package problem11;

/*

Largest product in a grid

Problem 11

In the 20x20 grid below, four numbers along a diagonal line have been marked in red.

(grid shown below)

The product of these numbers is 26 x 63 x 78 x 14 = 1788696.

What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20x20 grid?

*/

public class GridProduct{

public static void main(String[] args){

int[][] gridArray =

{{8, 2, 22, 97, 38, 15, 0, 40, 0, 75, 04, 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, 03, 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, 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}};

// putting the numbers into gridArray

int maxProduct = 0;

// Left to right multiplication

for (int i = 0; i < 20; i++) {

for (int j = 0; j < 17; j++) {

int product = 1;

for (int k = 0; k < 4; k++) {

product = product * gridArray[i][j + k];

}

if (product > maxProduct) {

maxProduct = product;

}

}

}

// Up and down multiplcation

for (int i = 0; i < 17; i++) {

for (int j = 0; j < 20; j++) {

int product = 1;

for (int k = 0; k < 4; k++) {

product = product * gridArray[i + k][j];

}

if (product > maxProduct) {

maxProduct = product;

}

}

}

// Diagonal multiplication (\)

for (int i = 0; i < 17; i++) {

for (int j = 0; j < 17; j++) {

int product = 1;

for (int k = 0; k < 4; k++) {

product = product * gridArray[i + k][j + k];

}

if (product > maxProduct) {

maxProduct = product;

}

}

}

// Diagonal multiplication(/)

for (int i = 0; i < 17; i++) {

for (int j = 3; j < 20; j++) {

int product = 1;

for (int k = 0; k < 4; k++) {

product = product * gridArray[i + k][j - k];

}

if (product > maxProduct) {

maxProduct = product;

}

}

}

System.out.println(maxProduct);

} // end of main method

} // end of gridProduct