Suppose, we are given a m x n grid box, where each cell has a board that is positioned either from the top-right to bottom-left, or from the top-left to the bottom-right. Now from the top cells, a ball is put into the box and we have to check if that ball reaches the bottom of the box. The grid is given as a matrix. If a cell is marked 1 the diagonal board spans from the top-left to the bottom-right; if it is marked -1 it spans from the top-right to the bottom-left corner. If n balls are put into the box, we have to find out how many balls reach the bottom.
Example of a 3x3 grid box.
So, if the input is like mat =
| 1 | 1 | 1 | -1 |
| -1 | 1 | 1 | -1 |
| 1 | -1 | -1 | 1 |
| 1 | -1 | 1 | -1 |
then the output will be [-1, -1, -1, -1]
To solve this, we will follow these steps −
i := number of rows in mat
j := number of columns in mat
res := a new list
for val in range 0 to j, do
x := val
for r in range 0 to i, do
s := mat[r, x]
x := x + mat[r, x]
if x < 0 or x >= j or mat[r, x] is not same as s, then
add element -1 at the end of res
come out from the loop
otherwise,
add x at the end of res
return res
Example
Let us see the following implementation to get better understanding
def solve(mat): i, j = map(len, (mat, mat[0])) res = [] for val in range(j): x = val for r in range(i): s = mat[r][x] x += mat[r][x] if x < 0 or x >= j or mat[r][x] != s: res += [-1] break else: res += [x] return res print(solve([[1, 1, 1, -1], [-1, 1, 1, -1], [1, -1, -1, 1],[1, -1, 1, -1] ]))
Input
[[1, 1, 1, -1], [-1, 1, 1, -1], [1, -1, -1, 1],[1, -1, 1, -1] ]
Output
[-1, -1, -1, -1]