155 lines
4.9 KiB
C++
155 lines
4.9 KiB
C++
/*
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* File: binary_search_tree.cpp
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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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#include "../include/include.hpp"
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/* 二叉搜索树 */
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class BinarySearchTree {
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private:
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TreeNode* root;
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public:
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BinarySearchTree(vector<int> nums) {
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sort(nums.begin(), nums.end()); // 排序数组
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root = buildTree(nums, 0, nums.size() - 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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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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TreeNode* buildTree(vector<int> nums, int i, int j) {
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if (i > j) return nullptr;
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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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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 != nullptr) {
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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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TreeNode* insert(int num) {
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// 若树为空，直接提前返回
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if (root == nullptr) return nullptr;
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TreeNode *cur = root, *pre = nullptr;
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// 循环查找，越过叶结点后跳出
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while (cur != nullptr) {
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// 找到重复结点，直接返回
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if (cur->val == num) return nullptr;
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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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TreeNode* remove(int num) {
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// 若树为空，直接提前返回
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if (root == nullptr) return nullptr;
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TreeNode *cur = root, *pre = nullptr;
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// 循环查找，越过叶结点后跳出
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while (cur != nullptr) {
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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 == nullptr) return nullptr;
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// 子结点数量 = 0 or 1
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if (cur->left == nullptr || cur->right == nullptr) {
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// 当子结点数量 = 0 / 1 时， child = nullptr / 该子结点
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TreeNode* child = cur->left != nullptr ? 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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TreeNode* min(TreeNode* root) {
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if (root == nullptr) 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 != nullptr) {
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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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/* Driver Code */
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int main() {
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/* 初始化二叉搜索树 */
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vector<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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cout << endl << "初始化的二叉树为\n" << endl;
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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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cout << endl << "查找到的结点对象为 " << node << "，结点值 = " << node->val << endl;
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/* 插入结点 */
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node = bst->insert(16);
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cout << endl << "插入结点 16 后，二叉树为\n" << endl;
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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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cout << endl << "删除结点 1 后，二叉树为\n" << endl;
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PrintUtil::printTree(bst->getRoot());
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bst->remove(2);
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cout << endl << "删除结点 2 后，二叉树为\n" << endl;
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PrintUtil::printTree(bst->getRoot());
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bst->remove(4);
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cout << endl << "删除结点 4 后，二叉树为\n" << endl;
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PrintUtil::printTree(bst->getRoot());
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return 0;
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}
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