LeetCode 222 Count Complete Tree Nodes

题目描述

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.

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分析

如果层序遍历，时间复杂度是O(n)。可以使用类似二分查找的方法，因为二叉树是完全二叉树，计算leftHeight和rightHeight，最大相差1，然后递归求解。

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代码

    public int countNodes(TreeNode root) {        if (root == null) {            return 0;        }        int leftHeight = 0;        int rightHeight = 0;        // 计算leftHeight        TreeNode p = root;        while (p != null) {            p = p.left;            leftHeight++;        }        // 计算rightHeight        p = root;        while (p != null) {            p = p.right;            rightHeight++;        }        // 如果相等，满足2^n-1        if (leftHeight == rightHeight) {            return (1 << leftHeight) - 1;        }        return 1 + countNodes(root.left) + countNodes(root.right);    }