问证明一个特定的矩阵存在

EN

# -*- coding: utf-8 -*-

# Returns -1 if can not put and value how good a solution is if can be put. Bigger value of x is better.
def can_put_on_grid(grid, number, start_x, start_y, direction):
#   Check that the new number lies inside the grid.
    x = 0
    if start_x < 0 or start_x > len(grid[0]) - 1 or start_y < 0 or start_y > len(grid) - 1:
        return -1
    end = end_coordinates(number, start_x, start_y, direction)
    if end[0] < 0 or end[0] > len(grid[0]) - 1 or end[1] < 0 or end[1] > len(grid) - 1:
        return -1
#   Test if new number does not intersect any previous number.
    A = [-1,-1,-1,0,0,1,1,1]
    B = [-1,0,1,-1,1,-1,0,1]
    for i in range(0,len(number)):
        if grid[start_x + A[direction] * i][start_y + B[direction] * i] not in ("X", number[i]):
            return -1
        else:
            if grid[start_x + A[direction] * i][start_y + B[direction] * i] == number[i]:
                x += 1
    return x

def end_coordinates(number, start_x, start_y, direction):
    end_x = None
    end_y = None
    l = len(number)
    if direction in (1, 4, 7):
        end_x = start_x - l + 1
    if direction in (3, 6, 5):
        end_x = start_x + l - 1
    if direction in (2, 0):
        end_x = start_x
    if direction in (1, 2, 3):
        end_y = start_y - l + 1
    if direction in (7, 0, 5):
        end_y = start_y + l - 1
    if direction in (4, 6):
        end_y = start_y
    return (end_x, end_y)

if __name__ == "__main__":
    A = [['X' for x in range(13)] for y in range(9)]
    numbers = [str(i*i) for i in range(1, 101)]
    directions = [0, 1, 2, 3, 4, 5, 6, 7]
    for i in directions:
        C = can_put_on_grid(A, "10000", 3, 5, i)
        if C > -1:
            print("One can put the number to the grid!")
    exit(0)