
     public static void main(String[] args) {
         /* 初始化二叉树 */
         // 这里借助了一个从数组直接生成二叉树的函数
-        TreeNode root = TreeNode.arrToTree(new Integer[] { 1, 2, 3, 4, 5, 6, 7 });
+        TreeNode root = TreeNode.listToTree(Arrays.asList(1, 2, 3, 4, 5, 6, 7));
         System.out.println("\n初始化二叉树\n");
         PrintUtil.printTree(root);
 

codes/java/chapter_tree/binary_tree_dfs.java

@@ -43,7 +43,7 @@ static void postOrder(TreeNode root) {
     public static void main(String[] args) {
         /* 初始化二叉树 */
         // 这里借助了一个从数组直接生成二叉树的函数
-        TreeNode root = TreeNode.arrToTree(new Integer[] { 1, 2, 3, 4, 5, 6, 7 });
+        TreeNode root = TreeNode.listToTree(Arrays.asList(1, 2, 3, 4, 5, 6, 7));
         System.out.println("\n初始化二叉树\n");
         PrintUtil.printTree(root);
 

codes/java/include/PrintUtil.java

@@ -105,10 +105,16 @@ public static <K, V> void printHashMap(Map<K, V> map) {
         }
     }
 
-    public static void printHeap(PriorityQueue<Integer> queue) {
-        Integer[] nums = (Integer[])queue.toArray();
-        TreeNode root = TreeNode.arrToTree(nums);
-
+    /**
+     * Print a heap (PriorityQueue)
+     * @param queue
+     */
+    public static void printHeap(Queue<Integer> queue) {
+        List<Integer> list = new ArrayList<>(queue);
+        System.out.print("堆的数组表示：");
+        System.out.println(list);
+        System.out.println("堆的树状表示：");
+        TreeNode root = TreeNode.listToTree(list);
         printTree(root);
     }
 }

codes/java/include/TreeNode.java

@@ -23,26 +23,27 @@ public TreeNode(int x) {
 
     /**
      * Generate a binary tree given an array
-     * @param arr
+     * @param list
      * @return
      */
-    public static TreeNode arrToTree(Integer[] arr) {
-        if (arr.length == 0)
+    public static TreeNode listToTree(List<Integer> list) {
+        int size = list.size();
+        if (size == 0)
             return null;
 
-        TreeNode root = new TreeNode(arr[0]);
+        TreeNode root = new TreeNode(list.get(0));
         Queue<TreeNode> queue = new LinkedList<>() {{ add(root); }};
         int i = 0;
         while(!queue.isEmpty()) {
             TreeNode node = queue.poll();
-            if (++i >= arr.length) break;
-            if(arr[i] != null) {
-                node.left = new TreeNode(arr[i]);
+            if (++i >= size) break;
+            if (list.get(i) != null) {
+                node.left = new TreeNode(list.get(i));
                 queue.add(node.left);
             }
-            if (++i >= arr.length) break;
-            if(arr[i] != null) {
-                node.right = new TreeNode(arr[i]);
+            if (++i >= size) break;
+            if (list.get(i) != null) {
+                node.right = new TreeNode(list.get(i));
                 queue.add(node.right);
             }
         }