leetcode543. Diameter of Binary Tree

题目要求

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.

二叉树的直径是指从一个叶节点到另一个叶节点的最远距离，而这个距离是指两个节点之间的路径长，注意，这条路径不一定经过根节点。

思路和代码

这里可以通过递归来完成计算，通过先递归的计算出左子树的最大高度，再递归的计算出右子树的最大高度，就可以得出当前节点可以构成的最长路径。需要将该值记录下来。再递归的返回该节点的最大高度给外层调用方运用。

int max = 0;  
public int diameterOfBinaryTree(TreeNode root) {  
    heightOfBinaryTree(root);  
    return max;  
}  
  
public int heightOfBinaryTree(TreeNode root) {  
    if (root == null) {  
        return 0;  
    }  
    int left = heightOfBinaryTree(root.left);  
    int right = heightOfBinaryTree(root.right);  
    max = Math.max(left + right + 1, max);  
    return Math.max(left, right) + 1;  
}