I am given an M * N (M > 1, N > 1) matrix with all the numbers blackened but their row and column sums are visible.
For example, I am given this 3 * 3 matrix.
And one of the possible matrix values are
My question is, can one solve one set of possible M * N matrix values, depending on just the row and column sums, in polynomial time? For example, can one use those 6 red values in the picture to solve those 9 black values as a possible solution, in polynomial time? For a matrix of M * N values, there will be M + N sum values. M and N can be very large.