【二叉查找树】03验证是否为二叉查找树【Validate Binary Search Tree】
本质上是递归遍历左右后在与根节点做判断,本质上是后序遍历
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给你一个二叉树,判断他是否是个有效的二叉查找树(BST)。
假定一个BST树按照下面的内容定义:
- 左子树的节点的值都小于父节点。
- 右子树的节点的值都大于父节点。
- 左子树和右子树都得是合法的而二叉查找树。
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Given a binary tree, determine if it is a valid binary search tree (BST).
Assume a BST is defined as follows:
- The left subtree of a node contains only nodes with keys less than the node's key.
- The right subtree of a node contains only nodes with keys greater than the node's key.
- Both the left and right subtrees must also be binary search trees.
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test.cpp:
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#include <iostream>
#include <cstdio> #include <stack> #include <vector> #include "BinaryTree.h" using namespace std; /** * Definition for binary tree * struct TreeNode { * int val; * TreeNode *left; * TreeNode *right; * TreeNode(int x) : val(x), left(NULL), right(NULL) {} * }; */ bool islessthanroot(TreeNode *left, int val) { if(left == NULL) { return true; } if(left->val >= val) { return false; } return islessthanroot(left->left, val) && islessthanroot(left->right, val); } bool islargethanroot(TreeNode *right, int val) { if(right == NULL) { return true; } if(right->val <= val) { return false; } return islargethanroot(right->left, val) && islargethanroot(right->right, val); } bool isValidBST(TreeNode *root) { if(root == NULL) { return true; } if(islessthanroot(root->left, root->val) && islargethanroot(root->right, root->val)) { return isValidBST(root->left) && isValidBST(root->right); } else { return false; } } // 树中结点含有分叉, // 6 // / \ // 2 7 // / \ // 1 4 // / \ // 3 5 int main() { TreeNode *pNodeA1 = CreateBinaryTreeNode(6); TreeNode *pNodeA2 = CreateBinaryTreeNode(2); TreeNode *pNodeA3 = CreateBinaryTreeNode(7); TreeNode *pNodeA4 = CreateBinaryTreeNode(1); TreeNode *pNodeA5 = CreateBinaryTreeNode(4); TreeNode *pNodeA6 = CreateBinaryTreeNode(3); TreeNode *pNodeA7 = CreateBinaryTreeNode(5); ConnectTreeNodes(pNodeA1, pNodeA2, pNodeA3); ConnectTreeNodes(pNodeA2, pNodeA4, pNodeA5); ConnectTreeNodes(pNodeA5, pNodeA6, pNodeA7); bool ans = isValidBST(pNodeA1); if (ans == true) { cout << "Valid BST" << endl; } else { cout << "Not Valid BST" << endl; } DestroyTree(pNodeA1); return 0; } |
结果输出:
Valid BST
BinaryTree.h:
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#ifndef _BINARY_TREE_H_
#define _BINARY_TREE_H_ struct TreeNode { int val; TreeNode *left; TreeNode *right; TreeNode(int x) : val(x), left(NULL), right(NULL) {} }; TreeNode *CreateBinaryTreeNode(int value); void ConnectTreeNodes(TreeNode *pParent, TreeNode *pLeft, TreeNode *pRight); void PrintTreeNode(TreeNode *pNode); void PrintTree(TreeNode *pRoot); void DestroyTree(TreeNode *pRoot); #endif /*_BINARY_TREE_H_*/ |
BinaryTree.cpp:
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#include <iostream>
#include <cstdio> #include "BinaryTree.h" using namespace std; /** * Definition for binary tree * struct TreeNode { * int val; * TreeNode *left; * TreeNode *right; * TreeNode(int x) : val(x), left(NULL), right(NULL) {} * }; */ //创建结点 TreeNode *CreateBinaryTreeNode(int value) { TreeNode *pNode = new TreeNode(value); return pNode; } //连接结点 void ConnectTreeNodes(TreeNode *pParent, TreeNode *pLeft, TreeNode *pRight) { if(pParent != NULL) { pParent->left = pLeft; pParent->right = pRight; } } //打印节点内容以及左右子结点内容 void PrintTreeNode(TreeNode *pNode) { if(pNode != NULL) { printf("value of this node is: %d\n", pNode->val); if(pNode->left != NULL) printf("value of its left child is: %d.\n", pNode->left->val); else printf("left child is null.\n"); if(pNode->right != NULL) printf("value of its right child is: %d.\n", pNode->right->val); else printf("right child is null.\n"); } else { printf("this node is null.\n"); } printf("\n"); } //前序遍历递归方法打印结点内容 void PrintTree(TreeNode *pRoot) { PrintTreeNode(pRoot); if(pRoot != NULL) { if(pRoot->left != NULL) PrintTree(pRoot->left); if(pRoot->right != NULL) PrintTree(pRoot->right); } } void DestroyTree(TreeNode *pRoot) { if(pRoot != NULL) { TreeNode *pLeft = pRoot->left; TreeNode *pRight = pRoot->right; delete pRoot; pRoot = NULL; DestroyTree(pLeft); DestroyTree(pRight); } } |