543. Diameter of Binary Tree

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.

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这一题要我们求一棵树里面的最长路径。采用分治算法会使这题变得很容易解决。

一条最长路径，必定是由一个根的左子树和右子树来构成。只要我们计算出左子树最大深度max_left和右子树最大深度max_right，那么它们的和就是以这个根为中心的最长路径。我们可以定义一个整数max = 0，如果在某个根上，有 max_left + max_right > max，则更新max。每次递归返回该根的最大深度并加1 return  max(max_right, max_left) + 1

代码如下：

/**
 * 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 m = 0;   //最大值
    int find_max(TreeNode* root){
        if (root == NULL) return NULL;
        int left = find_max(root -> left);
        int right = find_max(root -> right);
        if (left + right > m)
            m = left + right;
        return max(left, right)+1;
    }
    
    int diameterOfBinaryTree(TreeNode* root) {
        find_max(root);
        return m;
    }
    
};