Skip to content

1238. Circular Permutation in Binary Representation

Difficulty Topics

Description

Given 2 integers n and start. Your task is return any permutation p of (0,1,2.....,2^n -1) such that :

  • p[0] = start
  • p[i] and p[i+1] differ by only one bit in their binary representation.
  • p[0] and p[2^n -1] must also differ by only one bit in their binary representation.

 

Example 1:

Input: n = 2, start = 3
Output: [3,2,0,1]
Explanation: The binary representation of the permutation is (11,10,00,01). 
All the adjacent element differ by one bit. Another valid permutation is [3,1,0,2]

Example 2:

Input: n = 3, start = 2
Output: [2,6,7,5,4,0,1,3]
Explanation: The binary representation of the permutation is (010,110,111,101,100,000,001,011).

 

Constraints:

  • 1 <= n <= 16
  • 0 <= start < 2 ^ n

Solution

circular-permutation-in-binary-representation.py
class Solution:
    def circularPermutation(self, n: int, start: int) -> List[int]:
        res = []

        for i in range(1 << n):
            res.append(i ^ i >> 1)

        i = res.index(start)
        return res[i:] + res[:i]