Count Complete Tree Nodes

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.

 

思路

计算根节点的左右子树的高度，如果高度相等则说明是满二叉树，节点数直接使用公式计算：2^h - 1；

否则，对左右孩子递归调用，即countNodes(left) + countNodes(right) + 1.

 

时间/空间复杂度

最好情况下为满二叉树，时间复杂度为O(h);

最坏情况下为O(n) （？）

 

程序

 

/**

 * 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 lh = getLeftHeight(root);

        int rh = getRightHeight(root);

        

        if (lh == rh) {

            return (1 << lh) - 1;

        }

        return countNodes(root.left) + countNodes(root.right) + 1;

    }

    

    private static int getLeftHeight(TreeNode root) {

        if (root == null) {

            return 0;

        }

        

        int count = 0;

        while (root != null) {

            ++count;

            root = root.left;

        }

        

        return count;

    }

    

    private static int getRightHeight(TreeNode root) {

        if (root == null) {

            return 0;

        }

        

        int count = 0;

        while (root != null) {

            ++count;

            root = root.right;

        }

        

        return count;

    }

}