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75 lines
2.5 KiB
Lua
75 lines
2.5 KiB
Lua
--ProjectEuler/lua/Problem15.lua
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--Matthew Ellison
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-- Created: 02-07-19
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--Modified: 03-28-19
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--How many routes from the top left corner to the bottom right corner are there through a 20×20 grid if you can only move right and down?
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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) 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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require "Stopwatch"
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timer = Stopwatch:create();
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timer:start();
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GRID_WIDTH = 20;
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GRID_HEIGHT = 20;
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lowestXReached = 20;
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function movement(currentX, currentY)
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--Return 1 if you are at the finish location
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if((currentX == GRID_WIDTH) and (currentY == GRID_HEIGHT)) then
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return 1;
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end
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local numberMoves = 0;
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--Otherwise move one right if you can and recurse
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if(currentX < GRID_WIDTH) then
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numberMoves = numberMoves + movement(currentX + 1, currentY);
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end
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--Then move one down and recurse
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if(currentY < GRID_HEIGHT) then
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numberMoves = numberMoves + movement(currentX, currentY + 1);
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end
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---Helps keep track of where it is for timing purposes
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if(currentX < lowestXReached) then
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lowestXReached = currentX;
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print("X hit");
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print("NumberMoves = " .. numberMoves);
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print("position = " .. currentX .. "; " .. currentY);
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end
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return numberMoves; --Return the number of moves that have been found so far
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end
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--Start the recursion at the correct location and catch what is returned
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numberMoves = movement(0, 0);
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timer:stop();
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--Print the results
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print("The number of paths from 1 corner of a " .. GRID_WIDTH .. " x " .. GRID_HEIGHT .. " grid to the opposite corner is " .. numberMoves);
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print("It took " .. timer:getMinutes() .. " seconds to run this algorithm");
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--[[Results:
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Did not run this program to completion. It ran for 12.5 hours and was over half way done, but I got tired of waiting.
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It is coded the same way as the C++ version so should come up to the same answer.
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There has got to be a better way to do this problem.
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]]
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