You are given a binary tree in which each node contains an integer value.
Find the number of paths that sum to a given value.
The path does not need to start or end at the root or a leaf, but it must go downwards (traveling only from parent nodes to child nodes).
The tree has no more than 1,000 nodes and the values are in the range -1,000,000 to 1,000,000.
Example:
root = [10,5,-3,3,2,null,11,3,-2,null,1], sum = 8
10
/ \
5 -3
/ \ \
3 2 11
/ \ \
3 -2 1
Return 3. The paths that sum to 8 are:
1. 5 -> 3
2. 5 -> 2 -> 1
3. -3 -> 11
// Brute Force
int helper(TreeNode* node, int sum) {
if (!node) return 0;
return (node->val == sum ? 1 : 0) + helper(node->left, sum - node->val) + helper(node->right, sum - node->val);
}
int pathSum(TreeNode* root, int sum) { // time: O(n^2); space: O(n)
if (!root) return 0;
return helper(root, sum) + pathSum(root->left, sum) + pathSum(root->right, sum);
}
// Use hashmap to avoid duplicate calculation
int helper(TreeNode* node, int sum, int curSum, unordered_map<int, int>& m) { // time: O(n); space: O(n)
if (!node) return 0;
curSum += node->val;
int res = m[curSum - sum];
++m[curSum];
res += helper(node->left, sum, curSum, m) + helper(node->right, sum, curSum, m);
--m[curSum];
return res;
}
int pathSum(TreeNode* root, int sum) {
unordered_map<int, int> m;
m[0] = 1;
return helper(root, sum, 0, m);
}