leetcode 222: Count Complete Tree Nodes
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Count Complete Tree Nodes
Total Accepted: 93 Total Submissions: 678Given 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; }}
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