Problem11.java

/*
* Prompt: What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20×20 grid?
*
* Execute: javac Problem11.java; java Problem11; rm Problem11.class
*
* Answer: 70600674
*/
public class Problem11 {
  public static final int[][] grid = {
    { 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}
  };

  public static void main(String[] args) {
    int greatestProduct = 0;
    for (int i = 0; i < grid.length; i++) {
      for (int j = 0; j < grid[i].length - 3; j++) {
        // Product left to right
        int product = grid[i][j] * grid[i][j + 1] * grid[i][j + 2] * grid[i][j + 3];
        if (product > greatestProduct) {
          greatestProduct = product;
        }
        // Product top to bottom
        product = grid[j][i] * grid[j + 1][i] * grid[j + 2][i] * grid[j + 3][i];
        if (product > greatestProduct) {
          greatestProduct = product;
        }
      }
    }
    for (int i = 0; i < grid.length - 3; i++) {
      for (int j = 0; j < grid[i].length - 3; j++) {
        // Product diagonally upper left to lower right
        int product = grid[i][j] * grid[i + 1][j + 1] * grid[i + 2][j + 2] * grid[i + 3][j + 3];
        if (product > greatestProduct) {
          greatestProduct = product;
        }
      }
    }
    for (int i = 3; i < grid.length; i++) {
      for (int j = 0; j < grid[i].length - 3; j++) {
        // Diagonally (2)
        int product = grid[i][j] * grid[i - 1][j + 1] * grid[i - 2][j + 2] * grid[i - 3][j + 3];
        if (product > greatestProduct) {
          greatestProduct = product;
        }
      }
    }
    System.out.println(greatestProduct);
  }
}