# 938. Range Sum of BST

## Description

Given the root node of a binary search tree and two integers low and high, return the sum of values of all nodes with a value in the inclusive range [low, high].

Example 1:

Input: root = [10,5,15,3,7,null,18], low = 7, high = 15
Output: 32
Explanation: Nodes 7, 10, and 15 are in the range [7, 15]. 7 + 10 + 15 = 32.


Example 2:

Input: root = [10,5,15,3,7,13,18,1,null,6], low = 6, high = 10
Output: 23
Explanation: Nodes 6, 7, and 10 are in the range [6, 10]. 6 + 7 + 10 = 23.


Constraints:

• The number of nodes in the tree is in the range [1, 2 * 104].
• 1 <= Node.val <= 105
• 1 <= low <= high <= 105
• All Node.val are unique.

## Solutions

• /**
* Definition for a binary tree node.
* public class TreeNode {
*     int val;
*     TreeNode left;
*     TreeNode right;
*     TreeNode() {}
*     TreeNode(int val) { this.val = val; }
*     TreeNode(int val, TreeNode left, TreeNode right) {
*         this.val = val;
*         this.left = left;
*         this.right = right;
*     }
* }
*/
class Solution {
public int rangeSumBST(TreeNode root, int low, int high) {
if (root == null) {
return 0;
}
if (low <= root.val && root.val <= high) {
return root.val + rangeSumBST(root.left, low, high)
+ rangeSumBST(root.right, low, high);
} else if (root.val < low) {
return rangeSumBST(root.right, low, high);
} else {
return rangeSumBST(root.left, low, high);
}
}
}

• /**
* Definition for a binary tree node.
* struct TreeNode {
*     int val;
*     TreeNode *left;
*     TreeNode *right;
*     TreeNode() : val(0), left(nullptr), right(nullptr) {}
*     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
*     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
* };
*/
class Solution {
public:
int rangeSumBST(TreeNode* root, int low, int high) {
if (root == nullptr) return 0;
if (low <= root->val && root->val <= high) {
return root->val + rangeSumBST(root->left, low, high) + rangeSumBST(root->right, low, high);
} else if (root->val < low) {
return rangeSumBST(root->right, low, high);
} else {
return rangeSumBST(root->left, low, high);
}
}
};

• # Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
def rangeSumBST(self, root: TreeNode, low: int, high: int) -> int:
def search(node):
if not node:
return
if low <= node.val <= high:
self.ans += node.val
search(node.left)
search(node.right)
elif node.val < low:
search(node.right)
elif node.val > high:
search(node.left)

self.ans = 0
search(root)
return self.ans


• /**
* Definition for a binary tree node.
* type TreeNode struct {
*     Val int
*     Left *TreeNode
*     Right *TreeNode
* }
*/
func rangeSumBST(root *TreeNode, low int, high int) int {
if root == nil {
return 0
}
if low <= root.Val && root.Val <= high {
return root.Val + rangeSumBST(root.Left, low, high) + rangeSumBST(root.Right, low, high)
} else if root.Val < low {
return rangeSumBST(root.Right, low, high)
} else {
return rangeSumBST(root.Left, low, high)
}
}

• /**
* Definition for a binary tree node.
* class TreeNode {
*     val: number
*     left: TreeNode | null
*     right: TreeNode | null
*     constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {
*         this.val = (val===undefined ? 0 : val)
*         this.left = (left===undefined ? null : left)
*         this.right = (right===undefined ? null : right)
*     }
* }
*/

function rangeSumBST(root: TreeNode | null, low: number, high: number): number {
const dfs = (root: TreeNode | null): number => {
if (!root) {
return 0;
}
const { val, left, right } = root;
let ans = low <= val && val <= high ? val : 0;
if (val > low) {
ans += dfs(left);
}
if (val < high) {
ans += dfs(right);
}
return ans;
};
return dfs(root);
}


• /**
* Definition for a binary tree node.
* public class TreeNode {
*     public int val;
*     public TreeNode left;
*     public TreeNode right;
*     public TreeNode(int val=0, TreeNode left=null, TreeNode right=null) {
*         this.val = val;
*         this.left = left;
*         this.right = right;
*     }
* }
*/
public class Solution {
public int RangeSumBST(TreeNode root, int low, int high) {
return dfs(root, low, high);
}

private int dfs(TreeNode root, int low, int high) {
if (root == null) {
return 0;
}
int x = root.val;
int ans = low <= x && x <= high ? x : 0;
if (x > low) {
ans += dfs(root.left, low, high);
}
if (x < high) {
ans += dfs(root.right, low, high);
}
return ans;
}
}