PE011.py

#!/usr/bin/env python
# -*coding:UTF-8-*-
"""
@Project hello_world
@File PE011.py
@Author Haosen Luo
@Date 2025/1/19 11:36

方阵中的最大乘积
在如下的20×20方阵中，有四个呈对角线排列的数被标记为红色。

08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48

这四个数的乘积是 26×63×78×14=1788696
在这个20×20方阵中，四个呈一直线（竖直、水平或对角线）相邻的数的乘积最大是多少？

程序解答：70600674，矩阵副对角线 [87, 97, 94, 89]
"""
from pprint import pprint

Str = '08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08 \
49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00 \
81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65 \
52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91 \
22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80 \
24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50 \
32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70 \
67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21 \
24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72 \
21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95 \
78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92 \
16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57 \
86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58 \
19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40 \
04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66 \
88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69 \
04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36 \
20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16 \
20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54 \
01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48'


def get_matrix(string=Str, matrix_size=20):
    """
    获取矩阵数据结构
    :param matrix_size:
    :param string:
    :return:
    """
    matrix = []
    list_string = string.split(' ')

    for i in range(matrix_size):
        matrix.append([])
        for j in range(matrix_size):
            matrix[i].append(int(list_string[i * matrix_size + j]))

    return matrix


def calculate(m=[[1, 2, 3, 4], [2, 3, 4, 5], [3, 4, 5, 6], [4, 66, 6, 7]]):
    """
    小矩阵通用方法计算
    :param m:
    :return:
    """
    m_1, m_2, m_3_value, m_4_value = [1, 1, 1, 1], [1, 1, 1, 1], 1, 1
    m_3, m_4 = [1, 1, 1, 1], [1, 1, 1, 1]

    m_size = len(m[0])

    for r in range(0, m_size):
        # 方法1：横向乘积
        m_1[r] = eval('*'.join(map(str, m[r])))

        # 方法2：纵向乘积
        m_2[r] = eval('*'.join([str(m[i][r]) for i in range(m_size)]))

        for c in range(0, m_size):

            # 方法3：主对角线乘积
            if r == c:
                m_3_value *= m[r][c]
                m_3[c] = m[r][c]

            # 方法4：副对角线乘积
            # r + c == 3
            elif r + c == m_size - 1:
                m_4_value *= m[r][c]
                m_4[c] = m[r][c]

    max_m_1 = max(m_1)
    max_m_2 = max(m_2)

    max_value = max(max_m_1, max_m_2, m_3_value, m_4_value)

    if max_value == max_m_1:
        return max_value, m_1, '横向'
    elif max_value == max_m_2:
        return max_value, m_2, '纵向'
    elif max_value == m_3_value:
        return max_value, m_3, '主对角线'
    else:
        return max_value, m_4, '副对角线'


def main():
    """
    主程序
    :return:
    """
    matrix = get_matrix(Str)

    # m1 = [matrix[0][0:4], matrix[1][0:4], matrix[2][0:4], matrix[3][0:4]]
    # m2 = [matrix[0][1:5], matrix[1][1:5], matrix[2][1:5], matrix[3][1:5]]
    # m3 = [matrix[0][2:6], matrix[1][2:6], matrix[2][2:6], matrix[3][2:6]]
    #
    # print(m1)
    # print(m2)
    # print(m3)
    # ...
    #
    # m17 = [matrix[1][0:4], matrix[2][0:4], matrix[3][0:4], matrix[4][0:4]]
    # m18 = [matrix[1][1:5], matrix[2][1:5], matrix[3][1:5], matrix[4][1:5]]
    # m19 = [matrix[1][2:6], matrix[2][2:6], matrix[3][2:6], matrix[4][2:6]]
    #
    # print(m17)
    # print(m18)
    # print(m19)
    #
    # m240 = [matrix[16][0:4], matrix[17][0:4], matrix[18][0:4], matrix[19][0:4]]
    # m241 = [matrix[16][1:5], matrix[17][1:5], matrix[18][1:5], matrix[19][1:5]]
    # m242 = [matrix[16][2:6], matrix[17][2:6], matrix[18][2:6], matrix[19][2:6]]
    #
    # print(m240)
    # print(m241)
    # print(m242)

    total_max_value = 1
    max_matrix_combo = []
    combo_way = ''

    # 表示从第几行为第一行
    for row_index in range(16 + 1):

        for idx in range(16 + 1):
            temp_matrix = [matrix[row_index + 0][idx: idx + 4],
                           matrix[row_index + 1][idx: idx + 4],
                           matrix[row_index + 2][idx: idx + 4],
                           matrix[row_index + 3][idx: idx + 4]
                           ]

            temp_max, temp_m, temp_combo_way = calculate(temp_matrix)

            if temp_max > total_max_value:
                total_max_value = temp_max
                max_matrix_combo = temp_m
                combo_way = temp_combo_way

    print(total_max_value, max_matrix_combo, combo_way)

    return total_max_value


if __name__ == '__main__':
    main()

    # 程序解答：
    # 70600674[87, 97, 94, 89] 副对角线