C ++ ProjectEuler＃11
[英]C++ ProjectEuler #11
问题描述
I'm trying to solve the 11th problem on ProjectEuler.net. 
我正在尝试解决ProjectEuler.net上的第11个问题。 The goal for this problem is to find the largest product in a 20x20 grid of 4 adjacent numbers in any direction (up, down, right, left, diagonal). 此问题的目标是在任何方向（向上，向下，向右，向左，对角线）上找到4个相邻数字的20x20网格中的最大产品。
I'm using the BigInteger library because I don't know how large will the numbers be and I don't want an overflow - but I think this might be the problem. 我正在使用BigInteger库，因为我不知道数字有多大而我不想溢出 - 但我认为这可能是问题所在。 Every time I restart the program I get a different answer. 每次重新启动程序时，我都会得到不同的答案。 :/ I also tried to use an unsigned long long int just to see what will happen - the answer remained the same. ：/我也尝试使用unsigned long long int来看看会发生什么 - 答案保持不变。
This is the code (Nothing complicated; I just test every element in the grid to see if it has 3 adjacent numbers in any direction, compute the product and set it as the new largest if it is larger than the previous one. On the end I print the largest product.): 这是代码（没什么复杂的;我只测试网格中的每个元素，看看它是否在任何方向上有3个相邻的数字，计算产品并将其设置为新的最大值，如果它大于前一个。最后我打印最大的产品。）：
//NO.11
#include <iostream>
#include <BigIntegerLibrary.hh>
#include <windows.h>
int main()
{
int grid[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, 01, 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, 03, 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, 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, 4, 89, 55, 40},
{ 4, 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, 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, 04, 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}
};
BigInteger biggestProduct = 0;
//unsigned long long int biggestProduct = 0;
for (int row = 0; row < 20; row++)
{
for (int col = 0; col < 20; col++)
{
BigInteger product;
//unsigned long long int product;
//std::cout << grid[row][col] << ":" << std::endl; system("pause>nul");
//UP
if ((row-1 >= 0) && (row-2 >= 0) && (row-3 >= 0))
{
product = grid[row][col] * grid[row-1][col] * grid[row-2][col] * grid[row-3][col];
//std::cout << " U: " << grid[row][col] << "*" << grid[row-1][col] << "*" << grid[row-2][col] << "*" << grid[row-3][col] << "= \t" << product << std::endl; system("pause>nul");
if (product > biggestProduct)
biggestProduct = product;
}
//DOWN
if ((row+1 >= 0) && (row+2 >= 0) && (row+3 >= 0))
{
product = grid[row][col] * grid[row+1][col] * grid[row+2][col] * grid[row+3][col];
//std::cout << " D: " << grid[row][col] << "*" << grid[row+1][col] << "*" << grid[row+2][col] << "*" << grid[row+3][col] << "= \t" << product << std::endl; system("pause>nul");
if (product > biggestProduct)
biggestProduct = product;
}
//RIGHT
if ((col+1 >= 0) && (col+2 >= 0) && (col+3 >= 0))
{
product = grid[row][col] * grid[row][col+1] * grid[row][col+2] * grid[row][col+3];
//std::cout << " R: " << grid[row][col] << "*" << grid[row][col+1] << "*" << grid[row][col+2] << "*" << grid[row][col+3] << "= \t" << product << std::endl; system("pause>nul");
if (product > biggestProduct)
biggestProduct = product;
}
//LEFT
if ((col-1 >= 0) && (col-2 >= 0) && (col-3 >= 0))
{
product = grid[row][col] * grid[row][col-1] * grid[row][col-2] * grid[row][col-3];
//std::cout << " L: " << grid[row][col] << "*" << grid[row][col-1] << "*" << grid[row][col-2] << "*" << grid[row][col-3] << "= \t" << product << std::endl; system("pause>nul");
if (product > biggestProduct)
biggestProduct = product;
}
//UP-RIGHT
if ((row-1 >= 0) && (row-2 >= 0) && (row-3 >= 0) && (col+1 >= 0) && (col+2 >= 0) && (col+3 >= 0))
{
product = grid[row][col] * grid[row-1][col+1] * grid[row-2][col+2] * grid[row-3][col+3];
//std::cout << " U-R: " << grid[row][col] << "*" << grid[row-1][col+1] << "*" << grid[row-2][col+2] << "*" << grid[row-3][col+3] << "= \t" << product << std::endl; system("pause>nul");
if (product > biggestProduct)
biggestProduct = product;
}
//DOWN-RIGHT
if ((row+1 >= 0) && (row+2 >= 0) && (row+3 >= 0) && (col+1 >= 0) && (col+2 >= 0) && (col+3 >= 0))
{
product = grid[row][col] * grid[row+1][col+1] * grid[row+2][col+2] * grid[row+3][col+3];
//std::cout << " D-R: " << grid[row][col] << "*" << grid[row+1][col+1] << "*" << grid[row+2][col+2] << "*" << grid[row+3][col+3] << "= \t" << product << std::endl; system("pause>nul");
if (product > biggestProduct)
biggestProduct = product;
}
//DOWN-LEFT
if ((row+1 >= 0) && (row+2 >= 0) && (row+3 >= 0) && (col-1 >= 0) && (col-2 >= 0) && (col-3 >= 0))
{
product = grid[row][col] * grid[row+1][col-1] * grid[row+2][col-2] * grid[row+3][col-3];
//std::cout << " D-L: " << grid[row][col] << "*" << grid[row+1][col-1] << "*" << grid[row+2][col-2] << "*" << grid[row+3][col-3] << "= \t" << product << std::endl; system("pause>nul");
if (product > biggestProduct)
biggestProduct = product;
}
//UP-LEFT
if ((row-1 >= 0) && (row-2 >= 0) && (row-3 >= 0) && (col-1 >= 0) && (col-2 >= 0) && (col-3 >= 0))
{
product = grid[row][col] * grid[row-1][col-1] * grid[row-2][col-2] * grid[row-3][col-3];
//std::cout << " U-L: " << grid[row][col] << "*" << grid[row-1][col-1] << "*" << grid[row-2][col-2] << "*" << grid[row-3][col-3] << "= \t" << product << std::endl; system("pause>nul");
if (product > biggestProduct)
biggestProduct = product;
}
}
}
std::cout << biggestProduct;
return 0;
}
Does anyone know what's wrong? 有谁知道什么是错的？
Thanks, Tuntuni. 谢谢，Tuntuni。
3 个解决方案
解决方案1
6 已采纳 2012-07-03 14:49:18
your problem are your range checks: 你的问题是你的范围检查：
example: 例：
// DOWN
if ((row+1 >= 0) && (row+2 >= 0) && (row+3 >= 0))
should be: 应该：
// DOWN
//if ((row+1 < 20 ) && (row+2 < 20 ) && (row+3 < 20 ))
//which still contains redundant comparisons (as pointed out by Blastfurnace),
//and thus can be can be simplified to :
if( row + 3 < 20 )
If you have random results on each run for a program, and you dont use concurrency, random number generators or something like that, most likely that randomness i caused by undefined behaviour like reading unallocated memory or reading using unintialised variables. 如果你在程序的每次运行中都有随机结果，并且你不使用并发，随机数生成器或类似的东西，很可能是由未定义的行为引起的随机性，如读取未分配的内存或使用未初始化的变量读取。
解决方案2
2 2012-07-03 14:49:15
Looks like you're reading off the bottom and right edges: 看起来你正在阅读底部和右边：
if ((row+1 >= 0) && (row+2 >= 0) && (row+3 >= 0))
if ((col+1 >= 0) && (col+2 >= 0) && (col+3 >= 0))
and the same test with the diagonals. 和对角线一样的测试。
You should be checking that the index doesn't reach 20. 您应该检查索引是否达到20。
解决方案3
0 2014-02-19 08:45:21
visit this link for code http://codingloverlavi.blogspot.in/2013/06/project-euler-solution-11.html 访问此链接获取代码http://codingloverlavi.blogspot.in/2013/06/project-euler-solution-11.html
#include<stdio.h>
#include<conio.h>
#include<stdlib.h>
long find_max(int **);
int main()
{
FILE *f;
int **arr,i=0,j;
arr=(int **)malloc(sizeof(int*)*20);
for(i=0;i<20;i++)
arr[i]=(int *)malloc(sizeof(int)*20);
f=fopen("D:/b.txt","r");
if(f)
for(i=0;i<20;i++)
for(j=0;j<20;j++)
fscanf(f,"%d",&arr[i][j]);
else
printf("file operation not successful\n");
printf("Answer = %ld\n",find_max(arr));
system("pause");
}
long find_max(int **arr)
{
int i,j,k;
long product,max=0;
for(i=0;i<20;i++)
for(j=0;j<20;j++)
{
/*checking for horizontal sequence*/
product=1;
for(k=0;k<4;k++)
{
if(j+k<20)
{
product*=arr[i][j+k];
}
}
if(product>max)
max=product;
/*checking for vertical sequence*/
product=1;
for(k=0;k<4;k++)
{
if(i+k<20)
{
product*=arr[i+k][j];
}
}
if(product>max)
max=product;
product=1;
for(k=0;k<4;k++)
{
if( (i+k<20) && (j+k<20) )
{
product*=arr[i+k][j+k];
}
}
if(product>max)
max=product;
product=1;
for(k=0;k<4;k++)
{
if( (i+k<20) && (j-k>0) )
{
product*=arr[i+k][j-k];
}
}
if(product>max)
max=product;
}
return max;
}
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