# Program to find matrix for which rows and columns holding sum of behind rows and columns in Python

PythonServer Side ProgrammingProgramming

Suppose we have a given matrix, We have to find a new matrix res, whose dimension is same as the given matrix where each element in res[i, j] = sum of the elements of matrix[r, c] for each r ≤ i, and c ≤ j.

So, if the input is like

 8 2 7 4

then the output will be

 8 10 15 21

To solve this, we will follow these steps −

• if matrix is empty, then

• return matrix

• R := row count of matrix

• C := column count of matrix

• for r in range 1 to R - 1, do

• for c in range 0 to C - 1, do

• matrix[r, c] := matrix[r, c] + matrix[r - 1, c]

• for r in range 0 to R - 1, do

• for c in range 1 to C - 1, do

• matrix[r, c] := matrix[r, c] + matrix[r, c - 1]

• return matrix

## Example

Let us see the following implementation to get better understanding

def solve(matrix):
if not matrix:
return matrix

R, C = len(matrix), len(matrix)
for r in range(1, R):
for c in range(C):
matrix[r][c] += matrix[r - 1][c]

for r in range(R):
for c in range(1, C):
matrix[r][c] += matrix[r][c - 1]

return matrix

matrix = [
[8, 2],
[7, 4]
]
print(solve(matrix))

## Input

[[8, 2],[7, 4]]


## Output

[[8, 10], [15, 21]]