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Problem11.m
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171
Problem11.m
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%ProjectEuler/Octave/Problem11.m
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%Matthew Ellison
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% Created:
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%Modified: 03-28-19
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%What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20×20 grid?
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%{
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08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
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49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
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81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
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52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
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22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
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24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
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32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
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67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
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24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
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21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
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78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
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16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
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86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
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19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
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04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
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88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
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04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
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20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
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20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
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01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
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%}
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%{
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Copyright (C) 2019 Matthew Ellison
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with this program. If not, see <https://www.gnu.org/licenses/>.
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%}
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%Create your variables
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grid = [08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08;
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49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00;
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81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65;
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52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91;
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22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80;
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24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50;
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32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70;
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67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21;
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24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72;
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21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95;
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78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92;
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16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57;
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86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58;
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19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40;
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04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66;
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88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69;
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04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36;
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20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16;
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20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54;
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01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48];
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currentLocation = [1, 1]; %The location you are checking now
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currentProduct = [0 0 0 0]; %The product you are currently looking at
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greatestProduct = [0 0 0 0]; %The greatest product of values you have found
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finished = false;
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%Start the timer
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startTime = clock();
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%Loop until you reach the last element
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while(~finished)
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left = false;
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right = false;
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down = false;
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%Check which directions you can go
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%When moving you will be moving 4 locations
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if((currentLocation(2) - 3) >= 1)
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left = true;
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end
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if((currentLocation(2) + 3) <= size(grid)(2))
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right = true;
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end
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if((currentLocation(1) + 3) <= size(grid)(1))
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down = true;
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end
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%Check the possible directions and check against greatest
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%Right
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if(right)
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currentProduct = grid(currentLocation(1), currentLocation(2):(currentLocation(2) + 3));
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%If the current numbers' product is greater than the greatest product so far, replace it
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if(prod(currentProduct) > prod(greatestProduct))
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greatestProduct = currentProduct;
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end
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end
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%Down
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if(down)
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currentProduct = grid(currentLocation(1):(currentLocation(1) + 3), currentLocation(2));
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%If the current numbers' product is greater than the greatest product so far, replace it
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if(prod(currentProduct) > prod(greatestProduct))
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greatestProduct = currentProduct;
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end
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end
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%LeftDown
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if(left && down)
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currentProduct(1) = grid(currentLocation(1), currentLocation(2));
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currentProduct(2) = grid(currentLocation(1) + 1,currentLocation(2) - 1);
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currentProduct(3) = grid(currentLocation(1) + 2,currentLocation(2) - 2);
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currentProduct(4) = grid(currentLocation(1) + 3,currentLocation(2) - 3);
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%If the current numbers' product is greater than the greatest product so far, replace it
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if(prod(currentProduct) > prod(greatestProduct))
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greatestProduct = currentProduct;
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end
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end
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%RightDown
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if(right && down)
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currentProduct(1) = grid(currentLocation(1), currentLocation(2));
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currentProduct(2) = grid(currentLocation(1) + 1,currentLocation(2) + 1);
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currentProduct(3) = grid(currentLocation(1) + 2,currentLocation(2) + 2);
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currentProduct(4) = grid(currentLocation(1) + 3,currentLocation(2) + 3);
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%If the current numbers' product is greater than the greatest product so far, replace it
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if(prod(currentProduct) > prod(greatestProduct))
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greatestProduct = currentProduct;
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end
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end
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%Move to the next column
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++currentLocation(2);
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%If you have moved too far in the columns move back to the beginning and to the next row
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if(currentLocation(2) > size(grid)(2))
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currentLocation(2) = 1;
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++currentLocation(1);
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end
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%If the row is currently greater than what is available you have traversed the list
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if(currentLocation(1) > size(grid)(1))
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finished = true;
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end
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end
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greatestProduct = reshape(greatestProduct, 1, 4); %For some reason it is coming out a 4X1 instead of 1X4
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%Stop the timer
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endTime = clock();
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%Print the result
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printf("The greatest product of 3 numbers in a line is %d\n", prod(greatestProduct))
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printf("It took %f seconds to run this algorithm\n", etime(endTime, startTime))
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%Cleanup the variables
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clear down;
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clear right;
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clear left;
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clear finished;
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clear startTime;
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clear endTime;
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clear grid;
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clear greatestProduct;
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clear currentLocation;
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clear currentProduct;
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clear ans;
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%{
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Results:
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The greatest product of 3 numbers in a line is 70600674
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It took 0.081856 seconds to run this algorithm
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%}
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