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#include <iostream>
const unsigned long long 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, 4,49,13,36,65},
{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, 4,45, 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, 4,80, 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, 4,46,33,67,46,55,12,32,63,93,53,69},
{ 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()
{
unsigned long long maxh = 0, maxv = 0, maxx = 0;
for(int r = 0; r < 20; ++r)
{
for(int c = 0; c < 20; ++c)
{
unsigned long long hsum = 0, vsum = 0, xsum = 0;
if(c < 10 && r < 10) // start in top left quad
{
hsum = grid[r][c] * grid[r][c+1] * grid[r][c+2] * grid[r][c+3]; // sum left to right
vsum = grid[r][c] * grid[r+1][c] * grid[r+2][c] * grid[r+3][c]; // sum top to bottom
xsum = grid[r][c] * grid[r+1][c+1] * grid[r+2][c+2] * grid[r+3][c+3]; // sum down right diagonally
} else {
if(c < 10 && r > 9) // start in bottom left quad
{
hsum = grid[r][c] * grid[r][c+1] * grid[r][c+2] * grid[r][c+3]; // sum left to right
vsum = grid[r][c] * grid[r-1][c] * grid[r-2][c] * grid[r-3][c]; // sum bottom to top
xsum = grid[r][c] * grid[r-1][c+1] * grid[r-2][c+2] * grid[r-3][c+3]; // sum up right diagonally
} else {
if(c > 9 && r < 10) // start in top right quad
{
hsum = grid[r][c] * grid[r][c-1] * grid[r][c-2] * grid[r][c-3]; // sum right to left
vsum = grid[r][c] * grid[r+1][c] * grid[r+2][c] * grid[r+3][c]; // sum top to bottom
xsum = grid[r][c] * grid[r+1][c-1] * grid[r+2][c-2] * grid[r+3][c-3]; // sum down left diagonally
} else { // start in bottom right quad
hsum = grid[r][c] * grid[r][c-1] * grid[r][c-2] * grid[r][c-3]; // sum right to left
vsum = grid[r][c] * grid[r-1][c] * grid[r-2][c] * grid[r-3][c]; // sum bottom to top
xsum = grid[r][c] * grid[r-1][c-1] * grid[r-2][c-2] * grid[r-3][c-3]; // sum up left diagonally
}
}
}
maxh = (hsum < maxh) ? maxh : hsum;
maxv = (vsum < maxv) ? maxv : vsum;
maxx = (xsum < maxx) ? maxh : xsum;
}
}
unsigned long long max = (maxh > maxv) ? ((maxh > maxx) ? maxh : maxx) : ((maxx > maxv) ? maxx : maxv);
std::cout << "The greatest product of four adjacent numbers in any direction on the grid is: " << max << std::endl;
return 0;
}
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