[LeetCode] 129. Sum Root to Leaf Numbers 求根到叶节点数字之和
Given a binary tree containing digits from 0-9 only, each root-to-leaf path could represent a number.
An example is the root-to-leaf path 1->2->3 which represents the number 123.
Find the total sum of all root-to-leaf numbers.
Note: A leaf is a node with no children.
Example:
Input: [1,2,3]1/ \2 3Output: 25Explanation:The root-to-leaf path
1->2
represents the number
12
.The root-to-leaf path
1->3
represents the number
13
.Therefore, sum = 12 + 13 =
25
.
Example 2:
Input: [4,9,0,5,1]4/ \9 0/ \5 1Output: 1026Explanation:The root-to-leaf path
4->9->5
represents the number 495.The root-to-leaf path
4->9->1
represents the number 491.The root-to-leaf path
4->0
represents the number 40.Therefore, sum = 495 + 491 + 40 =
1026
.
这道求根到叶节点数字之和的题跟之前的求 Path Sum 很类似，都是利用DFS递归来解，这道题由于不是单纯的把各个节点的数字相加，而是每遇到一个新的子结点的数字，要把父结点的数字扩大10倍之后再相加。如果遍历到叶结点了，就将当前的累加结果sum返回。如果不是，则对其左右子结点分别调用递归函数，将两个结果相加返回即可，参见代码如下：
解法一：
class Solution {public: int sumNumbers(TreeNode* root) { return sumNumbersDFS(root, 0); } int sumNumbersDFS(TreeNode* root, int sum) { if (!root) return 0; sum = sum * 10 + root->val; if (!root->left && !root->right) return sum; return sumNumbersDFS(root->left, sum) + sumNumbersDFS(root->right, sum); }};
我们也可以采用迭代的写法，这里用的是先序遍历的迭代写法，使用栈来辅助遍历，首先将根结点压入栈，然后进行while循环，取出栈顶元素，如果是叶结点，那么将其值加入结果res。如果其右子结点存在，那么其结点值加上当前结点值的10倍，再将右子结点压入栈。同理，若左子结点存在，那么其结点值加上当前结点值的10倍，再将左子结点压入栈，是不是跟之前的 Path Sum 极其类似呢，参见代码如下：
解法二：
class Solution {public: int sumNumbers(TreeNode* root) { if (!root) return 0; int res = 0; stack<TreeNode*> st{{root}}; while (!st.empty()) { TreeNode *t = st.top(); st.pop(); if (!t->left && !t->right) { res += t->val; } if (t->right) { t->right->val += t->val * 10; st.push(t->right); } if (t->left) { t->left->val += t->val * 10; st.push(t->left); } } return res; }};
Github 同步地址：
https://github.com/grandyang/leetcode/issues/129
类似题目：
Path Sum
Binary Tree Maximum Path Sum
参考资料：
https://leetcode.com/problems/sum-root-to-leaf-numbers/
https://leetcode.com/problems/sum-root-to-leaf-numbers/discuss/41367/Non-recursive-preorder-traverse-Java-solution
https://leetcode.com/problems/sum-root-to-leaf-numbers/discuss/41452/Iterative-C%2B%2B-solution-using-stack-(similar-to-postorder-traversal)
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