---
# System prepended metadata

title: 98. Validate Binary Search Tree
tags: [depth-first search, binary search tree, leetcode, binary tree]

---

# 98. Validate Binary Search Tree

題目：<https://leetcode.com/problems/validate-binary-search-tree/>

解法：DFS，設定最小邊界 minBound 和最大邊界 maxBound，判斷目前節點的值 val，如果 minBound < val < maxBound，則左子樹所有節點的值必須介於(minBound, val)之間，右子樹所有節點的值必須介於(val, maxBound)之間。

Python3：

``` python 3
class TreeNode:
    def __init__(self, x):
        self.val = x
        self.left = None
        self.right = None

def listToTree(arr):
    nodes = [TreeNode(arr[0])]
    i = 0
    j = 1
    length = len(arr)
    while j < length:
        if arr[j] is not None:
            tmp = TreeNode(arr[j])
            nodes[i].left = tmp
            nodes.append(tmp)
        j += 1
        if j >= length:
            break
        if arr[j] is not None:
            tmp = TreeNode(arr[j])
            nodes[i].right = tmp
            nodes.append(tmp)
        j += 1
        i += 1
    return nodes[0]

def treeToList(root):
    from collections import deque
    nodes = deque()
    nodes.append(root)
    arr = []
    arr.append(root.val)
    while len(nodes):
        node = nodes.popleft()
        if node.left:
            nodes.append(node.left)
            arr.append(node.left.val)
        else:
            arr.append(None)
        if node.right:
            nodes.append(node.right)
            arr.append(node.right.val)
        else:
            arr.append(None)
    return arr

class Solution:
    def isValidBST(self, root: TreeNode) -> bool:
        def isValid(root, minBound, maxBound):
            if not root:
                return True
            if root.val > minBound and root.val < maxBound:
                return isValid(root.left, minBound, root.val) \
                    and isValid(root.right, root.val, maxBound)
            else:
                return False
        return isValid(root, -2**31-1, 2**31)

if __name__ == '__main__':
    arr = [5,4,6,None,None,3,7]
    root = listToTree(arr)
    print(treeToList(root))

    ans = Solution().isValidBST(root)
    print(ans)
```

C：

``` c
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>

struct TreeNode {
    int val;
    struct TreeNode *left;
    struct TreeNode *right;
};

struct TreeNode* strToTree(char *str) {
    char *token = strtok(str, ",");
    struct TreeNode **nodes = (struct TreeNode**)malloc(sizeof(struct TreeNode*));
    nodes[0] = (struct TreeNode*)malloc(sizeof(struct TreeNode));
    nodes[0]->val = atoi(token);
    nodes[0]->left = NULL;
    nodes[0]->right = NULL;
    int i = 0, len = 1;
    token = strtok(NULL, ",");
    while (token != NULL) {
        if (strcmp(token, "null") != 0) {
            len++;
            nodes = (struct TreeNode**)realloc(nodes, sizeof(struct TreeNode*) * len);
            nodes[len - 1] = (struct TreeNode*)malloc(sizeof(struct TreeNode));
            nodes[len - 1]->val = atoi(token);
            nodes[len - 1]->left = NULL;
            nodes[len - 1]->right = NULL;
            nodes[i]->left = nodes[len - 1];
        }
        token = strtok(NULL, ",");
        if (token == NULL)
            break;
        if (strcmp(token, "null") != 0) {
            len++;
            nodes = (struct TreeNode**)realloc(nodes, sizeof(struct TreeNode*) * len);
            nodes[len - 1] = (struct TreeNode*)malloc(sizeof(struct TreeNode));
            nodes[len - 1]->val = atoi(token);
            nodes[len - 1]->left = NULL;
            nodes[len - 1]->right = NULL;
            nodes[i]->right = nodes[len - 1];
        }
        token = strtok(NULL, ",");
        i++;
    }
    return nodes[0];
}

void printLevelOrderWithNull(struct TreeNode* root) {
    struct TreeNode * bfs[10000] = {};
    bfs[0] = root;
    int i = 0, len = 1;
    printf("%d ", root->val);
    while (i < len) {
        if (bfs[i]->left != NULL) {
            bfs[len++] = bfs[i]->left;
            printf("%d ", bfs[i]->left->val);
        } else
            printf("null ");
        if (bfs[i]->right != NULL) {
            bfs[len++] = bfs[i]->right;
            printf("%d ", bfs[i]->right->val);
        } else
            printf("null ");
        i++;
    }
    printf("\n");
}

bool isValidBST(struct TreeNode* root){
    bool isValid(struct TreeNode* root, long long int minBound, long long int maxBound) {
        if (root == NULL)
            return true;
        if (root->val > minBound && root->val < maxBound)
            return isValid(root->left, minBound, root->val) && isValid(root->right, root->val, maxBound);
        else
            return false;
    }
    return isValid(root, LLONG_MIN, LLONG_MAX);
}

int main()
{
    char input[] = "5,4,6,null,null,3,7";
    struct TreeNode* root = strToTree(input);
    printLevelOrderWithNull(root);
    printf("\n");
    
    bool ans = isValidBST(root);
    printf("%s\n", ans ? "True": "False");
    return 0;
}
```

###### tags: `leetcode` `binary tree` `binary search tree` `depth-first search`
