一、题目描述
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.
二、题解
方法一:思考
注意点:最大直径可能不经过 root,所以你只能用变量 max 记录以每个结点为根的最大直径。
- 递推方程:最大直径 = 以每个结点为根的左右子树的高度和的最大值。
int max;
public int diameterOfBinaryTree(TreeNode root) {
dfs(root);
return max;
}
private int dfs(TreeNode root) {
if (root == null)
return 0;
int l = dfs(root.left);
int r = dfs(root.right);
max = Math.max(l+r, max);
return Math.max(l, r) + 1;
}
复杂度分析
- 时间复杂度: ,
- 空间复杂度: ,