K-th Symbol in Grammar——LeetCode进阶路

原题链接https://leetcode.com/problems/k-th-symbol-in-grammar/

题目描述

On the first row, we write a 0. Now in every subsequent row, we look at the previous row and replace each occurrence of 0 with 01, and each occurrence of 1 with 10.

Given row N and index K, return the K-th indexed symbol in row N. (The values of K are 1-indexed.) (1 indexed).

Examples:
Input: N = 1, K = 1
Output: 0

Input: N = 2, K = 1
Output: 0

Input: N = 2, K = 2
Output: 1

Input: N = 4, K = 5
Output: 1

Explanation:
row 1: 0
row 2: 01
row 3: 0110
row 4: 01101001
Note:

N will be an integer in the range [1, 30].
K will be an integer in the range [1, 2^(N-1)].

思路分析

第一行给定为0，之后行依照把0换为01,1换为10的规律

• 利用大一数据结构学的二叉树，可把规律理解为0的左右子树分别为0和1，1的子树分别为1和0
• all in all，
  • 判断所求的节点是左子节点还是右子节点
  • 判断他的父节点是0还是1
    //这是一道爆炸友善的题哇ヾ(✿ﾟ▽ﾟ)ノ

AC解

class Solution {
    public int kthGrammar(int N, int K) {
        if(K == 1)
        {
            return 0;
        }
        if(N == 1)
        {
            return 0;
        }

        if(K % 2 == 0)
        {
            return kthGrammar(N-1,K/2)==0 ? 1 : 0;
        }
        else
        {
            return kthGrammar(N-1,(K+1)/2)==0 ? 0 : 1;
        }
    }
}