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Largest Combination With Bitwise AND Greater Than Zero

This repository contains solutions to solve the problem "Largest Combination With Bitwise AND Greater Than Zero". The goal is to find the size of the largest subset from an array of integers such that the bitwise AND of the subset is greater than zero. Below is a step-by-step breakdown of the solution logic used in each language.

Problem Approach

  1. Intuition: The problem requires us to identify the largest group of numbers where, if bitwise AND is applied across all elements in the subset, the result remains greater than zero.
  2. Bit Manipulation Insight: If a certain bit position has many numbers with a 1 at that position, we can create a large subset with a non-zero bitwise AND.
  3. Optimization Strategy: Instead of calculating bitwise ANDs for each subset, we count how many numbers have a 1 in each bit position (0 to 30), then select the maximum count among these.

C++ Code Explanation

  1. Initialize Count Array: Create an array bitCount to hold counts of 1s for each of the 31 bit positions (since integers up to (10^7) have up to 31 bits).
  2. Counting Set Bits:
    • For each number in the input array:
      • Loop through each bit position from 0 to 30.
      • Check if the bit at that position is 1 using bitwise AND (num & (1 << i)).
      • If 1, increment the count in bitCount for that bit position.
  3. Get Maximum Count:
    • After counting all bit positions, find the highest value in bitCount.
    • This value represents the maximum subset size where bitwise AND will be greater than zero.
  4. Return Result: The highest count is returned as the solution.

Java Code Explanation

  1. Initialize Count Array: Create an array bitCount to store the count of 1s for each bit position from 0 to 30.
  2. Counting Set Bits:
    • For each integer in candidates:
      • Loop through bit positions from 0 to 30.
      • Use num & (1 << i) to check if the bit at that position is 1.
      • If 1, increment the corresponding index in bitCount.
  3. Get Maximum Count:
    • Iterate through bitCount to find the highest count.
    • This maximum count represents the largest subset size that can achieve a non-zero bitwise AND.
  4. Return Result: Return this maximum value as the result.

JavaScript Code Explanation

  1. Initialize Count Array: Use an array bitCount initialized to 31 zeros, each representing a bit position's count of 1s.
  2. Counting Set Bits:
    • For each number in candidates:
      • Loop over each bit position from 0 to 30.
      • Use num & (1 << i) to check if that bit position is 1.
      • If so, increment bitCount at that position.
  3. Get Maximum Count:
    • Use Math.max(...bitCount) to find the maximum count in bitCount.
    • This maximum value gives the size of the largest subset with a bitwise AND greater than zero.
  4. Return Result: Return this maximum value as the solution.

Python Code Explanation

  1. Initialize Count Array: Create a list bit_count with 31 zeros to store counts for each bit position.
  2. Counting Set Bits:
    • For each number in candidates:
      • Iterate over bit positions from 0 to 30.
      • Use num & (1 << i) to check if the i-th bit is 1.
      • If true, increment bit_count[i].
  3. Get Maximum Count:
    • Use max(bit_count) to find the highest count in bit_count.
    • This highest count represents the maximum subset size with a non-zero AND.
  4. Return Result: Return this maximum value.

Go Code Explanation

  1. Initialize Count Array: Declare a fixed-size array bitCount of 31 elements, initialized to zero, for each bit position count.
  2. Counting Set Bits:
    • For each element in candidates:
      • Loop through each bit position from 0 to 30.
      • Check if the bit is set using num & (1 << i).
      • If set, increment bitCount[i].
  3. Get Maximum Count:
    • Find the highest value in bitCount by iterating through it.
    • This maximum value is the largest subset size that can achieve a non-zero AND.
  4. Return Result: Return this maximum count.