Concepts5

Convolution turns local pairwise combinations (like matching characters or adding two dice) into a single fast transform–multiply–inverse pipeline.

Subset Sum Convolution (often called Subset Convolution) computes C[S] by summing A[T]×B[U] over all disjoint pairs T and U whose union is S.

Sum over Subsets (SOS) DP lets you compute F[mask] = sum of A[submask] over all submasks in O(n 2^n) instead of O(3^n).

Bitmask DP compresses the state of a subset of n elements into an integer mask, enabling elegant dynamic programming over all subsets.

Dynamic Programming (DP) state design is the art of choosing what information to remember so that optimal substructure can be reused efficiently.