222. Count Complete Tree Nodes

Description

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 2^h nodes inclusive at the last level h.

Solution

Recursive

注意一定要仔细理解complete tree。对于每层来说，要么是满的，要么是连续的。

从root开始，分别沿着最左边和最右边计算高度，如果高度相同，则证明树是完全填满的，node数量直接根据height计算出；若高度不同，则递归调用。

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public int countNodes(TreeNode root) {
        if (root == null) {
            return 0;
        }
        
        int leftHeight = height(root, true);
        if (height(root, false) == leftHeight) {
            // must use bit manipulation, otherwise it will TLE
            return (1 << leftHeight) - 1;   
        }
        
        return 1 + countNodes(root.left) + countNodes(root.right);
    }
    
    public int height(TreeNode root, boolean isLeft) {
        int height = 0;
        
        while (root != null) {
            ++height;
            root = isLeft ? root.left : root.right;
        }
        
        return height;
    }
}