# Program to count submatrices with all ones using Python

PythonServer Side ProgrammingProgramming

Suppose we have m x n binary matrix, we have to find how many submatrices have all ones.

So, if the input is like

 1 0 1 0 1 1 0 1 1

then the output will be 13 as there are 6 (1x1) matrices, 3 (2,1) matrices, 2 (1x2) matrices, 1 (3x1) matrix and 1 (4x4) matrix.

To solve this, we will follow these steps −

• m := row count of matrix

• n := column count of matrix

• dp := a zero matrix of same size m x n

• for i in range 0 to m - 1, do

• for j in range 0 to n - 1, do

• if i is same as 0 and matrix[i, j], then

• dp[i, j] := 1

• otherwise when matrix[i][j] is non-zero, then

• dp[i, j] := dp[i-1, j] + 1

• total := 0

• for i in range 0 to m - 1, do

• for j in range 0 to n - 1, do

• for k in range j+1 to n, do

• total := total + minimum of dp[i,j] to dp[i,k]

Let us see the following implementation to get better understanding −

## Example

Live Demo

def solve(matrix):
m = len(matrix)
n = len(matrix[0])
dp = [[0] * n for _ in range(m)]
for i in range(m):
for j in range(n):
if i == 0 and matrix[i][j]:
dp[i][j] = 1
elif matrix[i][j]:
dp[i][j] = dp[i-1][j] + 1
total = 0
for i in range(m):
for j in range(n):
for k in range(j+1, n+1):
total += min(dp[i][j:k])
print(solve(matrix))
[4,6,7,8], 11
13