Minimal traverse distance within a matrix

test.py

import numpy

y = numpy.zeros((3, 3))

def findLeastPath(matrix, row=0, column=0, path=[], sum_=0):
        row_max = matrix.shape[0]
        column_max = matrix.shape[1]

        if column == column_max - 1 and row == row_max - 1:
            y[row][column] = matrix[row][column]
            return matrix[row][column] + sum_
        else:
            current_cost = matrix[row][column]
            path.append((row, column, current_cost))
            if column == column_max - 1:
                if y[row+1][column] != 0:
                    y[row][column] = current_cost + y[row+1][column]
                    return current_cost + y[row+1][column]
                else:
                    down = findLeastPath(matrix, row + 1, column, path, sum_ + current_cost)
                    y[row][column] = current_cost + y[row+1][column]
                    return down
            elif row == row_max - 1:
                if y[row][column+1] != 0:
                    y[row][column] = current_cost + y[row][column + 1]
                    return current_cost + y[row][column + 1]
                else:
                    right = findLeastPath(matrix, row, column + 1, path, sum_ + current_cost)
                    y[row][column] = current_cost + y[row][column + 1]
                    return right
            else:
                if y[row][column + 1] != 0:
                    right = y[row][column + 1] + current_cost
                else:
                    findLeastPath(matrix, row, column + 1, path, sum_ + current_cost)
                    right = y[row][column + 1] + current_cost
                if y[row + 1][column] != 0:
                    down = y[row + 1][column] + current_cost
                else:
                    findLeastPath(matrix, row + 1, column, path, sum_ + current_cost)
                    down = y[row+1][column] + current_cost
                if y[row + 1][column + 1] != 0:
                    diagonal = y[row + 1][column + 1] + current_cost
                else:
                    findLeastPath(matrix, row + 1, column + 1, path, sum_ + current_cost)
                    diagonal = y[row+1][column+1] + current_cost

                #print right
                #print down
                #print diagonal

                min_val = min(right, down, diagonal)

                y[row][column] = min_val

                return min_val



if __name__ == "__main__":
    
    x = numpy.random.random((3, 3))

    print x
    print findLeastPath(x)
    print y