Problem 11

Problem 11
Filename: prob11.cc

//In the 2020 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 20x20 grid?
//
#include <iostream>

using namespace std;



int main()
{
  const int grid[20][20] =
    {
      { 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}
    };

  int max(0);

  // first calculate the horizontal products
  for(int row=0; row<20; ++row)
    {
      for(int col=0; col<16; ++col)
	{
	  const int working_num(grid[row][col] *
				grid[row][col+1] *
				grid[row][col+2] *
				grid[row][col+3]);
	  if(working_num > max)
	    {
	      cout << "MAX: " << working_num << endl << "\thor -> grid[" << row << "][" << col << "]" << endl;

	      max = working_num;
	    }
	}
    }
  
  // next calculate the vertical products
  for(int col=0; col<20; ++col)
    {
      for(int row=0; row<16; ++row)
	{
	  const int working_num(grid[row][col] *
				grid[row+1][col] *
				grid[row+2][col] *
				grid[row+3][col]);
	  if(working_num > max)
	    {
	      cout << "MAX: " << working_num << endl << "\tver -> grid[" << row << "][" << col << "]" << endl;

	      max = working_num;
	    }
	}
    }
  
  // next calculate the down/right diagnols
  for(int row=0; row<16; ++row)
    {
      for(int col=0; col<16; ++col)
	{
	  const int working_num(grid[row][col] *
				grid[row+1][col+1] *
				grid[row+2][col+2] *
				grid[row+3][col+3]);
	  if(working_num > max)
	    {
	      cout << "MAX: " << working_num << endl << "\tdr -> grid[" << row << "][" << col << "]" << endl;

	      max = working_num;
	    }
	}
    }

  // next calculate the up/right diagnols
  for(int row=3; row<20; ++row)
    {
      for(int col=0; col<16; ++col)
	{
	  const int working_num(grid[row][col] *
				grid[row-1][col+1] *
				grid[row-2][col+2] *
				grid[row-3][col+3]);
	  if(working_num > max)
	    {
	      cout << "MAX: " << working_num << endl << "\tur -> grid[" << row << "][" << col << "]" << endl;

	      max = working_num;
	    }
	}
    }
  


  return 0;
}

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