Generate n-bit Gray Codes | Set 2

Given a number n, generate bit patterns from 0 to 2^n-1 such that successive patterns differ by one bit.

Examples:

Input : n=2
Output :00 01 11 10

Input :n=3
Output :000 001 011 010 110 111 101 100

Another approach of Generate n-bit Gray Codes has been already discussed.



Approach is to get gray code of binary number using XOR and Right shift operation.

  • The first bit(MSB) of the gray code is same as the first bit(MSB) of binary number.
  • The second bit(from left side) of the gray code equals to XOR of first bit(MSB) and second bit(2nd MSB) of the binary number.
  • The third bit(from left side) of the gray code equals to XOR of the second bit(2nd MSB) and third bit(3rd MSB) and so on..
  • In this way we can get the gray code of corresponding binary number. So, observation is that to get i’th bit gray code, we have to do XOR operation of i’th bit and previous i-1’th bit. So by doing right shift, i-1’th bit and i’th bit come at same position and the XOR result of i’th bit and i-1’th bit will be the i’th bit gray code.That’s the intuition behind right shift operation.

    C++

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    // C++ program to generate n-bit
    // gray codes
    #include <bits/stdc++.h>
    using namespace std;
      
    // Function to convert decimal to binary
    void decimalToBinaryNumber(int x, int n)
    {
        int* binaryNumber = new int(x);
        int i = 0;
        while (x > 0) {
            binaryNumber[i] = x % 2;
            x = x / 2;
            i++;
        }
      
        // leftmost digits are filled with 0
        for (int j = 0; j < n - i; j++)
            cout << '0';
      
        for (int j = i - 1; j >= 0; j--)
            cout << binaryNumber[j];
    }
      
    // Function to generate gray code
    void generateGrayarr(int n)
    {
        int N = 1 << n;
        for (int i = 0; i < N; i++) {
      
            // generate gray code of corresponding
            // binary number of integer i.
            int x = i ^ (i >> 1);
      
            // printing gray code
            decimalToBinaryNumber(x, n);
      
            cout << endl;
        }
    }
      
    // Drivers code
    int main()
    {
        int n = 3;
        generateGrayarr(n);
        return 0;
    }

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    Java

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    // Java program to generate 
    // n-bit gray codes
    import java.io.*;
      
    class GFG 
    {
      
    // Function to convert
    // decimal to binary
    static void decimalToBinaryNumber(int x, 
                                      int n)
    {
        int []binaryNumber = new int[x];
        int i = 0;
        while (x > 0)
        {
            binaryNumber[i] = x % 2;
            x = x / 2;
            i++;
        }
      
        // leftmost digits are
        // filled with 0
        for (int j = 0; j < n - i; j++)
            System.out.print('0');
      
        for (int j = i - 1
                 j >= 0; j--)
            System.out.print(binaryNumber[j]);
    }
      
    // Function to generate
    // gray code
    static void generateGrayarr(int n)
    {
        int N = 1 << n;
        for (int i = 0; i < N; i++) 
        {
      
            // generate gray code of 
            // corresponding binary 
            // number of integer i.
            int x = i ^ (i >> 1);
      
            // printing gray code
            decimalToBinaryNumber(x, n);
      
            System.out.println();
        }
    }
      
    // Driver code
    public static void main (String[] args) 
    {
        int n = 3;
        generateGrayarr(n);
    }
    }
      
    // This code is contributed
    // by anuj_67.

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    C#

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    // C# program to generate 
    // n-bit gray codes
    using System;
      
    class GFG 
    {
      
    // Function to convert
    // decimal to binary
    static void decimalToBinaryNumber(int x, 
                                      int n)
    {
        int []binaryNumber = new int[x];
        int i = 0;
        while (x > 0)
        {
            binaryNumber[i] = x % 2;
            x = x / 2;
            i++;
        }
      
        // leftmost digits are
        // filled with 0
        for (int j = 0; j < n - i; j++)
        Console.Write('0');
      
        for (int j = i - 1; 
                j >= 0; j--)
            Console.Write(binaryNumber[j]);
    }
      
    // Function to generate
    // gray code
    static void generateGrayarr(int n)
    {
        int N = 1 << n;
        for (int i = 0; i < N; i++) 
        {
      
            // generate gray code of 
            // corresponding binary 
            // number of integer i.
            int x = i ^ (i >> 1);
      
            // printing gray code
            decimalToBinaryNumber(x, n);
      
            Console.WriteLine();
        }
    }
      
    // Driver code
    public static void Main () 
    {
        int n = 3;
        generateGrayarr(n);
    }
    }
      
    // This code is contributed
    // by anuj_67.

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    Output:

    000
    001
    011
    010
    110
    111
    101
    100
    


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