I am working on a question like, there is given a m \times n grid. Each cell holds value. What is the total number of paths from (a,b) to (c,d) given the sum of the values of cell in the path is m.
Possible movements from (i,j) are (i,j)\rightarrow(i+1,j), (i,j)\rightarrow(i-1,j), (i,j)\rightarrow(i,j+1), (i,j)\rightarrow(i,j-1)
I know it can be solved with dynamic programming but I was too much confused to what should I store. Because as contrasting to maximum cost path, it was not a stable value. What should I do in such case?