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#####   ####    #####   #   #   #   #   #   #   #  ####
##  #   ##      ##      ## ##    # #    #    # #   ##
##   #  ######  ##       ###      #    ###    #    ######

$ curl repovive.com/roadmaps/math-fundamentals/bit-manipulation/subsets-implementation

░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░██████████████████████████████████████████████████████████████████████████████████████

#####   ######  #####    ###    #   #  ###  #   #  ######
##  ##  ##      ##  ##  ## ##   #   #   #   #   #  ##
#####   ####    #####   #   #   #   #   #   #   #  ####
##  #   ##      ##      ## ##    # #    #    # #   ##
##   #  ######  ##       ###      #    ###    #    ######

$ curl repovive.com/roadmaps/math-fundamentals/bit-manipulation/subsets-implementation

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Subsets - Implementation - Bit Manipulation | Math Fundamentals | Repovive

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Math Fundamentals18 sections · 842 units13h total

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Subsets - Implementation

The code

Here's the complete bitmask solution:


function subsets(nums)
    n := length of nums
    total := 2^n
    result := []
    for mask from 0 to total - 1
        subset := []
        for i from 0 to n - 1
            if (mask & (1 << i)) ≠ 0 then
                append nums[i] to subset
        append subset to result
    return result

Outer loop generates all $2^n$ masks. Inner loop builds each subset by checking which bits are set. Time: $O(n \times 2^n)$ (for each of $2^n$ masks, you check $n$ bits). Space: $O(n \times 2^n)$ for the output.