Diameter of Binary Tree

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问题描述（难度简单）

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

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2
3
4
5
    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.

方法一：深度优先搜索

分解为子问题，当前root节点左子树最大深度为left,右边子树最大深度为right,那么root的最大深度为Math.max(left,right)+1。当前root为根节点的最大树连接长度为left+right+2。

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package P543;

import P104.TreeNode;

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    private int max=0;
    public int diameterOfBinaryTree(TreeNode root){
        diameterOfBinaryTreeDigui(root);
        return max;
    }
    public int diameterOfBinaryTreeDigui(TreeNode root) {
        if (root==null) {
            return -1;
        }
        int left=diameterOfBinaryTreeDigui(root.left);
        int right=diameterOfBinaryTreeDigui(root.right);

        int result=left+right+2;
        if (result>max) {
            max=result;
        }
        return left>right?left+1:right+1;
    }

    public static void main(String[] args) {

    }
}