One, Title Description
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.
Second, the problem solution
Method One: Reflections
Precautions: The maximum diameter possible without root, so you can only use variable max to record the maximum diameter of each node as the root.
- Recurrence equation: maximum height and the maximum diameter = root node to each of the left and right subtrees.
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;
}
Complexity Analysis
- time complexity: ,
- Space complexity: ,