Largest Combination With Bitwise AND Greater Than Zero

class Solution {
public:
    int maxSetBits(vector<int>& nums) {
        int highestBitCount = 0;
        for (int i = 0; i < 24; ++i) {
            int bitCount = 0;
            for (int number : nums) {
                if (number & (1 << i)) {
                    bitCount++;
                }
            }
            highestBitCount = max(highestBitCount, bitCount);
        }
        return highestBitCount;
    }
};

The solution involves finding the largest subset of numbers from a given vector such that there exists at least one bit position where the bitwise AND of all numbers in the subset results in a bit value greater than zero. This is accomplished using a C++ function.

• Start by initializing a variable highestBitCount to zero. This variable tracks the maximum count of numbers that share the same bit position set to 1.
• Iterate through each bit position from 0 to 23, inclusive (considering numbers can have up to 24 significant bits for the purpose).
• For each bit position, initialize bitCount to count how many numbers have the current bit set to 1.
• Using a nested loop, iterate over each number in the input vector.
• Check if the current bit position in the number is set by using the bitwise AND operation between the number and 1 shifted left by the bit position (1 << i).
• If true, increment bitCount.
• After iterating through all numbers for the current bit position, update highestBitCount to be the maximum of its current value or bitCount.
• Once all bit positions are checked, return the highestBitCount.

This function efficiently counts the number of numbers that can be combined such that the bitwise AND on a specific bit position yields a non-zero result, ensuring the largest subset is identified for any potential bit position.

class Solution {

    public int maxBitwiseCombination(int[] numbers) {
        int highestCount = 0; 
        for (int i = 0; i < 24; i++) {
            int bitCount = 0; 
            for (int value : numbers) {
                if ((value & (1 << i)) > 0) {
                    bitCount++;
                }
            }
            highestCount = Math.max(highestCount, bitCount); 
        }
        return highestCount;
    }
}

The provided Java solution determines the largest number of elements from an integer array that, when evaluated using bitwise AND operation with a power of two, results in a value greater than zero. This process is used to find which power of two (from 0 to 23) captures the most numbers from the array with non-zero results when the power is used as a mask in the AND operation.

• Start by initializing highestCount to zero. This variable will keep track of the maximum count of non-zero results across all bit positions.
• Iterate through bit positions from 0 to 23 using a loop. This represents each bit position to test in the numbers.
  • For each bit position (i), initiate bitCount to zero. This counter will tally how many numbers in the array have the ith bit set.
  • For each number in the input array, check if the ith bit is set by performing a bitwise AND between the number and 1 << i (which is 2 raised to the power i). If the result is greater than zero, increment bitCount.
  • Update highestCount to be the maximum value between the current highestCount and the bitCount for the current bit position. This ensures that after all bits are checked, highestCount holds the maximum number of integers that had non-zero results for any bit position.
• Return highestCount as the final result, which is the largest count of numbers from the array that, for any single bit, results in a non-zero outcome when applying the bitwise AND operation with powers of two.

class Solution:
    def findMaxCombination(self, numbers):
        max_bit_count = 0
        for position in range(24):
            bit_count = 0
            for value in numbers:
                if (value & (1 << position)) > 0:
                    bit_count += 1
            max_bit_count = max(max_bit_count, bit_count)
        return max_bit_count

The provided Python code defines a method findMaxCombination within a class Solution to solve the problem of finding the largest combination of numbers where the bitwise AND operation results in a value greater than zero. It operates as follows:

• Initialize a variable max_bit_count to store the maximum number of elements that contribute positively to the bitwise AND for any bit position.
• Iterate through each bit position from 0 to 23 (covering potential bit positions for up to 24-bit integers):
  • For each position, initialize a bit_count counter to zero.
  • Loop through all numbers in the provided list and use bitwise AND to check if the bit at the current position is set (i.e., not zero).
  • If the condition is true, increment the bit_count for the current bit position.
  • Update max_bit_count if the current bit_count is greater than the previously recorded maximum.
• The function finally returns the value of max_bit_count, which represents the maximum group of numbers that have at least one bit position in common when AND-ed together, resulting in a non-zero output.