我正在尝试遍历 20x20 网格并计算产品,但总是得到不正确的结果。你能帮忙发现我的错误吗?
I'm trying to traverse through a 20x20 grid and calculate products, but I keep getting incorrect results. Can you help spot my error(s)?
这是欧拉项目的问题11。 它给出了一个 20x20 的数字网格并询问:
20x20 网格中任意方向(向上、向下、向左、向右或对角线)的四个相邻数字的最大乘积是多少?
我已经查看了几次我的代码,但我似乎找不到为什么我的结果不正确。
#include <iostream>
using namespace std;
void find_greatest_product()
{
int grid[20][20] =
{{8, 02, 22, 97, 38, 15, 00, 40, 00, 75, 04, 05, 07, 78, 52, 12, 50, 77, 91, 8},
{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, 8, 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, 9, 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, 9, 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, 8, 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, 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, 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}};
int downRight_diag = 1;
int upRight_diag = 1;
int left = 1;
int right = 1;
int up = 1;
int down = 1;
int firstMax = 0;
int absoluteMax = 0;
for(int i = 0; i < 20; i++)
{
for(int j = 0; j < 20; j++)
{
for(int k = i; k < 17; k++)
{
downRight_diag = grid[i][j]*grid[i+1][j+1]*grid[i+2][j+2]*grid[i+3][j+3];
down = grid[i][j]*grid[i+1][j]*grid[i+2][j]*grid[i+3][j];
if(downRight_diag > down && downRight_diag > firstMax)
firstMax = downRight_diag;
else if(down > downRight_diag && down > firstMax)
firstMax = down;
}
for(int l = i; l >= 3 && l < 20; l++)
{
upRight_diag = grid[i][j]*grid[i-1][j+1]*grid[i-2][j+2]*grid[i-3][j+3];
up = grid[i][j]*grid[i-1][j]*grid[i-2][j]*grid[i-3][j];
if(upRight_diag > firstMax)
firstMax = upRight_diag;
else if(up > firstMax)
firstMax = up;
}
if(j < 17)
{
left = grid[i][j]*grid[i][j+1]*grid[i][j+2]*grid[i][j+3];
if(left > firstMax)
firstMax = left;
}
if(j >= 3)
{
right = grid[i][j]*grid[i][j-1]*grid[i][j-2]*grid[i][j-3];
if(right > firstMax)
firstMax = right;
}
if(firstMax > absoluteMax)
{
absoluteMax = firstMax;
}
downRight_diag = 1;
upRight_diag = 1;
left = 1;
right = 1;
up = 1;
down = 1;
firstMax = 0;
}
}
cout << absoluteMax << endl;
}
int main()
{
find_greatest_product();
system("pause");
}
澄清一下:left
从左到右计算产品,从右到左计算right
。
我知道这可能不是最有效的方法,但我仍然希望得到一些反馈。 谢谢!
正如 MRAB 所回答的那样,这很可能是由于数组溢出。
我注意到的另一件事(但由于冗余计算可能不是问题)是这样的:
if(upRight_diag > firstMax)
firstMax = upRight_diag;
else if(up > firstMax)
firstMax = up;
如果两者都大于firstMax
并且恰好是全局最大值up
那么您将错过它。 但这很奇怪,因为up
是多余的(由前面的down
处理)。
我要作一些一般性评论。 首先,为什么要在向上/向下测试中多次循环? 您甚至没有使用循环变量。 你只是想测试边界(事实上你没有这样做)。 此外,当您已经在计算right
时,无需计算left
。 与我已经提到的up
和down
相同。
下面是计算水平、垂直和两个对角线的简化:
for(int i = 0; i < 20; i++)
{
for(int j = 0; j < 20; j++)
{
int horz=0, vert=0, diagDR=0, diagUR=0;
if( j >= 3 )
horz = grid[i][j-3]*grid[i][j-2]*grid[i][j-1]*grid[i][j];
if( i >= 3 )
vert = grid[i-3][j]*grid[i-2][j]*grid[i-1][j]*grid[i][j];
if( i >= 3 && j >= 3 ) {
diagDR = grid[i-3][j-3]*grid[i-2][j-2]*grid[i-1][j-1]*grid[i][j];
diagUR = grid[i-3][j]*grid[i-2][j-1]*grid[i-1][j-2]*grid[i][j-3];
}
if( horz > absoluteMax ) absoluteMax = horz;
if( vert > absoluteMax ) absoluteMax = vert;
if( diagDR > absoluteMax ) absoluteMax = diagDR;
if( diagUR > absoluteMax ) absoluteMax = diagUR;
}
}
更笼统(不要假设它总是连续 4 个,或者总是 20 个)。 http://codepad.org/YkrT72kR 我得到了
70600674 (3,15) 处,对角线左下角线
#include <iostream>
#include <inttypes.h>
const uint8_t HEIGHT = 20;
const uint8_t WIDTH = 20;
const uint8_t CONSECUTIVE = 4;
const int GRID[HEIGHT][WIDTH] =
{{8, 02, 22, 97, 38, 15, 00, 40, 00, 75, 04, 05, 07, 78, 52, 12, 50, 77, 91, 8},
{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, 8, 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, 9, 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, 9, 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, 8, 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, 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, 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}};
int main()
{
uint64_t max = 0, temp_max = 0;
uint16_t max_x=0, max_y=0;
std::string direction = "";
for (uint8_t i=0; i<HEIGHT; i++)
{
for (uint8_t j=0; j<WIDTH; j++)
{
// Can we check right?
if (j < (WIDTH - CONSECUTIVE))
{
temp_max=1;
for (int k=0; k<CONSECUTIVE; k++)
{
temp_max *= GRID[i][j+k];
}
if (temp_max > max)
{
max = temp_max;
max_x = j;
max_y = i;
direction = "right";
}
}
// Can we check down?
if (i < (WIDTH - CONSECUTIVE))
{
temp_max=1;
for (int k=0; k<CONSECUTIVE; k++)
{
temp_max *= GRID[i+k][j];
}
if (temp_max > max)
{
max = temp_max;
max_x = j;
max_y = i;
direction = "down";
}
}
// Can we check down-right?
if ((i < (HEIGHT - CONSECUTIVE)) && (j < (WIDTH - CONSECUTIVE)))
{
temp_max=1;
for (int k=0; k<CONSECUTIVE; k++)
{
temp_max *= GRID[i+k][j+k];
}
if (temp_max > max)
{
direction = "diagonal down right";
max = temp_max;
max_x = j;
max_y = i;
}
}
// Can we check up-right?
if ((i > (CONSECUTIVE)) && (j < (WIDTH - CONSECUTIVE)))
{
temp_max=1;
for (int k=0; k<CONSECUTIVE; k++)
{
temp_max *= GRID[i-k][j+k];
}
if (temp_max > max)
{
direction = "diagonal up right";
max = temp_max;
max_x = j;
max_y = i;
}
}
}
}
std::cout << "Max product was " << max << " at (" << max_x << "," << max_y << ") in direction " << direction << std::endl;
return 0;
}
不错的小挑战。 请记住,检查向上,向左,向左诊断,向右诊断是不必要的。 如前所述,始终检查数组边界
这是因为您没有检查数组边界。
例如,当 i
为 19 且 j
为 0 时,您将有 downRight_diag = grid[19][0]*grid[20][1]*grid[21][2]*grid[22][3];
,但grid
定义为 int grid[20][20]
。
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