WCW

# Project Euler Problem 11

The problem:

Find the largest product of 4 adjacent numbers in a 20×20 grid. Numbers can be adjacent in any direction, vertical, horizontal, diagonal.

http://projecteuler.net/problem=11

My solution (in java):

```
// Author: Will Clausen
//
// Date: Jan. 16, 2013
//
// This program will solve Problem 11 from Project Euler.

import java.util.Scanner;

public class Problem11 {
// Grid to store all the numbers
int[][] grid;
// The number of adjacent numbers to use when looking for the maximum
// Grid dimensions
int gridWidth;
int gridHeight;

// To make my solution a little more general, I allow for the specification
// of the size of the grid and the number of adjacent entries in the matrix
// to consider.
Problem11(String input, int gw, int gh, int limit)
{
// Assign variables according to proper input.
gridWidth = gw;
gridHeight = gh;

// Create scanner for reading from the input string.
Scanner scanner = new Scanner(input);
Scanner line;

grid = new int[gridHeight][gridWidth];

// Variables for indexing into the grid when inserting numbers
int widthIndex = 0;
int heightIndex = 0;

// While there are still things to read from the input.
while (scanner.hasNextLine()) {

// Get the next line of numbers for the grid
line = new Scanner(scanner.nextLine());

// Take the numbers out of the line and put them in the grid.
while (line.hasNextInt()) {
int nextNum = line.nextInt();
grid[heightIndex][widthIndex] = nextNum;

// Update the indexing accordingly
widthIndex++;
}

// Update indexing accordingly
widthIndex = 0;
heightIndex++;
line.close();
}

// Remember to close the scanner.
scanner.close();

// Method to ensure everything was inputted properly.
printGrid();
}

// Method to actually solve problem 11.
public int solve()
{
int maxProd = 1;

// Initialize the next product to be checked to the mulitplicative identity.
int nextProd = 1;

// Arrays to keep track of the most recent numbers seen.

// To simplify things, loop through the array in different directions
// using multiple loops. It adds computation time, but it makes much
// more sense conceptually.

// get maximum horizontal product
for (int i = 0; i < gridHeight; i++) {
for (int j = 0; j <= (gridWidth - numAdjacent); j++) {
for (int k = j; k < (numAdjacent + j); k++) {
}
nextProd = calcProd(horiz);
if (nextProd > maxProd) {
maxProd = nextProd;
System.out.println("New max product is: " + maxProd);
System.out.print("The array is: ");
printArray(horiz);
max = horiz;
printArray(max);
}
}
}

System.out.print("The final horizontal array is: ");
printArray(horiz);

// get the maximum vertical product
for (int i = 0; i < gridWidth; i++) {
for (int j = 0; j <= (gridHeight - numAdjacent); j++) {
for (int k = j; k < (numAdjacent + j); k++) {
}
nextProd = calcProd(vert);
if (nextProd > maxProd) {
maxProd = nextProd;
System.out.println("New max product is: " + maxProd);
System.out.print("The array is: ");
printArray(vert);
max = vert;
printArray(max);
}
}
}

System.out.print("The final vertical array is: ");
printArray(vert);

// get the maximum diagonal product (down and to the right)
for (int i = 0; i <= (gridWidth - numAdjacent); i++) {
for (int j = 0; j <= (gridHeight - numAdjacent); j++) {
for (int k = 0; k < (numAdjacent); k++) {
diag[k] = grid[i + k][j + k];
}
nextProd = calcProd(diag);
if (nextProd > maxProd) {
maxProd = nextProd;
System.out.println("New max product is: " + maxProd);
System.out.print("The array is: ");
printArray(diag);
max = diag;
printArray(max);
}
}
}
System.out.print("The final diagonal array is: ");
printArray(diag);

// get the maximum diagonal product (up to the right)
for (int i = numAdjacent-1; i < gridHeight; i++) {
for (int j = 0; j <= (gridWidth - numAdjacent); j++) {
for (int k = 0; k < numAdjacent; k++) {
diag2[k] = grid[i - k][j + k];
}
nextProd = calcProd(diag2);
if (nextProd > maxProd) {
maxProd = nextProd;
System.out.println("New max product is: " + maxProd);
System.out.print("The array is: ");
printArray(diag2);
max = diag2;
printArray(max);
}
}
}

int finalProd = calcProd(max);
System.out.println("The product of the final array is: " + finalProd);
printArray(max);

return maxProd;
}

// Helper method for calculating the product of numbers in an array.
public int calcProd(int[] nums)
{
int prod = 1;

for (int i = 0; i < nums.length; i++) {
if (nums[i] == 0) {
return 0;
} else {
prod *= nums[i];
}
}

return prod;
}

// Helper method for printing the contents of an array of numbers in a nice way.
public static void printArray(int[] numArray)
{
System.out.print("[");
for (int i = 0; i < numArray.length; i++) {
System.out.print(numArray[i] + ", ");
}
System.out.println("]");
}

// Helper method for printing a gird of numbers in a nice way.
public void printGrid()
{
for (int i = 0; i < gridHeight; i++) {
System.out.print("[");
for(int j = 0; j < gridWidth; j++) {
System.out.print(grid[i][j] + ", ");
}
System.out.println("]");
}
}

/**
* @param args
*/
public static void main(String[] args) {
Problem11 prob11 = new Problem11("08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08 \n" +
"49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00 \n" +
"81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65 \n" +
"52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91 \n" +
"22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80 \n" +
"24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50 \n" +
"32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70 \n" +
"67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21 \n" +
"24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72 \n" +
"21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95 \n" +
"78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92 \n" +
"16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57 \n" +
"86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58 \n" +
"19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40 \n" +
"04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66 \n" +
"88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69 \n" +
"04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36 \n" +
"20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16 \n" +
"20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54 \n" +
"01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48", 20, 20, 4);
int solution = prob11.solve();
System.out.println("The solution is: " + solution);
}

}

```