The problem is on the initialization step.
for i in range (0,m):
matrix[i] = columns
This code actually makes every row of your matrix
refer to the same columns
object. If any item in any column changes – every other column will change:
>>> for i in range (0,m):
... matrix[i] = columns
...
>>> matrix
[[0, 0, 0], [0, 0, 0]]
>>> matrix[1][1] = 2
>>> matrix
[[0, 2, 0], [0, 2, 0]]
You can initialize your matrix in a nested loop, like this:
matrix = []
for i in range(0,m):
matrix.append([])
for j in range(0,n):
matrix[i].append(0)
or, in a one-liner by using list comprehension:
matrix = [[0 for j in range(n)] for i in range(m)]
or:
matrix = [x[:] for x in [[0]*n]*m]
See also:
Hope that helps.