LeetCode 543 Diameter of Binary Tree

題目：

Given a binary tree, you need to compute the length of the diameter of the tree. The diameter of a binary tree is the length of the longest path between any two nodes in a tree. This path may or may not pass through the root.

Example:
Given a binary tree 

          1
         / \
        2   3
       / \     
      4   5    

Return 3, which is the length of the path [4,2,1,3] or [5,2,1,3].

Note: The length of path between two nodes is represented by the number of edges between them.

題目鏈接

題意：

給一棵二叉樹，要求尋找其中最長的路徑，其中，路徑的定義是任意兩個節點之間的距離，，最長的路徑也可能不經過根節點。

通過觀察可以得出，對於一個父節點，兩個子節點都存在的節點而言，經過它的路徑有兩個方向可以選擇，假如從左子節點傳入，可從右子節點傳出尋找最大長度，也可能從父節點傳出尋找最大長度，假如只有一個子節點，那就只能選一條路。利用遍歷，從下層遞歸到上層，便可得到最大長度。

代碼如下：

class Solution {
public:
    int ans = 0;
    int dfs(TreeNode* node) {
        if (!node) return 0;
        int left = dfs(node->left);
        int right = dfs(node->right);
        ans = max(ans, left + right);
        return 1 + max(left, right);
    }
    int diameterOfBinaryTree(TreeNode* root) {
        dfs(root);
        return ans;
    }
};