Products on a grid
Published on Saturday, July 23, 2011This one was trivial. The problem reads:
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 any direction (up, down, left, right, or diagonally) in the 20×20 grid?
It took more code than the previous problems, but it was almost all boilerplate, splitting and parsing strings and typing and retyping i and j.
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
namespace Problem011
{
class Program
{
static void Main(string[] args)
{
string[] numGrid = {"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"};
int[,] eulerGrid = new int[20, 20];
string[] tempGrid = new string[20];
int[] products = new int[4];
int maxProduct = 1;
for (int i = 0; i < 20; i++)
{
tempGrid = numGrid[i].Split();
for (int j = 0; j < 20; j++)
{
eulerGrid[i, j] = Int32.Parse(tempGrid[j]);
}
}
tempGrid = null;
numGrid = null;
for (int i = 0; i < 20; i++)
{
for (int j = 0; j < 20; j++)
{
if (i < 17)
{
products[0] = eulerGrid[i, j] * eulerGrid[i + 1, j] *
eulerGrid[i + 2, j] * eulerGrid[i + 3, j];
}
if (j < 17)
{
products[1] = eulerGrid[i, j] * eulerGrid[i, j + 1] *
eulerGrid[i, j + 2] * eulerGrid[i, j + 3];
}
if ((i < 17) && (j < 17))
{
products[2] = eulerGrid[i, j] * eulerGrid[i + 1, j + 1] *
eulerGrid[i + 2, j + 2] * eulerGrid[i + 3, j + 3];
}
if ((i > 2) && (j < 17))
{
products[3] = eulerGrid[i, j] * eulerGrid[i - 1, j + 1] *
eulerGrid[i - 2, j + 2] * eulerGrid[i - 3, j + 3];
}
if (products.Max() > maxProduct)
{
maxProduct = products.Max();
}
}
}
Console.WriteLine("The largest product of four adjacent numbers on the grid is {0}", maxProduct);
}
}
}