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$ curl repovive.com/roadmaps/dynamic-programming/bitmask-dp/subset-sum-implementation

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$ curl repovive.com/roadmaps/dynamic-programming/bitmask-dp/subset-sum-implementation

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Subset Sum - Implementation - Bitmask DP | Dynamic Programming | Repovive

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Dynamic Programming21 sections · 918 units60h total

Open in Course

Subset Sum - Implementation

The code

Here's the full solution:

function subsetSumExists(arr, target)
    n := length of arr
    for mask := 0 to (1 << n) - 1
        sum := 0
        for i := 0 to n - 1
            if (mask >> i) & 1 = 1 then
                sum := sum + arr[i]
        if sum = target then
            return true
    return false

Time: $O(2^n \cdot n)$ . For each of $2^n$ masks, we check $n$ bits. Space: $O(1)$ extra. This is your first complete bitmask solution. The pattern is simple: iterate masks, extract bits, compute answer.

Time complexity: $O(n \cdot S)$ .

Space complexity: $O(S)$ .