问题
I am following https://taninamdar.files.wordpress.com/2013/11/submatrices3.pdf to find total number of sub matrix of a matrix.But am stuck how to find how many sub matrix of a given size is present in a matrix.
Also 0<=A<=M and 0<=B<=N.
where AxB(submatrix size) and MxN(matrix size).
回答1:
I didn't go through the pdf (math and I aren't friends), however simple logic is enough here. Simply, try to reduce the dimension: How many vectors of length m can you put in a vector of length n ?
Answer: n-m+1. To convince you, just go through the cases. Say n = 5 and m = 5. You've got one possibility. With n = 5 and m = 4, you've got two (second vector starts at index 0 or index 1). With n = 5 and m = 3, you've got three (vector can start at index 0, 1 or 2). And for n = 5 and m = 1, you've got 5, seems logic.
So, in order to apply that to a matrix, you have to add a dimension. How do you do that ? Multiplication. How many vectors of length a can you put inside a vector of length n ? n-a+1. How many vectors of length b can you put inside a vector of length m ? m-b+1.
So, how many matrices of size A*B can you put in a matrix of length N*M ? (N-A+1)*(M-B+1).
So, I didn't handle the case where one of the dimension is 0. It depends on how you consider this case.
来源：https://stackoverflow.com/questions/37634067/number-of-submatrix-of-size-axb-in-a-matrix-of-size-mxn