543. Diameter of Binary Tree 二叉树的直径

543. Diameter of Binary Tree

问题描述

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.

解题思路

  • 二叉树的直径:二叉树中从一个结点到另一个节点最长的路径,叫做二叉树的直径
  • 采用分治和递归的思想:根节点为root的二叉树的直径 = max(root-left的直径,root->right的直径,root->left的最大深度+root->right的最大深度+1)

代码

// 求二叉树的直径
int diameterOfBinaryTree(TreeNode* root) 
{
    if(root == nullptr)
        return 0;
    int d_l=diameterOfBinaryTree(root->left);
    int d_r = diameterOfBinaryTree(root->right);
    int height_l=getHeight(root->left);
    int height_r=getHeight(root->right);

    int tmp1=d_l > d_r ? d_l :d_r;
    int tmp2=height_l+height_r+1;
    return tmp1>tmp2 ? tmp1 :tmp2; 
}
// 获得二叉树的最大深度
int Solution::getHeight(TreeNode* root)
{
    if(root == nullptr)
        return 0;
    int h_l=getHeight(root->left);
    int h_r=getHeight(root->right);
    return ((h_l > h_r) ? h_l :h_r)+1;
}

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