Largest Combination With Bitwise AND Greater Than Zero

Problem Description

You are given an array of positive integers candidates. Compute the bitwise AND for all possible combinations of elements in the candidates array. Return the size of the largest combination of candidates with a bitwise AND greater than 0.

Key Insights

• The bitwise AND operation results in a number that retains a bit only if that bit is set in all operands.
• The largest combination with a bitwise AND greater than 0 can be found by identifying the bits that are set in the numbers of the array.
• Counting how many numbers have each bit set allows us to determine the largest valid combination.

Space and Time Complexity

Time Complexity: O(n * 32) - where n is the length of the candidates array, as we check each number for each of its 32 bits. Space Complexity: O(1) - since we only use a fixed-size array for counting bits.

Solution

To solve this problem, we will:

1. Initialize an array to count the number of integers that have each bit set (from 0 to 31).
2. Iterate through each integer in the candidates array, and for each integer, determine which bits are set.
3. Update the count for each bit in the count array.
4. The size of the largest combination with a bitwise AND greater than 0 will be the maximum value in the count array.

Code Solutions