437. Path Sum III

• Difficulty: Easy

• Topics: Tree

• Similar Questions:

  • Path Sum

  • Path Sum II

  • Path Sum IV

  • Longest Univalue Path

Problem:

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
 /  \
<b>5</b>   <b>-3</b>

/ \ \ 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 </pre> </p>

   Solutions:

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    int pathSum(TreeNode* root, int sum) {
        if (root == nullptr)    return 0;
        return helper(root, sum, 0) + pathSum(root->left, sum) + pathSum(root->right, sum);
    }

    int helper(TreeNode* root, int sum, int path) {
        if (root == nullptr)    return 0;
        int count = 0;
        count += ((sum == path + root->val) ? 1 : 0);       
        count += helper(root->left, sum, path + root->val);
        count += helper(root->right, sum, path + root->val);

        return count;
    }
};