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https://bitbucket.org/Mattrixwv/projecteulerlua.git
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228 lines
7.0 KiB
Lua
228 lines
7.0 KiB
Lua
--ProjectEuler/lua/Problem18.lua
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--Matthew Ellison
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-- Created: 03-12-19
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--Modified: 06-19-20
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--Find the maximum total from top to bottom
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--[[
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75
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95 64
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17 47 82
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18 35 87 10
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20 04 82 47 65
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19 01 23 75 03 34
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88 02 77 73 07 63 67
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99 65 04 28 06 16 70 92
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41 41 26 56 83 40 80 70 33
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41 48 72 33 47 32 37 16 94 29
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53 71 44 65 25 43 91 52 97 51 14
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70 11 33 28 77 73 17 78 39 68 17 57
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91 71 52 38 17 14 91 43 58 50 27 29 48
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63 66 04 68 89 53 67 30 73 16 69 87 40 31
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04 62 98 27 23 09 70 98 73 93 38 53 60 04 23
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]]
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--This is done using a breadth first search
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--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
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--[[
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Copyright (C) 2020 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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require "Stopwatch"
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--[[ This is what locations should look like
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location = {
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xLocation = 0,
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yLocation = 0,
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total = 0,
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fromRight = false
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};
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]]
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local function invert(list)
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for rowCnt=1,NUM_ROWS do
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for colCnt=1,#list[rowCnt] do
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list[rowCnt][colCnt] = 100 - list[rowCnt][colCnt];
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end
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end
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end
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local function foundInList(list, loc)
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for location=1,#list do
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if((list[location].xLocation == loc.xLocation) and (list[location].yLocation == loc.yLocation)) then
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return true;
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end
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end
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return false;
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end
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local function remove_if(list, loc)
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local location = 1;
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while(location <= #list) do
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if((list[location].xLocation == loc.xLocation) and (list[location].yLocation == loc.yLocation)) then
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table.remove(list, location);
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else
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location = location + 1;
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end
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end
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end
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--Create a timer and time the algorithm
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local timer = Stopwatch:create();
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timer:start();
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local NUM_ROWS = 15;
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local list = {};
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list[1] = {75};
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list[2] = {95, 64};
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list[3] = {17, 47, 82};
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list[4] = {18, 35, 87, 10};
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list[5] = {20, 04, 82, 47, 65};
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list[6] = {19, 01, 23, 75, 03, 34};
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list[7] = {88, 02, 77, 73, 07, 63, 67};
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list[8] = {99, 65, 04, 28, 06, 16, 70, 92};
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list[9] = {41, 41, 26, 56, 83, 40, 80, 70, 33};
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list[10] = {41, 48, 72, 33, 47, 32, 37, 16, 94, 29};
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list[11] = {53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14};
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list[12] = {70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57};
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list[13] = {91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48};
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list[14] = {63, 66, 04, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31};
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list[15] = {04, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 04, 23};
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--Invert the list so all elements are 100 - element
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invert(list);
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local foundPoints = {}; --This is a table of locations
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foundPoints[1] = {xLocation = 1, yLocation = 1, total = list[1][1], fromRight = false};
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local possiblePoints = {}; --This is a table of locations
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--Add the second row as possible points
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possiblePoints[1] = {xLocation = 1, yLocation = 2, total = (list[1][1] + list[2][1]), fromRight = true};
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possiblePoints[2] = {xLocation = 2, yLocation = 2, total = (list[1][1] + list[2][2]), fromRight = false};
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local foundBottom = false; --Used when you find a point at the bottom
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--Loop until you find the bottom
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while(not foundBottom) do
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--Check which possible point gives us the lowest number. If more than one has the same number simply keep the first one
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local minLoc = possiblePoints[1];
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for loc=1,#possiblePoints do
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if(possiblePoints[loc].total < minLoc.total) then
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minLoc = possiblePoints[loc];
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end
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end
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--Remove it from the list of possible points
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remove_if(possiblePoints, minLoc);
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--[[ Aids in tracing the trail instead of using line after this
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--Add that point to the list of found points
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if(not foundInList(foundPoints, minLoc)) then
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table.insert(foundPoints, minLoc);
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end
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]]
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table.insert(foundPoints, minLoc);
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--Add to the list of possible points from the point we just found and
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--If you are at the bottom raise the flag to end the program
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local xLoc = minLoc.xLocation;
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local yLoc = minLoc.yLocation + 1; --Add one because you will always be moving to the next row
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if(yLoc > NUM_ROWS) then
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foundBottom = true;
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else
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--print("minLoc.total = " .. minLoc.total);
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--print("list[" .. yLoc .. "][" .. xLoc .. "] = ");
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table.insert(possiblePoints, {xLocation = xLoc, yLocation = yLoc, total = (minLoc.total + list[yLoc][xLoc]), fromRight = true});
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xLoc = xLoc + 1; --Advance the x location to simulate going right
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table.insert(possiblePoints, {xLocation = xLoc, yLocation = yLoc, total = (minLoc.total + list[yLoc][xLoc]), fromRight = false});
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end
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end
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local actualTotal = ((100 * (NUM_ROWS)) - foundPoints[#foundPoints].total);
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--Stop the timer
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timer:stop();
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--Reinvert the list so it will print propperly
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invert(list);
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--Print the results
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print("The value of the longest path is " .. actualTotal);
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print("It took " .. timer:getMilliseconds() .. " milliseconds to run this algorithm");
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--[[
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--Print the pyramid of numbers out
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for rowCnt=1,NUM_ROWS do
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for colCnt=1,#list[rowCnt] do
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if(list[rowCnt][colCnt] < 10) then
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io.write(' ' .. list[rowCnt][colCnt] .. ' ');
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else
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io.write(list[rowCnt][colCnt] .. ' ');
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end
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end
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print("");
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end
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print("\n\n")
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--Find the trail followed
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trail = {}; --Holds the locations that were traveled along
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table.insert(trail, 1, foundPoints[#foundPoints]); --Start with the last point and continue adding to the front of the list
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top = false;
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while(not top) do
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--Find the shortest way from the last location to the current one
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found = false;
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location = #foundPoints;
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while(not found) do
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--print("Location: " .. location);
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--print("trail[1].xLocation = " .. trail[1].xLocation .. "\ntrail[1].yLocation = " .. trail[1].yLocation);
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--print("foundPoints[location].xLocation = " .. foundPoints[location].xLocation .. "\nfoundPoints[location].yLocation = " .. foundPoints[location].yLocation);
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if(trail[1].fromRight) then
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if((foundPoints[location].xLocation == trail[1].xLocation) and (foundPoints[location].yLocation == (trail[1].yLocation - 1))) then
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found = true;
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else
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location = location - 1;
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end
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else
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if((foundPoints[location].xLocation == (trail[1].xLocation) - 1) and (foundPoints[location].yLocation == (trail[1].yLocation - 1))) then
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found = true;
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else
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location = location - 1;
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end
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end
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end
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--Insert the location into the trail
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table.insert(trail, 1, foundPoints[location]);
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--If the current location is 1 then we are at the top
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if(trail[1].yLocation == 1) then
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top = true;
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end
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end
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--Print the trail
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for location=1,#trail do
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io.write(list[trail[location].yLocation][trail[location].xLocation] .. "->");
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end
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print("");
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]]
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--[[ Results:
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The value of the longest path is 1074
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It took 1.162 milliseconds to run this algorithm
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]]
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