回溯法 数独问题（sudoku） python

def print_grid(arr):    for i in range(9):        for j in range(9):            # 注意，在py3.x中，print函数默认都有换行            print(arr[i][j], end="")        print()# 找出目前没有被赋值的位置，若全部都被填满，则返回Falsedef find_empty_location(arr, l):    for row in range(9):        for col in range(9):            if arr[row][col] == 0:                l[0] = row                l[1] = col                # print("empty: row="+str(row)+" col="+str(col))                return True    return False# 找出num在该arr的row行是否出现过def used_in_row(arr, row, num):    for i in range(9):        if arr[row][i] == num:            return True    return False# 找出num在该arr的col列是否出现过def used_in_col(arr, col, num):    for i in range(9):        if arr[i][col] == num:            return True    return False# 找出num在该arr的3x3-box是否出现过，更应注意的是，传参技巧！def used_in_box(arr, row, col, num):    for i in range(3):        for j in range(3):            if arr[row+i][col+j] == num:                return True    return Falsedef check_location_is_safe(arr, row, col, num):    return not used_in_row(arr, row, num) and not used_in_col(arr, col, num) and not used_in_box(arr, row - row % 3, col - col % 3, num)def solve_sudoku(arr):    # 当前搜索的第几行、第几列    l = [0, 0]    # 找出还未被填充的位置    if not find_empty_location(arr, l):        return True    # 未被填充的位置，赋值给row，col    row = l[0]    col = l[1]    for num in range(1, 10):        if check_location_is_safe(arr, row, col, num):            arr[row][col] = num            #print_grid(arr)            if solve_sudoku(arr):                return True            # 若当前num导致未来并没有结果，则当前所填充的数无效，置0后选下一个数测试            arr[row][col] = 0    return Falseif __name__ == "__main__":    grid = [[0 for x in range(9)] for y in range(9)]    grid = [[3, 0, 6, 5, 0, 8, 4, 0, 0],            [5, 2, 0, 0, 0, 0, 0, 0, 0],            [0, 8, 7, 0, 0, 0, 0, 3, 1],            [0, 0, 3, 0, 1, 0, 0, 8, 0],            [9, 0, 0, 8, 6, 3, 0, 0, 5],            [0, 5, 0, 0, 9, 0, 6, 0, 0],            [1, 3, 0, 0, 0, 0, 2, 5, 0],            [0, 0, 0, 0, 0, 0, 0, 7, 4],            [0, 0, 5, 2, 0, 6, 3, 0, 0]]    if solve_sudoku(grid):        print_grid(grid)    else:        print("No solution exists\n")# output# 3 1 6 5 7 8 4 9 2# 5 2 9 1 3 4 7 6 8# 4 8 7 6 2 9 5 3 1# 2 6 3 4 1 5 9 8 7# 9 7 4 8 6 3 1 2 5# 8 5 1 7 9 2 6 4 3# 1 3 8 9 4 7 2 5 6# 6 9 2 3 5 1 8 7 4# 7 4 5 2 8 6 3 1 9