leetcode 222: Count Complete Tree Nodes

Count Complete Tree Nodes

Total Accepted: 93
Total Submissions: 678

Given a complete binary tree, count the number of nodes.

Definition of a complete binary tree from
Wikipedia:

In a complete binary tree every level, except possibly the last, is completely filled, and all nodes in the last level are as far left as possible. It can have between 1 and 2h nodes inclusive at the last level h.

[思路]

用暴力法, recursive求会超时 O(N). 如果从某节点一直向左的高度 = 一直向右的高度, 那么以该节点为root的子树一定是complete binary tree. 而 complete binary tree的节点数,可以用公式算出 2^h - 1. 如果高度不相等, 则递归调用 return countNode(left) + countNode(right) + 1. 复杂度为O(h^2)

[CODE]

/**
* Definition for a binary tree node.
* public class TreeNode {
*     int val;
*     TreeNode left;
*     TreeNode right;
*     TreeNode(int x) { val = x; }
* }
*/
public class Solution {
public int countNodes(TreeNode root) {
if(root==null) return 0;

int l = getLeft(root) + 1;
int r = getRight(root) + 1;

if(l==r) {
return (2<<(l-1)) - 1;
} else {
return countNodes(root.left) + countNodes(root.right) + 1;
}
}

private int getLeft(TreeNode root) {
int count = 0;
while(root.left!=null) {
root = root.left;
++count;
}
return count;
}

private int getRight(TreeNode root) {
int count = 0;
while(root.right!=null) {
root = root.right;
++count;
}
return count;
}
}