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Formatted question description: https://leetcode.ca/all/1238.html

# 1238. Circular Permutation in Binary Representation (Medium)

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

Related Topics:
Math

## Solution 1. Gray Code

// OJ: https://leetcode.com/problems/circular-permutation-in-binary-representation/
// Time: O(2^N)
// Space: O(1)
// Ref: https://leetcode.com/problems/circular-permutation-in-binary-representation/discuss/414203/JavaC%2B%2BPython-4-line-Gray-Code
class Solution {
public:
vector<int> circularPermutation(int n, int start) {
vector<int> ans;
for (int i = 0; i < (1 << n); ++i) ans.push_back(start ^ i ^ (i >> 1));
return ans;
}
};

• class Solution {
public List<Integer> circularPermutation(int n, int start) {
List<Integer> grayCodeList = new ArrayList<Integer>();
for (int i = 2; i <= n; i++) {
int power2 = (int) Math.pow(2, i - 1);
int size = grayCodeList.size();
for (int j = size - 1; j >= 0; j--) {
int prevNum = grayCodeList.get(j);
int curNum = prevNum + power2;
}
}
List<Integer> permutation = new ArrayList<Integer>();
int index = grayCodeList.indexOf(start);
int size = grayCodeList.size();
for (int i = 0; i < size; i++) {
index = (index + 1) % size;
}
return permutation;
}
}

############

class Solution {
public List<Integer> circularPermutation(int n, int start) {
List<Integer> ans = new ArrayList<>();
for (int i = 0; i < 1 << n; ++i) {
ans.add(i ^ (i >> 1) ^ start);
}
return ans;
}
}

• // OJ: https://leetcode.com/problems/circular-permutation-in-binary-representation/
// Time: O(2^N)
// Space: O(1)
// Ref: https://leetcode.com/problems/circular-permutation-in-binary-representation/discuss/414203/JavaC%2B%2BPython-4-line-Gray-Code
class Solution {
public:
vector<int> circularPermutation(int n, int start) {
vector<int> ans;
for (int i = 0; i < (1 << n); ++i) ans.push_back(start ^ i ^ (i >> 1));
return ans;
}
};

• # 1238. Circular Permutation in Binary Representation
# https://leetcode.com/problems/circular-permutation-in-binary-representation/

class Solution:
def circularPermutation(self, n: int, start: int) -> List[int]:
return [start ^ i ^ i>>1 for i in range(1 << n)]


• func circularPermutation(n int, start int) (ans []int) {
for i := 0; i < 1<<n; i++ {
ans = append(ans, i^(i>>1)^start)
}
return
}

• function circularPermutation(n: number, start: number): number[] {
const ans: number[] = [];
for (let i = 0; i < 1 << n; ++i) {
ans.push(i ^ (i >> 1) ^ start);
}
return ans;
}