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How to find all the sub matrix of a N*N matrix?

Let’s say we have a matrix A,

A = [[1,2],
     [3,4]
    ]

and I want to find all the submatrix ie,

1,2,3,4,(1,2),(3,4),(1,3),(2,4),(1,2,3,4)

Using basic for loops. I tried but this doesn’t give correct results.

def mtx(arr):
    n = len(arr)
    for i in range(n,1,-1):
        off_cnt = n - i + 1
        for j in range(off_cnt):
            for k in range(off_cnt):
                for p in range(i):
                    for q in range(i):
                        print(arr[p+j][q+k])
                    print('--------')
# print(mtx(a)

Stack Overflow Asked by Dronzer on November 15, 2021

1 Answers

One Answer

You need to find all sizes of submatrices of N*N, which is suppose are matrices of size H*W, where H and W range from 1 to N (included) - that is your first range of for loops. Then you need to create all submatrices of this size from all possible starting coordinates, that means, given submatrix may start from a position x, y; where x, y range from start index (let's say 0) to last possible index, which is for x N - W (included) and for y N - H (included). Anything above won't fit. Then, just fill your submatrix and do whatever you want (print it?) as shown in code below:

def print_submatrices(matrix):
    
    # all possible submatrices heights
    for height in range(1, len(matrix)+1): 
        
        # all possible submatrices width
        for width in range(1, len(matrix[0]) + 1): 
            
            # create empty submatrix of given size
            template = list()
            for i in range(height):
                template.append([None]*width)
                
            # fill submatrix
            for y in range(len(matrix) - height + 1): # every possible start on y axis
                for x in range(len(matrix[0]) - width + 1): # every possible start on x axis
                    
                    # fill submatrix of given size starting at y, x coords
                    for i in range(y, y + height):
                        for j in range(x, x + width):
                            template[i-y][j-x] = matrix[i][j]
                            
                    # when the matrix is filled, print it
                    print(template)

Answered by Ecto on November 15, 2021

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