Problem

Suppose you have a matrix of given shape RxC where R=number of rows and C=number of columns each cell can have two possible values 0 or 1.

[0 1 1 0 1 0]
[0 1 0 1 1 0]
[1 0 0 0 0 0]
[0 0 0 1 0 0]
[0 0 0 0 1 1]
[0 1 0 0 0 0]

the sum of each row and sum of each column will be calculated and the hash of this matrix's bytes will be computed.

 1 3 1 2 3 1
 -----------
[0 1 1 0 1 0] | 3
[0 1 0 1 1 0] | 3
[1 0 0 0 0 0] | 1
[0 0 0 1 0 0] | 1
[0 0 0 0 1 1] | 2
[0 1 0 0 0 0] | 1

row_sums=[3, 3, 1, 1, 2, 1]
col_sums=[1, 3, 1, 2, 3, 1]
hash=62d5e751d2e57a7c737998df5b55b9f9

Restrictions

1. cells value can be 1 or 0.
2. row_sums and col_sums are valid sums for an existing matrix.
3. hash is a valid hash for an existing matrix.

these inputs are then given to another program which will only know three things.

1. colum_sums
2. row_sums
3. matrix hash

the program must solve all the posibilities and only return the valid matrix.

this repository has an implementation which can solve in complexcity of O((R*C)*log(2^(R*C)))) best being O(R*C) and worst O(2^(R*C)) in short O(nlog(n)).
the program runs with parallelism to speed up the solving process using MPI.

python implementation will solve 6x6 matrix in ~2seconds.
c++ implementation will solve 40 times faster

Try Live

run project in google notebooks