154 lines
4.9 KiB
Java
154 lines
4.9 KiB
Java
/*
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* File: binary_search_tree.java
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* Created Time: 2022-11-25
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* Author: Krahets (krahets@163.com)
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*/
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package chapter_tree;
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import java.util.*;
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import include.*;
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/* 二叉搜索树 */
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class BinarySearchTree {
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private TreeNode root;
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public BinarySearchTree(int[] nums) {
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Arrays.sort(nums); // 排序数组
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root = buildTree(nums, 0, nums.length - 1); // 构建二叉搜索树
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}
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/* 获取二叉树根结点 */
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public TreeNode getRoot() {
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return root;
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}
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/* 构建二叉搜索树 */
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public TreeNode buildTree(int[] nums, int i, int j) {
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if (i > j) return null;
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// 将数组中间结点作为根结点
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int mid = (i + j) / 2;
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TreeNode root = new TreeNode(nums[mid]);
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// 递归建立左子树和右子树
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root.left = buildTree(nums, i, mid - 1);
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root.right = buildTree(nums, mid + 1, j);
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return root;
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}
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/* 查找结点 */
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public TreeNode search(int num) {
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TreeNode cur = root;
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// 循环查找，越过叶结点后跳出
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while (cur != null) {
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// 目标结点在 root 的右子树中
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if (cur.val < num) cur = cur.right;
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// 目标结点在 root 的左子树中
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else if (cur.val > num) cur = cur.left;
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// 找到目标结点，跳出循环
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else break;
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}
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// 返回目标结点
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return cur;
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}
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/* 插入结点 */
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public TreeNode insert(int num) {
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// 若树为空，直接提前返回
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if (root == null) return null;
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TreeNode cur = root, pre = null;
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// 循环查找，越过叶结点后跳出
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while (cur != null) {
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// 找到重复结点，直接返回
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if (cur.val == num) return null;
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pre = cur;
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// 插入位置在 root 的右子树中
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if (cur.val < num) cur = cur.right;
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// 插入位置在 root 的左子树中
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else cur = cur.left;
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}
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// 插入结点 val
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TreeNode node = new TreeNode(num);
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if (pre.val < num) pre.right = node;
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else pre.left = node;
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return node;
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}
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/* 删除结点 */
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public TreeNode remove(int num) {
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// 若树为空，直接提前返回
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if (root == null) return null;
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TreeNode cur = root, pre = null;
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// 循环查找，越过叶结点后跳出
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while (cur != null) {
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// 找到待删除结点，跳出循环
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if (cur.val == num) break;
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pre = cur;
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// 待删除结点在 root 的右子树中
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if (cur.val < num) cur = cur.right;
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// 待删除结点在 root 的左子树中
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else cur = cur.left;
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}
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// 若无待删除结点，则直接返回
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if (cur == null) return null;
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// 子结点数量 = 0 or 1
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if (cur.left == null || cur.right == null) {
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// 当子结点数量 = 0 / 1 时， child = null / 该子结点
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TreeNode child = cur.left != null ? cur.left : cur.right;
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// 删除结点 cur
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if (pre.left == cur) pre.left = child;
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else pre.right = child;
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}
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// 子结点数量 = 2
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else {
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// 获取中序遍历中 cur 的下一个结点
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TreeNode nex = min(cur.right);
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int tmp = nex.val;
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// 递归删除结点 nex
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remove(nex.val);
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// 将 nex 的值复制给 cur
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cur.val = tmp;
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}
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return cur;
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}
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/* 获取最小结点 */
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public TreeNode min(TreeNode root) {
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if (root == null) return root;
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// 循环访问左子结点，直到叶结点时为最小结点，跳出
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while (root.left != null) {
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root = root.left;
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}
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return root;
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}
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}
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public class binary_search_tree {
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public static void main(String[] args) {
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/* 初始化二叉搜索树 */
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int[] nums = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 };
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BinarySearchTree bst = new BinarySearchTree(nums);
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System.out.println("\n初始化的二叉树为\n");
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PrintUtil.printTree(bst.getRoot());
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/* 查找结点 */
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TreeNode node = bst.search(5);
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System.out.println("\n查找到的结点对象为 " + node + "，结点值 = " + node.val);
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/* 插入结点 */
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node = bst.insert(16);
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System.out.println("\n插入结点 16 后，二叉树为\n");
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PrintUtil.printTree(bst.getRoot());
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/* 删除结点 */
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bst.remove(1);
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System.out.println("\n删除结点 1 后，二叉树为\n");
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PrintUtil.printTree(bst.getRoot());
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bst.remove(2);
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System.out.println("\n删除结点 2 后，二叉树为\n");
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PrintUtil.printTree(bst.getRoot());
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bst.remove(4);
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System.out.println("\n删除结点 4 后，二叉树为\n");
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PrintUtil.printTree(bst.getRoot());
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}
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}
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