Concepts4
โMathAdvanced
Mรถbius Function and Inversion
The Mรถbius function ฮผ(n) is 0 if n has a squared prime factor, otherwise it is (-1)^k where k is the number of distinct prime factors.
#mobius function#mobius inversion#dirichlet convolution+12
โMathAdvanced
Divisor Function Sums
Summing the divisor function d(i) up to n equals counting lattice points under the hyperbola xy โค n, which can be done in O(โn) using floor-division blocks.
#divisor function#euler totient#mobius function+11
โ๏ธAlgorithmAdvanced
Subset Sum Convolution
Subset Sum Convolution (often called Subset Convolution) computes C[S] by summing A[T]รB[U] over all disjoint pairs T and U whose union is S.
#subset convolution#subset sum convolution#sos dp+11
โ๏ธAlgorithmAdvanced
Sum over Subsets (SOS) DP
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).
#sos dp#subset zeta transform#mobius inversion+11