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# Program to find the sum of elements that forms a Z shape on matrix in Python

Suppose we have one n x n matrix M, we have to find the sum of all elements that form a Z shape in the matrix.

So, if the input is like

4 | 3 | 2 |

9 | 1 | 8 |

2 | 5 | 6 |

then the output will be 23, as elements are [4+3+2+1+2+5+6] = 23.

To solve this, we will follow these steps −

- n := row count of matrix
- if n <= 2, then
- return sum of all elements in matrix

- first_row := sum of first row
- last_row := sum of last row
- diagonal = sum of matrix[i, n-1-i] for all i from 1 to n-2
- return first_row + last_row + diagonal

Let us see the following implementation to get better understanding −

## Example

class Solution: def solve(self, matrix): n = len(matrix) if n <= 2: return sum(sum(row) for row in matrix) first_row = sum(matrix[0]) last_row = sum(matrix[n-1]) diagonal = sum(matrix[i][n-1-i] for i in range(1, n-1)) return first_row + last_row + diagonal ob = Solution() matrix = [ [4, 3, 2], [9, 1, 8], [2, 5, 6] ] print(ob.solve(matrix))

## Input

matrix = [[4, 3, 2], [9, 1, 8], [2, 5, 6]]

## Output

23

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