Grid Matrix!

I’ve been busy with projects for the lab, but I got the chance to do one quick coding challenge this weekend. The challenge presented a 20 X 20 matrix of numbers, and asked:

What is the greatest product of four adjacent numbers in any direction (up, down, left, right, or diagonally) in the 20×20 grid?

As an example, the numbers 26, 63, 78, and 14 were highlighted in red.

I particularly like this challenge because it’s very cut and dry. I know that if I create an algorithm that goes through all the possibilities, I will undoubtedly find the answer! And I had to use matlab for this one… because it is the Matrix Laboratory! It was a nice little bit of fun after a Sunday filled with running analysis and practicing a journal club presentation. Ok, I know, I shouldn’t try to deceive anyone that I suffered though that. I very much enjoyed both those things, otherwise I wouldn’t have chosen to do them!

function grid_product()
%--------------------------------------------------------------------------
% This function finds the greatest product for any four diagonal, vertical,
% or horizontal numbers in a 20 X 20 grid
%--------------------------------------------------------------------------

% Read in the grid matrix
grid_matrix ={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;};

highestproduct = 0;

% DIAGONAL RIGHT: Go through the grid, and for each spot, find the product of the diagonal.
for i=1:17

for j=1:17
product = grid_matrix{i,j}*grid_matrix{i+1,j+1}*grid_matrix{i+2,j+2}*grid_matrix{i+3,j+3};
if (product > highestproduct)
highestproduct = product;
end
end
end

% RIGHT and LEFT: Go through the grid, and for each spot, find the % product of horizontal numbers.
for i=1:20
for j=1:17
product = grid_matrix{i,j}*grid_matrix{i,j+1}*grid_matrix{i,j+2}*grid_matrix{i,j+3};
if (product > highestproduct)
highestproduct = product;
end
end
end

% DIAGONAL LEFT: Go through the grid, and for each spot, find the product of the diagonal.
for i=1:17
for j=4:20
product = grid_matrix{i,j}*grid_matrix{i+1,j-1}*grid_matrix{i+2,j-2}*grid_matrix{i+3,j-3};
if (product > highestproduct)
highestproduct = product;
end
end
end

% UP AND DOWN: Go through the grid, and for each spot, find the vertical
% product,vstarting at the top.
for i=1:17
for j=1:20
% Check if the farthest out value exists, 4 rows down, 1 to the
% right
product = grid_matrix{i,j}*grid_matrix{i+1,j}*grid_matrix{i+2,j}*grid_matrix{i+3,j};
if (product > highestproduct)
highestproduct = product;
end
end
end

fprintf('%s%d\n','The highest product is ',highestproduct);
end

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Suggested Citation:

Sochat, Vanessa. "Grid Matrix!." @vsoch (blog), 08 Nov 2010, https://vsoch.github.io/2010/grid-matrix/ (accessed 22 Dec 24).