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$ curl repovive.com/roadmaps/fundamental-algorithms/bit-manipulation/subset-iteration-with-bitmasks

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Subset Iteration with Bitmasks - Bit Manipulation | Fundamental Algorithms | Repovive

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Fundamental Algorithms8 sections · 294 units2h total

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Subset Iteration with Bitmasks

Iterating over subsets of a subset.

Iterate all subsets of a mask:

sub = mask
while sub > 0:
    // process subset 'sub'
    sub = (sub - 1) & mask
// don't forget empty subset

Why it works: Decrementing flips trailing $1$ s and sets next $0$ to $1$ . The & mask keeps only bits from the original mask.

Example: mask $= 1011$ , subsets: $1011, 1010, 1001, 1000, 0011, 0010, 0001, 0000$ .

Time: $O(3^n)$ for iterating all subsets of all masks from $0$ to $2^n - 1$ .