# 11 Largest Product in a Grid

In the 20×20 grid below, four numbers along a diagonal line have been marked in red.
Note from the author: My goal when writing this program was to encapsulate a universal solution to the problem. Depending on the 3 parameters you change in the program:
#define WIDTH 20 // Specifies the columns of the array of numbers
#define HEIGHT 20 //Specifies the rows of the array of numbers
int adjacentNumbers = 4; //Specifies the amount of adjacent numbers you wish to multiply.
Given these arbitrary set of parameters, you should be able to find the solution of an arbitrary table.
#include <iostream>
#include <limits>
#include <vector>
using namespace std;
void pause() { cin.ignore(numeric_limits<streamsize>::max(), '\n'); }
vector <int> thedigits = { 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 };
// Special debug case:
//vector <int> thedigits = { 1, 2, 3, 4, 5, 6,
// 7, 8, 9, 10, 11, 12,
// 13, 14, 15, 16, 17, 18,
// 19, 20, 21, 22, 23, 24,
// 25, 26, 27, 28, 29, 30,
// 31, 32, 33, 34, 35, 36 };
//
#define WIDTH 20
#define HEIGHT 20
vector <long long int> searchLeftandRight()
{
int nextRow = 0;
int goUntil = 4;
int rowsThatFit = WIDTH - adjacentNumbers + 1;
int rowsThatFitCounter = 0;
vector < long long int > products;
long long int product = 1;
/*vector <int> thedigits = { 1, 2, 3, 4, 5,
6, 7, 8, 9, 10,
11, 12, 13, 14, 15,
16, 17, 18, 19, 20,
21, 22, 23, 24, 25 };*/
while (1)
{
if (rowsThatFitCounter == rowsThatFit)
{
nextRow = goUntil - 1;
goUntil = nextRow + 4;
rowsThatFitCounter = 0;
}
if (nextRow >= WIDTH * HEIGHT)
{
break;
}
for (int i = nextRow; i < goUntil; i++)
{
product *= thedigits[i];
}
products.push_back(product);
product = 1;
rowsThatFitCounter++;
nextRow++;
goUntil++;
}
return products;
}
vector <long long int> searchUpandDown()
{
int nextGeneration = 0;
int nextColumnSupporter = 0;
int start = 0;
int columnsThatFit = HEIGHT - adjacentNumbers + 1;
int columnsThatFitCounter = 0;
vector < long long int > products;
long long int product = 1;
/*vector <int> thedigits = { 1, 2, 3, 4, 5,
6, 7, 8, 9, 10,
11, 12, 13, 14, 15,
16, 17, 18, 19, 20,
21, 22, 23, 24, 25 };*/
while (1)
{
if (columnsThatFitCounter == columnsThatFit)
{
nextColumnSupporter = 0;
start = 0;
nextGeneration++;
columnsThatFitCounter = 0;
}
if (nextGeneration >= WIDTH)
{
break;
}
for (int i = 0; i < adjacentNumbers; i++)
{
product *= thedigits[nextColumnSupporter + nextGeneration + start];
nextColumnSupporter += WIDTH;
}
products.push_back(product);
product = 1;
nextColumnSupporter = 0;
start += WIDTH;
columnsThatFitCounter++;
}
return products;
}
vector <long long int> searchRightDiagonal()
{
int totaldiagNeeded = (WIDTH - adjacentNumbers + 1) * (HEIGHT - adjacentNumbers + 1);
int totaldiagCounter = 0;
int nextDiagonal = 0;
int nextDiagonalMultiplier = 0;
int diagonalsThatFit = HEIGHT - adjacentNumbers + 1;
int diagonalsThatFitCounter = 0;
int nextDiagonalSupporter = 0;
vector < long long int > products;
long long int product = 1;
while (1)
{
if (nextDiagonalSupporter == diagonalsThatFit)
{
nextDiagonalMultiplier++;
nextDiagonalSupporter = 0;
}
if (totaldiagCounter == totaldiagNeeded + 1) break;
for (int i = 0; i < adjacentNumbers; i++)
{
product *= thedigits[nextDiagonal + nextDiagonalSupporter];
nextDiagonal += WIDTH + 1;
}
products.push_back(product);
//cout << product << endl;
product = 1;
nextDiagonal = HEIGHT * nextDiagonalMultiplier;
totaldiagCounter++;
diagonalsThatFitCounter++;
nextDiagonalSupporter++;
}
return products;
}
vector <long long int> searchLeftDiagonal()
{
int totaldiagNeeded = (WIDTH - adjacentNumbers + 1) * (HEIGHT - adjacentNumbers + 1);
int totaldiagCounter = 0;
int nextDiagonal = 3;
int nextDiagonalMultiplier = 0;
int diagonalsThatFit = HEIGHT - adjacentNumbers + 1;
int diagonalsThatFitCounter = 0;
int nextDiagonalSupporter = 0;
vector < long long int > products;
long long int product = 1;
while (1)
{
if (nextDiagonalSupporter == diagonalsThatFit)
{
nextDiagonalMultiplier++;
nextDiagonalSupporter = 0;
}
if (totaldiagCounter == totaldiagNeeded + 1) break;
for (int i = 0; i < adjacentNumbers; i++)
{
product *= thedigits[nextDiagonal + nextDiagonalSupporter];
nextDiagonal += WIDTH - 1;
}
products.push_back(product);
//cout << product << endl;
product = 1;
nextDiagonal = HEIGHT * nextDiagonalMultiplier + 3;
totaldiagCounter++;
diagonalsThatFitCounter++;
nextDiagonalSupporter++;
}
return products;
}
long long int findmax(vector<long long int> someVectorProduct)
{
long long int max = someVectorProduct[0];
for (int i = 1; i < someVectorProduct.size(); i++)
{
if (someVectorProduct[i] > max)
{
max = someVectorProduct[i];
}
}
return max;
}
int main()
{
long long int maxLeftorRight = findmax(searchLeftandRight());
long long int maxUporDown = findmax(searchUpandDown());
long long int maxRightDiagonal = findmax(searchRightDiagonal());
long long int maxLeftDiagonal = findmax(searchLeftDiagonal());
cout << "Select the largest number from the following as the solution: " << endl;
cout << maxLeftorRight << endl;
cout << maxUporDown << endl;
cout << maxRightDiagonal << endl;
cout << maxLeftDiagonal << endl;
pause();
}
Solution: 70600674