Monday, October 21, 2013

Largest product in a grid algorithm implementation in C#

Hi,
A few days ago I started practicing in  problem solving. I've picked projecteuler for this purpose.
I think it would be great to share some interesting solutions in my blog.

Problem 11. Largest product in a grid
Nothing special, just a good example   to show you a complex "for" loop, nothing else.
So here is algorithm:

  • Do loop through matrix, for each cell
    • Calculate horizontal product and check if it's largest product for now
    • Calculate vertical product and check if it's largest product for now
    • Calculate Right diagonal and check if it's largest product for now
    • Calculate left diagonal and check if it's largest product for now



using System;

namespace LargestProductInGrid
{
 public class Solver
 {
  private int largestProduct=Int32.MinValue;
  private const int SIZE=20;
  private const int COUNT=4;
  private int[,] m=new int[SIZE,SIZE]
{{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}};
  
  
  public Solver ()
  {
  }
  
  public int GetLargestProductInGrid()
  {
   int tmp=0;
   for(int i=0; i<SIZE; i++)
    for(int j=0; j<SIZE; j++)
    {
    tmp=this.HorizontalProduct(i,j);
    if(tmp>this.largestProduct)
     this.largestProduct=tmp;
    
    
    tmp=this.VerticalProduct(i,j);
    if(tmp>this.largestProduct)
     this.largestProduct=tmp;
    
    
    tmp=this.DiagonalRight(i,j);
    if(tmp>this.largestProduct)
     this.largestProduct=tmp;
    
    
    tmp=this.DiagonalLeft(i,j);
    if(tmp>this.largestProduct)
     this.largestProduct=tmp;
    
    
    }
   
   return this.largestProduct; 
  }
  
  private int HorizontalProduct(int i, int j)
  {
   int result=1;
   for(int k=i; (k<i+COUNT &&k<SIZE); k++)
    result=result*m[j,k];
   
   return result;
  }
  
  //[column, row]
  private int DiagonalRight(int i, int j)
  {
   int result=1;
   for (int n=i, k=j;  (n<i+COUNT &&n<SIZE && k<j+COUNT &&k<SIZE); n++, k++)
    result=result*m[n,k];
   return result;
  }
  
  //[column, row]
  private int DiagonalLeft(int i, int j)
  {
   int result=1;
   for (int n=i, k=j;  (n>i-COUNT &&n<SIZE && n>0 && k<j+COUNT &&k<SIZE); n--, k++)
    result=result*m[n,k];
   return result;
  }
  
  private int VerticalProduct(int i, int j)
  {
   int result=1;
   for(int k=i; (k<i+COUNT &&k<SIZE); k++)
    result=result*m[k,j];
   return result;
  }
 }
}


That's all, feel free  post your comments.





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