题目11：在20×20的网格中同一直线上四个数的最大乘积是多少？

ft215378 · 发表于 2021-10-12 12:41:54

s ='''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
'''
#转换为二维列表
#'''
index = 0
list1 = []
s_list = []
while True:
list1.append(s[index:index+2])
index += 3
if index in [i for i in range(60, 1200, 60)]:
      s_list.append(list1)
      list1 = []
      continue

if index == 1200:
      s_list.append(list1)
      list1 = []
      break
#print(s_list)
#'''
a,b,c,d = 0,0,0,0
row = 0
result = []
res = 1
position = []
while (row + 1):
for column in range(20):
      #向右
      if column <= 16:
         res = int(s_list[row][column]) * int(s_list[row][column+1]) *\
               int(s_list[row][column+2]) * int(s_list[row][column+3])
         result.append(res)
         result = [max(result)]
         if res == max(result):
            position = []
            position.append(s_list[row][column])
            position.append(s_list[row][column+1])
            position.append(s_list[row][column+2])
            position.append(s_list[row][column+3])

         #向下
         res = int(s_list[row][column]) * int(s_list[row+1][column]) *\
               int(s_list[row+2][column]) * int(s_list[row+3][column])
         result.append(res)
         result = [max(result)]
         if res == max(result):
            position = []
            position.append(s_list[row][column])
            position.append(s_list[row+1][column])
            position.append(s_list[row+2][column])
            position.append(s_list[row+3][column])
            result = [max(result)]

         #向右下
         res = int(s_list[row][column]) * int(s_list[row+1][column+1]) *\
               int(s_list[row+2][column+2]) * int(s_list[row+3][column+3])
         result.append(res)
         result = [max(result)]
         if res == max(result):
            position = []
            position.append(s_list[row][column])
            position.append(s_list[row+1][column+1])
            position.append(s_list[row+2][column+2])
            position.append(s_list[row+3][column+3])

row += 1
if row == 17:
      break
a = position[0]
b = position[1]
c = position[2]
d = position[3]
e = result[0]
print("乘积最大的四个数字是：%s * %s * %s * %s = %s" % (a,b,c,d,e))

mathtimes · 发表于 2022-1-29 17:40:15

#include <cstdio>
int table[20][20] = 
{
    { 8, 2,22,97,38,15, 0,40, 0,75, 4, 5, 7,78,52,12,50,77,91, 8},
    {49,49,99,40,17,81,18,57,60,87,17,40,98,43,69,48, 4,56,62, 0},
    {81,49,31,73,55,79,14,29,93,71,40,67,53,88,30, 3,49,13,36,65},
    {52,70,95,23, 4,60,11,42,69,24,68,56, 1,32,56,71,37, 2,36,91},
    {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, 3,45, 2,44,75,33,53,78,36,84,20,35,17,12,50},
    {32,98,81,28,64,23,67,10,26,38,40,67,59,54,70,66,18,38,64,70},
    {67,26,20,68, 2,62,12,20,95,63,94,39,63, 8,40,91,66,49,94,21},
    {24,55,58, 5,66,73,99,26,97,17,78,78,96,83,14,88,34,89,63,72},
    {21,36,23, 9,75, 0,76,44,20,45,35,14, 0,61,33,97,34,31,33,95},
    {78,17,53,28,22,75,31,67,15,94, 3,80, 4,62,16,14, 9,53,56,92},
    {16,39, 5,42,96,35,31,47,55,58,88,24, 0,17,54,24,36,29,85,57},
    {86,56, 0,48,35,71,89, 7, 5,44,44,37,44,60,21,58,51,54,17,58},
    {19,80,81,68, 5,94,47,69,28,73,92,13,86,52,17,77, 4,89,55,40},
    { 4,52, 8,83,97,35,99,16, 7,97,57,32,16,26,26,79,33,27,98,66},
    {88,36,68,87,57,62,20,72, 3,46,33,67,46,55,12,32,63,93,53,69},
    { 4,42,16,73,38,25,39,11,24,94,72,18, 8,46,29,32,40,62,76,36},
    {20,69,36,41,72,30,23,88,34,62,99,69,82,67,59,85,74, 4,36,16},
    {20,73,35,29,78,31,90, 1,74,31,49,71,48,86,81,16,23,57, 5,54},
    { 1,70,54,71,83,51,54,69,16,92,33,48,61,43,52, 1,89,19,67,48}
};
int main()
{
    long long max = 0;
    for(int i=0;i<20;i++)
        for(int j=0;j<17;j++)
        {
            long long mul = 1;
            for(int k=j;k<j+4;k++)
                mul *= table[i][k];
            if(mul>max)
                max = mul;
        }
    for(int i=0;i<17;i++)
        for(int j=0;j<20;j++)
        {
            long long mul = 1;
            for(int k=i;k<i+4;k++)
                mul *= table[k][j];
            if(mul>max)
                max = mul;
        }
    for(int i=0;i<17;i++)
        for(int j=0;j<17;j++)
        {
            long long mul = 1;
            for(int k=0;k<4;k++)
                mul *= table[i+k][j+k];
            if(mul>max)
                max = mul;
        }
    for(int i=0;i<17;i++)
        for(int j=3;j<20;j++)
        {
            long long mul = 1;
            for(int k=0;k<4;k++)
                mul *= table[i+k][j-k];
            if(mul>max)
                max = mul;
        }
    printf("%lld",max);
}

B1tetheDust · 发表于 2022-3-22 11:25:02

本帖最后由 B1tetheDust 于 2022-3-22 11:26 编辑

It takes 0.002208 s
第 13 行，第 7 列，anti-diagonal 方向
70600674

import numpy as np
import time


def mult_em(row_num, col_num, row_f=0, col_f=0, direction=None):
    global maximum
    res = 1
    for i in range(4):
        res *= array1[row_num + i*row_f][col_num + i*col_f]
    if maximum < res:
        maximum = res
        position[0], position[1], position[2] = row_num, col_num, direction


str1 = '''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'''
list1 = [int(i) for i in str1.split()]
array1 = np.array(list1)
array1 = array1.reshape(20, 20)
maximum, position = 0, [0, 0, '0']
start = time.perf_counter()

for row in range(20):
    for col in range(20):
        if (row < 17) and (col < 17):
            mult_em(row, col, 1, 1, 'diagonal')
        if row < 17:
            mult_em(row, col, 1, 0, 'column')
        if col < 17:
            mult_em(row, col, 0, 1, 'row')
        if (row < 17) and (col > 2):
            mult_em(row, col, 1, -1, 'anti-diagonal')

print('It takes %f s' % (time.perf_counter() - start))
print('第 %d 行，第 %d 列，%s 方向' % (position[0] + 1, position[1] + 1, position[2]))
print(maximum)

Asss-whom · 发表于 2022-8-9 17:55:47

本帖最后由 Asss-whom 于 2022-8-9 17:58 编辑

pub fn run() -> Result<(), Box<dyn std::error::Error>> {
    let arr = [
        [
            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,
        ],
    ];
    let num = (0..4)
        .filter_map(|i| match i {
            0 => (0..20)
                .filter_map(|j| {
                    (0..17)
                        .map(|k| (0..4).map(|l| arr[j][k + l]).fold(1, |acc, x| acc * x))
                        .max()
                })
                .max(),
            1 => (0..17)
                .filter_map(|j| {
                    (0..20)
                        .map(|k| (0..4).map(|l| arr[j + l][k]).fold(1, |acc, x| acc * x))
                        .max()
                })
                .max(),
            2 => (0..17)
                .filter_map(|j| {
                    (0..17)
                        .map(|k| (0..4).map(|l| arr[j + l][k + l]).fold(1, |acc, x| acc * x))
                        .max()
                })
                .max(),
            3 => (3..20)
                .filter_map(|j| {
                    (0..17)
                        .map(|k| (0..4).map(|l| arr[j - l][k + l]).fold(1, |acc, x| acc * x))
                        .max()
                })
                .max(),
            _ => unreachable!(),
        })
        .max();
    println!("{:?}", num);
    Ok(())
}

[Project Euler 11]
Some(70600674)
[Task finished in 0.0003528s]

KeyError · 发表于 2023-1-13 14:06:42

口算2115927

Kazimierz · 发表于 2023-7-2 20:07:55

pixie99 · 发表于 2023-7-11 13:46:30

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题目11：在20×20的网格中同一直线上四个数的最大乘积是多少？

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