Initial commit

Practical-Teaching/Data-Sructure/Big/4/4.1.cpp

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+#include <iostream>
+#include <limits>
+
+using namespace std;
+
+struct TreeNode {
+	int val;
+	TreeNode *left;
+	TreeNode *right;
+	TreeNode(int x) : val(x), left(NULL), right(NULL) {}
+};
+
+// 插入节点
+TreeNode *insertNode(TreeNode *root, int val) {
+	if (root == NULL) {
+		return new TreeNode(val);
+	}
+	if (val < root->val) {
+		root->left = insertNode(root->left, val);
+	}
+	else if (val > root->val) {
+		root->right = insertNode(root->right, val);
+	}
+	return root;
+}
+
+// 删除节点
+TreeNode *deleteNode(TreeNode *root, int key) {
+	if (root == NULL)
+		return root;
+	if (key < root->val) {
+		root->left = deleteNode(root->left, key);
+	}
+	else if (key > root->val) {
+		root->right = deleteNode(root->right, key);
+	}
+	else {
+		if (root->left == NULL) {
+			TreeNode *temp = root->right;
+			delete root;
+			return temp;
+		}
+		else if (root->right == NULL) {
+			TreeNode *temp = root->left;
+			delete root;
+			return temp;
+		}
+		TreeNode *temp = root->right;
+		while (temp && temp->left != NULL)
+			temp = temp->left;
+		root->val = temp->val;
+		root->right = deleteNode(root->right, temp->val);
+	}
+	return root;
+}
+
+// 判断是否为二叉搜索树
+bool isValidBST(TreeNode *root, TreeNode *minNode = NULL, TreeNode *maxNode = NULL) {
+	if (root == NULL)
+		return true;
+	if (minNode != NULL && root->val <= minNode->val || maxNode != NULL && root->val >= maxNode->val) {
+		return false;
+	}
+	return isValidBST(root->left, minNode, root) && isValidBST(root->right, root, maxNode);
+}
+
+// 查找最大值和第二大值
+pair<int, int> findMaxAndSecondMax(TreeNode *root) {
+	int maxVal = numeric_limits<int>::min();
+	int secondMaxVal = numeric_limits<int>::min();
+	TreeNode *curr = root;
+	while (curr) {
+		if (curr->val > maxVal) {
+			secondMaxVal = maxVal;
+			maxVal = curr->val;
+		}
+		else if (curr->val > secondMaxVal && curr->val < maxVal) {
+			secondMaxVal = curr->val;
+		}
+		curr = curr->right;
+	}
+	return { maxVal, secondMaxVal };
+}
+
+// 主函数，用于测试以上所有功能
+int main() {
+	int n;
+	TreeNode *root = NULL;
+	cout << "Enter a number to insert: ";
+	while (true) {
+		int val;
+		cin >> val;
+		if (val == -1)
+			break;
+		root = insertNode(root, val);
+	}
+
+	cout << "Is valid BST: " << (isValidBST(root) ? "Yes" : "No") << endl;
+
+	auto maxAndSecondMax = findMaxAndSecondMax(root);
+	cout << "Max: " << maxAndSecondMax.first << ", Second Max: " << maxAndSecondMax.second << endl;
+
+	cout << "Enter a number to delete: ";
+	cin >> n;
+	root = deleteNode(root, n);
+	cout << "After deleting " << n << ", is valid BST: " << (isValidBST(root) ? "Yes" : "No") << endl;
+
+	return 0;
+}