> ## Documentation Index
> Fetch the complete documentation index at: https://leetcode-py.wisl.dev/llms.txt
> Use this file to discover all available pages before exploring further.

> ## Agent Instructions
> leetcode-py is a Python LeetCode practice environment generator with one CLI: lcpy. It is not a service or platform.
> Each problem is a directory under leetcode/ with README.md, solution.py, test_solution.py, helpers.py, and playground.ipynb. lcpy gen creates them from JSON templates bundled with the package.
> Examples are backed by tests; copy them verbatim.

# Largest Combination With Bitwise AND Greater

> Tested Python solution for LeetCode 2275 with 24 pytest cases. Generate a practice environment with lcpy.

LeetCode 2275, [Medium](/catalog/medium). Topics: [Array](/catalog/topics/array), [Hash Table](/catalog/topics/hash-table), [Bit Manipulation](/catalog/topics/bit-manipulation), [Counting](/catalog/topics/counting). [View on LeetCode](https://leetcode.com/problems/largest-combination-with-bitwise-and-greater-than-zero/description/).

Generate this problem as a practice environment: tested reference solution, 24 [parametrized pytest cases](/practice/testing), and a playground notebook:

```bash theme={"theme":{"light":"github-light","dark":"github-dark"}}
lcpy gen -n 2275   # by problem number
lcpy gen -s largest_combination_with_bitwise_and_greater_than_zero   # by problem name
```

## Problem

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`. 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`.

### Examples

```
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`.

```
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 <= 10^5`
* `1 <= candidates[i] <= 10^7`

## Solution

Reference implementation from [solution.py on GitHub](https://github.com/wislertt/leetcode-py/blob/main/leetcode/largest_combination_with_bitwise_and_greater_than_zero/solution.py), full suite in [test\_solution.py](https://github.com/wislertt/leetcode-py/blob/main/leetcode/largest_combination_with_bitwise_and_greater_than_zero/test_solution.py):

```python theme={"theme":{"light":"github-light","dark":"github-dark"}}
class Solution:
    # Time: O(n * b) where b is the bit width of the largest value (<= 24)
    # Space: O(1)
    def largest_combination(self, candidates: list[int]) -> int:
        best = 0
        for bit in range(24):
            count = 0
            for value in candidates:
                count += (value >> bit) & 1
            best = max(best, count)
        return best
```

## Complexity

| Time | Space |
| - | - |
| O(n \* b) where b is the bit width of the largest value (\<= 24) | O(1) |

## Tags

[NeetCode All](/catalog/neetcode).


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