In this problem we are searching for the largest product of four consecutive numbers in any row, column, or diagonal of a given 20 by 20 matrix. This is a nice sort of problem to do in Matlab because it is so well-suited for working with matrices. I wrote a separate function for scooting along a vector looking for the greatest product. Matlab has a built-in diag function that gives you a matrix diagonal as a vector. The 0th diagonal is the central one, the negative indices give you the lower triangle, and positive indices give you the upper triangle. Without further ado...
function euler11
global nn;
global mm;
global max_product;
grid = [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];
nn = 20;
mm = 4;
max_product = 0;
% Go through rows
for ii = 1:nn
get_product(grid(ii,:));
end
% Go through columns
for ii = 1:nn
get_product(grid(:,ii));
end
% Go through upper left lower right diagonals
for ii = (-nn+mm):(nn-mm)
clear vv;
vv = diag(grid, ii);
get_product(vv);
end
% Go through lower left upper right diagonals
grid = flipud(grid);
for ii = (-nn+mm-1):(nn-mm+1)
clear vv;
vv = diag(grid, ii);
get_product(vv);
end
max_product
function get_product(vv)
global mm;
global max_product;
for ii = 1:(length(vv)-mm+1)
product = vv(ii);
for jj = 1:mm-1
product = product * vv(ii+jj);
end
if product > max_product
max_product = product;
end
end