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Find Kth Bit in Nth Binary String

程序员文章站 2022-05-18 20:30:21
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Given two positive integers n and k, the binary string  Sn is formed as follows:

  • S1 = "0"
  • Si = Si-1 + "1" + reverse(invert(Si-1)) for i > 1

Where + denotes the concatenation operation, reverse(x) returns the reversed string x, and invert(x) inverts all the bits in x (0 changes to 1 and 1 changes to 0).

For example, the first 4 strings in the above sequence are:

  • S1 = "0"
  • S2 = "011"
  • S3 = "0111001"
  • S4 = "011100110110001"

Return the kth bit in Sn. It is guaranteed that k is valid for the given n.

Example 1:

Input: n = 3, k = 1
Output: "0"
Explanation: S3 is "0111001". The first bit is "0".

Example 2:

Input: n = 4, k = 11
Output: "1"
Explanation: S4 is "011100110110001". The 11th bit is "1".

思路:这题就是递归,就是明白这一层的答案由上一层推倒得来,注意index的计算,是用数学公式推出来的,1234567, 顺数第三个是反着数第5个, 7 - 3 + 1;

class Solution {
    public char findKthBit(int n, int k) {
        if(n == 1) {
            return '0';
        }
        int length = len(n - 1);
        if(k <= length) {
            return findKthBit(n - 1, k);
        } else if( k == length + 1) {
            return '1';
        } else {
            // k > len(n - 1) + 1;
            return findKthBit(n - 1, length - (k - (length + 1)) + 1) == '0' ? '1' : '0';
        }
    }
    
    private int len(int n) {
        if(n == 1) {
            return 1;
        } else {
            return 2*len(n - 1) + 1;
        }
    }
}

 

相关标签: Recursion