leetcode437

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     public int val;
 *     public TreeNode left;
 *     public TreeNode right;
 *     public TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public int PathSum(TreeNode root, int sum)
        {
            if (root == null)
            {
                return 0;
            }
            return PathSumFrom(root, sum) + PathSum(root.left, sum) + PathSum(root.right, sum);
        }

        private int PathSumFrom(TreeNode node, int sum)
        {
            if (node == null)
            {
                return 0;
            }
            return (node.val == sum ? 1 : 0)
                + PathSumFrom(node.left, sum - node.val) + PathSumFrom(node.right, sum - node.val);
        }
}

 https://leetcode.com/problems/path-sum-iii/#/description

补充一个python实现，使用递归：

class Solution:
    def pathSum(self, root: 'TreeNode', sum: 'int') -> 'int':
        if root == None:
            return 0
        return self.pathSumWithRoot(root,sum) + self.pathSum(root.left,sum) + self.pathSum(root.right,sum)
        
    def pathSumWithRoot(self,root,sum):
        if root == None:
            return 0
        ret = 0
        if root.val == sum:
            ret += 1
        ret += self.pathSumWithRoot(root.left,sum-root.val) + self.pathSumWithRoot(root.right,sum-root.val)
        return ret

这种实现的时间复杂度是O(n^2)，执行效率比较低。

再补充一个更高效的实现，使用hash表进行缓存：（如果必须符合这个时间复杂度的要求O(n)，就可以当作hard级别的题目了）

class Solution(object):
    def pathSum(self, root, target):
        # define global result and path
        self.result = 0
        cache = {0:1}
        
        # recursive to get result
        self.dfs(root, target, 0, cache)
        
        # return result
        return self.result
    
    def dfs(self, root, target, currPathSum, cache):
        # exit condition
        if root is None:
            return  
        # calculate currPathSum and required oldPathSum
        currPathSum += root.val
        oldPathSum = currPathSum - target
        # update result and cache
        self.result += cache.get(oldPathSum, 0)
        cache[currPathSum] = cache.get(currPathSum, 0) + 1
        
        # dfs breakdown
        self.dfs(root.left, target, currPathSum, cache)
        self.dfs(root.right, target, currPathSum, cache)
        # when move to a different branch, the currPathSum is no longer available, hence remove one. 
        cache[currPathSum] -= 1