K-th Symbol in Grammar

class Solution {
public:
    int kthSymbol(int N, int K) {
        int popCount = __builtin_popcount(K - 1);
        return popCount & 1 ? 1 : 0;
    }
};

The given C++ solution defines a function named kthSymbol which determines the K-th symbol in an N-th row of a specific grammar sequence. The essence of this solution leverages built-in bit manipulation functions provided by C++ to achieve its goal effectively. Here's how it operates:

1. The function kthSymbol receives two parameters: N and K, where N represents the row number and K indicates the position in that row.
2. The code computes the population count (number of 1's in the binary representation) of K-1 using the function __builtin_popcount.
3. It then checks if this population count is odd or even using a bitwise AND operation with 1 (popCount & 1).
4. If the result is odd (popCount & 1 ? 1 : 0), it returns 1; otherwise, it returns 0.

This method utilizes the properties of binary representation and population count to dissect the recursive pattern presented by this specific grammar sequence efficiently. Keep in mind the direct use of bit manipulation functions for optimized computation.

class Solution {
    public int findKthSymbol(int level, int position) {
        int bits = Integer.bitCount(position - 1);
        return bits % 2 == 0 ? 0 : 1;
    }
}

The problem involves finding the K-th symbol in a specific grammar sequence at a given level and position. The solution utilizes the Java programming language.

To determine the K-th symbol:

• The method findKthSymbol receives two parameters: level, which specifies the depth of the sequence, and position, which identifies the specific position in that level for which the symbol is required.
• Calculate the Hamming weight (number of 1s) in the binary representation of position - 1 using the Java method Integer.bitCount(position - 1).
• Determine the symbol by checking if the count of 1s is even or odd. If even, the method returns 0; if odd, it returns 1.

This approach effectively uses bitwise calculation to find the required symbol, utilizing properties of binary numbers to determine the pattern of the sequence at any depth and position. The use of bitCount provides a compact and efficient way to compute the solution.

let grammarValue = function(level, position) {
    const bitCount = (position - 1).toString(2).split('1').length - 1;
    return bitCount % 2 === 0 ? 0 : 1;
};

The problem "K-th Symbol in Grammar" involves determining the nth symbol in a binary grammar sequence at a given level, where the sequence grows exponentially. The provided JavaScript solution leverages bitwise operations and properties of binary numbers to efficiently solve the problem.

The function grammarValue accepts two parameters:

• level: The specific level in the grammar sequence where the symbol is located.
• position: The position of the symbol in the sequence at the specified level.

Here’s a breakdown of how the solution works:

• Compute the zero-based index by subtracting one from position.
• Convert this index to a binary string to easily count the number of '1's. This is crucial because the k-th grammar sequence can be visualized as a binary tree where flips in values occur with each '1' in the binary sequence.
• Count the occurrences of '1's in the binary representation. This is done by converting the number to a binary string, splitting the string by '1', and subtracting one to get the total count of '1's.
• Determine the final value at the position by checking if the count of '1's is even or odd. If even, the function returns 0; if odd, it returns 1.

This solution efficiently uses binary properties to decide the value at any given position in the sequence without generating the entire sequence, effectively reducing time and space complexity.

class Solution:
    def findKthBit(self, level: int, position: int) -> int:
        bitCount = bin(position - 1).count('1')
        return 0 if bitCount % 2 == 0 else 1

The Python3 program titled "K-th Symbol in Grammar" presents a solution for determining the K-th bit in a specific grammar sequence rule. In this sequence, the way bits are generated involves flipping and inverting elements from the previous level.

• The findKthBit function in the Solution class accepts two parameters: level and position.
• It calculates the bit's value by determining the number of 1s in the binary representation of position-1.
• This count determines the parity of the number of 1s. If the count of 1s is even, the function returns 0, otherwise, it returns 1.

Ensure the level and position values adhere to your specific case constraints when implementing or testing this function in different scenarios to guarantee appropriate functionality. This algorithm optimally determines the desired position bit, leveraging binary operations for efficiency.