Subsets

class Solution {
public:
    vector<vector<int>> getSubsets(vector<int>& nums) {
        int numsCount = nums.size();
        vector<vector<int>> result;
        for (int i = pow(2, numsCount); i < pow(2, numsCount + 1); ++i) {
            // convert integer to binary string mask
            string binaryMask = bitset<32>(i).to_string().substr(32 - numsCount);
            // pick elements based on binary mask
            vector<int> subset;
            for (int j = 0; j < numsCount; ++j) {
                if (binaryMask.at(j) == '1') subset.push_back(nums[j]);
            }
            result.push_back(subset);
        }
        return result;
    }
};

This C++ solution generates all possible subsets of a given array of integers. The main function getSubsets operates by using binary masking to create each possible combination of the input array elements.

• The input is a vector of integers, nums.
• The output is a vector of vectors, where each inner vector is a subset of nums.

The function works as follows:

1. Calculate the number of elements, numsCount, in the input vector.
2. Initialize an empty vector of vectors result to store the subsets.
3. Iterate from 2^numsCount to 2^(numsCount + 1) - 1. Each number in this range represents a binary mask of the elements that will be included in a subset.
4. For each number:
   • Convert the number to a binary string (binaryMask) that is precisely numsCount characters long, corresponding to each element in the input vector.
   • Initialize an empty vector subset.
   • Iterate through each character in binaryMask. If a character is '1', the corresponding element from nums is added to subset.
   • Add subset to result.
5. Return the result vector which now contains all subsets.

The binary mask approach efficiently covers all possible combinations of elements because each bit in the mask corresponds to the presence (1) or absence (0) of an element from nums in the subset. Each subset corresponds uniquely to a binary number in the range from 2^numsCount to 2^(numsCount + 1) - 1.

class Solution {
    
    public List<List<Integer>> generateSubsets(int[] elements) {
        List<List<Integer>> result = new ArrayList();
        int length = elements.length;
    
        for (int i = (int) Math.pow(2, length); i < (int) Math.pow(2, length + 1); ++i) {
            // convert to binary and skip the highest bit
            String binary = Integer.toBinaryString(i).substring(1);
    
            // create a new subset based on the binary representation
            List<Integer> subset = new ArrayList();
            for (int j = 0; j < length; ++j) {
                if (binary.charAt(j) == '1') subset.add(elements[j]);
            }
            result.add(subset);
        }
        return result;
    }
}

This Java solution effectively generates all possible subsets of an input array of integers. The method generateSubsets initializes by creating an empty list of lists result, which will store each subset. It leverages binary strings to represent the inclusion (1) or exclusion (0) of each element in a subset for the array of length length.

• Begin by iterating over a range determined by powers of 2, specifically from 2^length to 2^(length+1). This range covers all possible combinations for array elements.
• For each number in this range, convert it to a binary string and ignore the most significant bit (leftmost bit). This binary representation helps in determining which elements to include in the subset.
• Iterate through the binary string. If a character is '1', add the corresponding element from the original array to the current subset.
• Add each constructed subset to result.

Finally, the method returns result, which contains all subsets, including the empty subset, each represented as a list of integers. This implementation provides a clear and straightforward approach to solve the subset generation problem using bitwise operations and binary representations.

class Solution:
    def generate_subsets(self, elements: List[int]) -> List[List[int]]:
        total_elements = len(elements)
        results = []
    
        for i in range(2**total_elements, 2 ** (total_elements + 1)):
            bitmask = bin(i)[3:]
            results.append([elements[idx] for idx in range(total_elements) if bitmask[idx] == '1'])
    
        return results

The provided Python code efficiently solves the problem of generating all possible subsets of a given list of integers. It utilizes bitwise operations to generate subsets. Here's how it works:

• The given list, elements, has its subsets computed based on the length of the list. The generate_subsets method determines the total number of elements in the list (total_elements).
• The code iterates over a range from 2**total_elements to 2**(total_elements + 1). This range leverages binary counting where each number in the range represents a potential subset.
• For each number in the range, a binary representation (bitmask) is created by stripping the first three characters of the binary string to align with the indices of the list.
• A list comprehension is used inside the loop. It checks each character in the bitmask. If a character is '1', the corresponding index in the elements list is chosen. This way, each subset is formed based on the 1's in the bitmask.
• The subsets are collected in the list results, which is returned at the end of the function.

This approach ensures that all possible combinations of elements are considered without the need for recursive calls, which can lead to a more efficient solution in terms of run time and memory usage, especially for larger lists.