05 August 2008
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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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.
要求求出一个二叉树的直径，所谓直径就是树中一个结点到另外一个结点距离最长，用边表示直径。树的做法就用递归，DFS检查所有结点为顶点的直径，选择一个最大的，在每次递归的层里面，将所有结点的左子树和右子树递归的结果选择一个较大值，进入递归的上一层。时间复杂度O(n)，空间复杂度 O(H)。
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/**
* Definition for a binary tree node.
* public class TreeNode {
* int val;
* TreeNode left;
* TreeNode right;
* TreeNode() {}
* TreeNode(int val) { this.val = val; }
* TreeNode(int val, TreeNode left, TreeNode right) {
* this.val = val;
* this.left = left;
* this.right = right;
* }
* }
*/
class Solution {
private int diameter;
public int diameterOfBinaryTree(TreeNode root) {
diameter = 0;
dfs(root);
return diameter;
}
private int dfs(TreeNode node) {
if (node == null) {
return 0;
}
int leftHeight = dfs(node.left);
int rightHeight = dfs(node.right);
diameter = Math.max(diameter, leftHeight + rightHeight);
return Math.max(leftHeight, rightHeight) + 1;
}
}