Leetcode437

Path Sum III:
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.

Solution:

#include 

using namespace std;


struct TreeNode {
    int val;
    TreeNode *left;
    TreeNode *right;
    TreeNode(int x) : val(x), left(NULL), right(NULL) {}
};

class Solution {
public:
    // 在以root为根结点的二叉树中，寻找和为sum的路径，返回这样的路径个数
    int pathSum(TreeNode* root, int sum) {

        if ( root == NULL )
            return 0;

        int res = findpath( root, sum );
        res += pathSum( root->left, sum);
        res += pathSum( root->right, sum);

        return res;

    }

private:
    // 在以node为根结点的二叉树中，寻找包含node的路径，和为sum
    // 返回这样的路径个数
    int findpath( TreeNode* root, int sum){

        if ( root == NULL )
            return 0;

        int res = 0;
        if ( root->val == sum )
            res += 1;

        res += findpath( root->left, sum - root->val );
        res += findpath( root->right, sum - root->val );

        return res;

    }

};

总结： 用了分类讨论的思想，将问题分为：包含根结点的路径和为sum，和不包含根结点的路径和为sum。