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$ curl repovive.com/roadmaps/dynamic-programming/bitmask-dp/bit-problem-implementation

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$ curl repovive.com/roadmaps/dynamic-programming/bitmask-dp/bit-problem-implementation

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Bit Problem - Implementation - Bitmask DP | Dynamic Programming | Repovive

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Dynamic Programming21 sections · 918 units60h total

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Bit Problem - Implementation

Three SOS passes

Build a frequency array $f[\text{mask}]$ counting occurrences of each value. Then run two SOS passes:

function solveBitProblem(nums, maxVal)
    n := bits needed for maxVal
    f := frequency array of size 2^n
    sub := copy of f
    for i := 0 to n - 1
        for mask := 0 to 2^n - 1
            if (mask >> i) & 1 then
                sub[mask] += sub[mask ^ (1 << i)]
    sup := copy of f
    for i := 0 to n - 1
        for mask := 0 to 2^n - 1
            if not ((mask >> i) & 1) then
                sup[mask] += sup[mask | (1 << i)]
    ALL := 2^n - 1
    for x in nums
        print(sub[x], sup[x], len(nums) - sub[ALL ^ x])

Time: $O(n \cdot 2^n)$ Each SOS pass, where $n = \log(\max)$ . Space: $O(2^n)$ .

Time: $O(n \cdot 2^n)$ . Space: $O(2^n)$ .