Largest product in a grid
Problem 11 Project Euler
In the 20×20 grid below, four numbers along a diagonal line have been marked in red.
08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 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 03 45 02 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 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
04 52 08 83 97 35 99 16 07 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
04 42 16 73 38 25 39 11 24 94 72 18 08 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
The product of these numbers is 26 × 63 × 78 × 14 = 1788696.
What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20×20 grid?
using System; using System.Collections.Generic; using System.IO; using System.Linq; class Solution { static void Main(String[] args) { int[][] grid = new int[20][]; for(int grid_i = 0; grid_i < 20; grid_i++){ string[] grid_temp = Console.ReadLine().Split(' '); grid[grid_i] = Array.ConvertAll(grid_temp,Int32.Parse); } Console.WriteLine(ProductOfNumbers(grid)); } static long ProductOfNumbers(int[][] grid) { long product = 0; for (int i = 0; i < grid.Length; i++) { for (int j = 0; j < grid.Length; j++) { var arr = new long[6]; var r = grid.Length-3; // Horizontally if (j < r) arr[0] = grid[i][j] * grid[i][j + 1] * grid[i][j + 2] * grid[i][j + 3]; // Vertically if (i < r) arr[1] = grid[i][j] * grid[i + 1][j] * grid[i + 2][j] * grid[i + 3][j]; // Diagonnally Right if (i < r && j < r) arr[2] = grid[i][j] * grid[i + 1][j + 1] * grid[i + 2][j + 2] * grid[i + 3][j + 3]; // Diagonnally if (i >= 3 && j >= 3 && i< r) { // Left Down arr[3] = grid[i][j] * grid[i + 1][j - 1] * grid[i + 2][j - 2] * grid[i + 3][j-3]; // Right Up if(j < r) arr[4] = grid[i][j]*grid[i-1][j+1]*grid[i-2][j+2]*grid[i-3][j+3]; } arr[5] = product; product = arr.Max(); } } return product; } }
Live Code On Ide One
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