Gray Code

class Solution {
public:
    vector<int> generateGrayCode(int bits) {
        vector<int> sequence;
        int total = 1 << bits;
        for (int i = 0; i < total; i++) {
            int gray = i ^ (i >> 1);
            sequence.push_back(gray);
        }
        return sequence;
    }
};

The solution provided is a C++ implementation of generating a Gray code sequence. Gray code is a binary numeral system where two successive values differ in only one bit.

In this implementation:

• The generateGrayCode function accepts an integer bits, which represents the number of bits in each Gray code value.
• The function initializes an empty vector sequence that will store the Gray code sequence.
• It calculates the total number of Gray code elements, denoted by total, as (2^{bits}).
• The function employs a for-loop running from 0 to total - 1. For each iteration:
  • It calculates the Gray code using the formula i ^ (i >> 1), where ^ is the XOR operator and >> is the right shift operator.
  • The calculated Gray code is then appended to the sequence vector.
• Finally, the function returns the vector containing all the Gray codes.

This approach ensures efficient computation of Gray codes for a specified number of bits.

class Solution {
    public List<Integer> generateGrayCode(int bits) {
        List<Integer> codes = new ArrayList<>();
        int total = 1 << bits;
        for (int index = 0; index < total; index++) {
            int grayCode = index ^ (index >> 1);
            codes.add(grayCode);
        }
        return codes;
    }
}

The task is to generate a sequence known as Gray Code for a given number of bits. The Gray Code sequence ensures that two consecutive values differ in only one bit which makes it useful in various digital communications to prevent errors.

Implement the Gray Code generator using Java with the following steps:

1. Create a generateGrayCode method that accepts an integer bits, which signifies the number of bits.
2. Initialize an ArrayList called codes to store the sequence of Gray Codes.
3. Compute the total number of codes possible, which is 1 << bits (equivalent to 2 raised to the power of bits).
4. Use a for-loop to iterate from 0 to total - 1. For each index i, calculate the Gray Code using the formula i ^ (i >> 1). This formula represents XOR of the number with itself right-shifted by one bit.
5. Add the computed Gray Code to the codes list.
6. Finally, return the codes list containing the complete Gray Code sequence for the specified number of bits.

Ensure the use of bitwise operations like XOR and right shift effectively as they are crucial for calculating the Gray Code values efficiently.

int* generateGrayCode(int bits, int* outputSize) {
    int length = 1 << bits;
    *outputSize = length;
    int* sequence = (int*)malloc(sizeof(int) * length);
    for (int index = 0; index < length; index++) {
        sequence[index] = index ^ (index >> 1);
    }
    return sequence;
}

The Gray Code sequence is generated using a C function named generateGrayCode, which computes sequences where successive values differ in only one bit. Here is how the function operates:

• Define the function generateGrayCode that accepts an integer bits, representing the number of bits in the Gray code, and a pointer outputSize used to store the size of the generated sequence.
• Calculate the length of the Gray code sequence as (2^{\text{bits}}), and store this value in outputSize.
• Dynamically allocate an array sequence to hold the Gray code using malloc.
• Populate the sequence array. Conversion of a binary number to its Gray code equivalent is done using the formula ( \text{index} \oplus (\text{index} >> 1) ) in a loop that iterates through index from 0 to length - 1.
• Return the pointer to the sequence array.

This function efficiently outputs a complete sequence of Gray codes for a given number of bits, offering a straightforward method for generating such sequences in C.

var generateGrayCode = function (numBits) {
    let sequence = [];
    let totalLength = 1 << numBits;
    for (let index = 0; index < totalLength; index++) {
        let grayValue = index ^ (index >> 1);
        sequence.push(grayValue);
    }
    return sequence;
};

The problem involves generating a sequence known as Gray code for a given number of bits. Gray code is a binary numeral system where two successive values differ in only one bit, making it useful in error correction in digital communications and other applications.

Here’s a breakdown of the JavaScript solution you provided:

• Define the function generateGrayCode which takes one parameter numBits indicating the number of bits in each code.
• Instantiate sequence as an empty array to store the resulting Gray codes.
• Calculate totalLength as (2^{numBits}), which represents the total number of Gray codes to generate.
• Use a for-loop to iterate through each integer from 0 to totalLength - 1, computing corresponding Gray codes.
• Inside the loop, calculate grayValue by XOR-ing the current index with the right-shifted version of the index. The right shift effectively halves the index, ensuring the desired property that consecutive Gray codes differ by only one bit.
• Append each grayValue to the sequence array.
• Finally, return the sequence array containing all Gray codes for the provided numBits.

This function efficiently generates a sequence of Gray codes for a specified number of bits using bit manipulation which is optimal for such operations. Make sure to call this function with a desired number of bits to obtain the sequence.

class Solution:
    def generateGrayCode(self, num_bits: int):
        output_sequence = []
        total_codes = 1 << num_bits
        for idx in range(total_codes):
            code = idx ^ idx >> 1
            output_sequence.append(code)
        return output_sequence

The Gray Code solution provided is implemented in Python 3 and involves generating a sequence where each successive entry differs from the previous one by exactly one bit. This sequence is known as Gray code and is often used in position encoders, digital communications, and error correction. The primary function, generateGrayCode, takes one parameter num_bits, which defines the number of bits for the Gray code sequence.

Here's a brief breakdown of the solution approach:

1. Initialize an empty list called output_sequence to store the Gray codes.
2. Calculate total_codes by left-shifting 1 by num_bits. This operation determines the total number of Gray codes that can be formed with the given number of bits.
3. Use a loop to iterate through the range of total_codes. For each index idx, compute the Gray code.
4. The Gray code computation is done by XOR-ing idx with idx shifted right by 1 bit; this is represented as idx ^ (idx >> 1).
5. Append the computed Gray code to output_sequence.
6. Return the list output_sequence containing all Gray codes up to the specified number of bits.

This function efficiently generates the list of Gray codes by utilizing bit manipulation techniques which offer a direct and fast method for Gray code conversion.