Generating N-bit Grey Code starting from K

Given a value N and K, the task is to generate N-bits Gray Code starting from the value K.

Examples:

Input: N = 2, K = 3
Output: 3 2 0 1
Explanation:
3 -> 11
2 -> 10
0 -> 00
1 -> 01
Each value differ by only one bit from the next value in their binary representation.

Input: N = 3, K = 2
Output: 2 3 1 0 4 5 7 6

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

• Gray code are numbers with hamming distance 1 between two consecutive numbers in it.
• The XOR with each element of N bit Gray code generates a sequence of Hamming distance of 1.
• As the first element of N bit Gray code is K, it can be obtained by doing is XOR with 0, i.e. (K ^ 0) = K.
• So the sequence will start with 0 with every consecutive element differ by only one bit in their binary representation.

Below is the implementation of the above approach:

C++

 `// C++ program Generating N-bit ` `// Gray Code starting from K ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Function to Generating N-bit ` `// Gray Code starting from K ` `void` `genSequence(``int` `n, ``int` `val) ` `{ ` ` `  `    ``for` `(``int` `i = 0; i < (1 << n); i++) { ` ` `  `        ``// Generate gray code of corresponding ` `        ``// binary number of integer i. ` `        ``int` `x = i ^ (i >> 1) ^ val; ` `        ``cout << x << ``" "``; ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 3, k = 2; ` `    ``genSequence(n, k); ` ` `  `    ``return` `0; ` `} `

Java

 `// Java program Generating N-bit  ` `// Gray Code starting from K  ` ` `  `class` `GFG { ` `     `  `    ``// Function to Generating N-bit  ` `    ``// Gray Code starting from K  ` `    ``static` `void` `genSequence(``int` `n, ``int` `val)  ` `    ``{  ` `     `  `        ``for` `(``int` `i = ``0``; i < (``1` `<< n); i++) {  ` `     `  `            ``// Generate gray code of corresponding  ` `            ``// binary number of integer i.  ` `            ``int` `x = i ^ (i >> ``1``) ^ val;  ` `            ``System.out.print(x + ``" "``);  ` `        ``}  ` `    ``}  ` `     `  `    ``// Driver code  ` `    ``public` `static` `void` `main (String[] args) ` `    ``{  ` `        ``int` `n = ``3``, k = ``2``;  ` `        ``genSequence(n, k);  ` `     `  `    ``}  ` `} ` ` `  `// This code is contributed by AnkitRai01 `

Python3

 `# Python3 program Generating N-bit  ` `# Gray Code starting from K  ` ` `  `# Function to Generating N-bit  ` `# Gray Code starting from K  ` `def` `genSequence(n, val) : ` ` `  `    ``for` `i ``in` `range``(``1` `<< n) : ` ` `  `        ``# Generate gray code of corresponding  ` `        ``# binary number of integer i.  ` `        ``x ``=` `i ^ (i >> ``1``) ^ val;  ` `        ``print``(x, end``=` `" "``);  ` ` `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"` `:  ` ` `  `    ``n ``=` `3``; k ``=` `2``;  ` `    ``genSequence(n, k);  ` ` `  `# This code is contributed by AnkitRai01 `

C#

 `// C# program Generating N-bit  ` `// Gray Code starting from K  ` `using` `System; ` ` `  `class` `GFG  ` `{ ` `     `  `    ``// Function to Generating N-bit  ` `    ``// Gray Code starting from K  ` `    ``static` `void` `genSequence(``int` `n, ``int` `val)  ` `    ``{  ` `     `  `        ``for` `(``int` `i = 0; i < (1 << n); i++) ` `        ``{  ` `     `  `            ``// Generate gray code of corresponding  ` `            ``// binary number of integer i.  ` `            ``int` `x = i ^ (i >> 1) ^ val;  ` `            ``Console.Write(x + ``" "``);  ` `        ``}  ` `    ``}  ` `     `  `    ``// Driver code  ` `    ``public` `static` `void` `Main() ` `    ``{  ` `        ``int` `n = 3, k = 2;  ` `        ``genSequence(n, k);  ` `     `  `    ``}  ` `} ` ` `  `// This code is contributed by AnkitRai01 `

Output:

```2 3 1 0 4 5 7 6
```

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