LeetCode 1238: Circular Permutation in Binary Representation Solution

Master LeetCode problem 1238 (Circular Permutation in Binary Representation), a medium challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

1238. Circular Permutation in Binary Representation

Medium

Math Backtracking Bit Manipulation

Problem Explanation

Explanation

To solve this problem, we can use Gray code which is a binary numeral system where two successive values differ in only one bit. We can generate the Gray code sequence by using a specific formula. The key idea is to convert the given integer start into a Gray code and then generate the Gray code sequence based on the value of n. We can achieve this by XORing the Gray code with each number in the sequence from 0 to 2^n - 1.

Convert start to Gray code.
Generate the Gray code sequence from 0 to 2^n - 1.
XOR each element in the sequence with the Gray code of start to get the final circular permutation.

Time complexity: O(2^n)
Space complexity: O(2^n)

Solution Code

import java.util.*;

class Solution {
    public List<Integer> circularPermutation(int n, int start) {
        List<Integer> result = new ArrayList<>();
        
        // Convert start to Gray code
        int grayCodeStart = start ^ (start >> 1);
        
        // Generate Gray code sequence
        for (int i = 0; i < (1 << n); i++) {
            result.add(i ^ (i >> 1) ^ grayCodeStart);
        }
        
        return result;
    }
}

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