2275

2275. Largest Combination With Bitwise AND Greater Than Zero (Medium)

The bitwise AND of an array nums is the bitwise AND of all integers in nums.

• For example, for nums = [1, 5, 3], the bitwise AND is equal to 1 & 5 & 3 = 1.
• Also, for nums = [7], the bitwise AND is 7.

You are given an array of positive integers candidates. Evaluate the bitwise AND of every combination of numbers of candidates. Each number in candidates may only be used once in each combination.

Return the size of the largest combination of candidates with a bitwise AND greater than 0.

 

Example 1:

Input: candidates = [16,17,71,62,12,24,14]
Output: 4
Explanation: The combination [16,17,62,24] has a bitwise AND of 16 & 17 & 62 & 24 = 16 > 0.
The size of the combination is 4.
It can be shown that no combination with a size greater than 4 has a bitwise AND greater than 0.
Note that more than one combination may have the largest size.
For example, the combination [62,12,24,14] has a bitwise AND of 62 & 12 & 24 & 14 = 8 > 0.

Example 2:

Input: candidates = [8,8]
Output: 2
Explanation: The largest combination [8,8] has a bitwise AND of 8 & 8 = 8 > 0.
The size of the combination is 2, so we return 2.

 

Constraints:

• 1 <= candidates.length <= 105
• 1 <= candidates[i] <= 107

Companies: Adobe, Jump Trading, Hudson River Trading

Related Topics:
Array, Hash Table, Bit Manipulation, Counting

Similar Questions:

• Count Number of Maximum Bitwise-OR Subsets (Medium)

Hints:

• For the bitwise AND to be greater than zero, at least one bit should be 1 for every number in the combination.
• The candidates are 24 bits long, so for every bit position, we can calculate the size of the largest combination such that the bitwise AND will have a 1 at that bit position.

Solution 1.

// OJ: https://leetcode.com/problems/largest-combination-with-bitwise-and-greater-than-zero
// Author: github.com/lzl124631x
// Time: O(N)
// Space: O(1)
class Solution {
public:
    int largestCombination(vector<int>& A) {
        int ans = 0;
        for (int i = 0; i < 32; ++i) {
            int cnt = 0;
            for (int n : A) cnt += (n >> i & 1);
            ans = max(ans, cnt);
        }
        return ans;
    }
};