mirror of
https://bitbucket.org/Mattrixwv/projecteulerlua.git
synced 2025-12-06 17:43:57 -05:00
Initial commit with existing files
This commit is contained in:
227
Problem18.lua
Normal file
227
Problem18.lua
Normal file
@@ -0,0 +1,227 @@
|
||||
--ProjectEuler/lua/Problem18.lua
|
||||
--Matthew Ellison
|
||||
-- Created: 03-12-19
|
||||
--Modified: 03-28-19
|
||||
--Find the maximum total from top to bottom
|
||||
--[[
|
||||
75
|
||||
95 64
|
||||
17 47 82
|
||||
18 35 87 10
|
||||
20 04 82 47 65
|
||||
19 01 23 75 03 34
|
||||
88 02 77 73 07 63 67
|
||||
99 65 04 28 06 16 70 92
|
||||
41 41 26 56 83 40 80 70 33
|
||||
41 48 72 33 47 32 37 16 94 29
|
||||
53 71 44 65 25 43 91 52 97 51 14
|
||||
70 11 33 28 77 73 17 78 39 68 17 57
|
||||
91 71 52 38 17 14 91 43 58 50 27 29 48
|
||||
63 66 04 68 89 53 67 30 73 16 69 87 40 31
|
||||
04 62 98 27 23 09 70 98 73 93 38 53 60 04 23
|
||||
]]
|
||||
--This is done using a breadth first search
|
||||
--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
|
||||
--[[
|
||||
Copyright (C) 2019 Matthew Ellison
|
||||
|
||||
This program is free software: you can redistribute it and/or modify
|
||||
it under the terms of the GNU Lesser General Public License as published by
|
||||
the Free Software Foundation, either version 3 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
This program is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU Lesser General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU Lesser General Public License
|
||||
along with this program. If not, see <https://www.gnu.org/licenses/>.
|
||||
]]
|
||||
|
||||
|
||||
require "Stopwatch"
|
||||
|
||||
--[[ This is what locations should look like
|
||||
location = {
|
||||
xLocation = 0,
|
||||
yLocation = 0,
|
||||
total = 0,
|
||||
fromRight = false
|
||||
};
|
||||
]]
|
||||
|
||||
function invert(list)
|
||||
for rowCnt=1,NUM_ROWS do
|
||||
for colCnt=1,#list[rowCnt] do
|
||||
list[rowCnt][colCnt] = 100 - list[rowCnt][colCnt];
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
function foundInList(list, loc)
|
||||
for location=1,#list do
|
||||
if((list[location].xLocation == loc.xLocation) and (list[location].yLocation == loc.yLocation)) then
|
||||
return true;
|
||||
end
|
||||
end
|
||||
return false;
|
||||
end
|
||||
|
||||
function remove_if(list, loc)
|
||||
location = 1;
|
||||
while(location <= #list) do
|
||||
if((list[location].xLocation == loc.xLocation) and (list[location].yLocation == loc.yLocation)) then
|
||||
table.remove(list, location);
|
||||
else
|
||||
location = location + 1;
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
--Create a timer and time the algorithm
|
||||
timer = Stopwatch:create();
|
||||
timer:start();
|
||||
|
||||
NUM_ROWS = 15;
|
||||
|
||||
|
||||
list = {};
|
||||
list[1] = {75};
|
||||
list[2] = {95, 64};
|
||||
list[3] = {17, 47, 82};
|
||||
list[4] = {18, 35, 87, 10};
|
||||
list[5] = {20, 04, 82, 47, 65};
|
||||
list[6] = {19, 01, 23, 75, 03, 34};
|
||||
list[7] = {88, 02, 77, 73, 07, 63, 67};
|
||||
list[8] = {99, 65, 04, 28, 06, 16, 70, 92};
|
||||
list[9] = {41, 41, 26, 56, 83, 40, 80, 70, 33};
|
||||
list[10] = {41, 48, 72, 33, 47, 32, 37, 16, 94, 29};
|
||||
list[11] = {53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14};
|
||||
list[12] = {70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57};
|
||||
list[13] = {91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48};
|
||||
list[14] = {63, 66, 04, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31};
|
||||
list[15] = {04, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 04, 23};
|
||||
|
||||
--Invert the list so all elements are 100 - element
|
||||
invert(list);
|
||||
|
||||
foundPoints = {}; --This is a table of locations
|
||||
foundPoints[1] = {xLocation = 1, yLocation = 1, total = list[1][1], fromRight = false};
|
||||
possiblePoints = {}; --This is a table of locations
|
||||
--Add the second row as possible points
|
||||
possiblePoints[1] = {xLocation = 1, yLocation = 2, total = (list[1][1] + list[2][1]), fromRight = true};
|
||||
possiblePoints[2] = {xLocation = 2, yLocation = 2, total = (list[1][1] + list[2][2]), fromRight = false};
|
||||
foundBottom = false; --Used when you find a point at the bottom
|
||||
|
||||
--Loop until you find the bottom
|
||||
while(not foundBottom) do
|
||||
--Check which possible point gives us the lowest number. If more than one has the same number simply keep the first one
|
||||
minLoc = possiblePoints[1];
|
||||
for loc=1,#possiblePoints do
|
||||
if(possiblePoints[loc].total < minLoc.total) then
|
||||
minLoc = possiblePoints[loc];
|
||||
end
|
||||
end
|
||||
|
||||
--Remove it from the list of possible points
|
||||
remove_if(possiblePoints, minLoc);
|
||||
|
||||
--[[ Aids in tracing the trail instead of using line after this
|
||||
--Add that point to the list of found points
|
||||
if(not foundInList(foundPoints, minLoc)) then
|
||||
table.insert(foundPoints, minLoc);
|
||||
end
|
||||
]]
|
||||
table.insert(foundPoints, minLoc);
|
||||
|
||||
--Add to the list of possible points from the point we just found and
|
||||
--If you are at the bottom raise the flag to end the program
|
||||
xLoc = minLoc.xLocation;
|
||||
yLoc = minLoc.yLocation + 1; --Add one because you will always be moving to the next row
|
||||
if(yLoc > NUM_ROWS) then
|
||||
foundBottom = true;
|
||||
else
|
||||
--print("minLoc.total = " .. minLoc.total);
|
||||
--print("list[" .. yLoc .. "][" .. xLoc .. "] = ");
|
||||
table.insert(possiblePoints, {xLocation = xLoc, yLocation = yLoc, total = (minLoc.total + list[yLoc][xLoc]), fromRight = true});
|
||||
xLoc = xLoc + 1; --Advance the x location to simulate going right
|
||||
table.insert(possiblePoints, {xLocation = xLoc, yLocation = yLoc, total = (minLoc.total + list[yLoc][xLoc]), fromRight = false});
|
||||
end
|
||||
end
|
||||
|
||||
actualTotal = ((100 * (NUM_ROWS)) - foundPoints[#foundPoints].total);
|
||||
|
||||
--Stop the timer
|
||||
timer:stop();
|
||||
|
||||
--Reinvert the list so it will print propperly
|
||||
invert(list);
|
||||
|
||||
--Print the results
|
||||
print("The value of the longest path is " .. actualTotal);
|
||||
print("It took " .. timer:getMilliseconds() .. " milliseconds to run this algorithm");
|
||||
|
||||
--[[
|
||||
--Print the pyramid of numbers out
|
||||
for rowCnt=1,NUM_ROWS do
|
||||
for colCnt=1,#list[rowCnt] do
|
||||
if(list[rowCnt][colCnt] < 10) then
|
||||
io.write(' ' .. list[rowCnt][colCnt] .. ' ');
|
||||
else
|
||||
io.write(list[rowCnt][colCnt] .. ' ');
|
||||
end
|
||||
end
|
||||
print("");
|
||||
end
|
||||
print("\n\n")
|
||||
|
||||
--Find the trail followed
|
||||
trail = {}; --Holds the locations that were traveled along
|
||||
table.insert(trail, 1, foundPoints[#foundPoints]); --Start with the last point and continue adding to the front of the list
|
||||
top = false;
|
||||
while(not top) do
|
||||
--Find the shortest way from the last location to the current one
|
||||
found = false;
|
||||
location = #foundPoints;
|
||||
while(not found) do
|
||||
--print("Location: " .. location);
|
||||
--print("trail[1].xLocation = " .. trail[1].xLocation .. "\ntrail[1].yLocation = " .. trail[1].yLocation);
|
||||
--print("foundPoints[location].xLocation = " .. foundPoints[location].xLocation .. "\nfoundPoints[location].yLocation = " .. foundPoints[location].yLocation);
|
||||
if(trail[1].fromRight) then
|
||||
if((foundPoints[location].xLocation == trail[1].xLocation) and (foundPoints[location].yLocation == (trail[1].yLocation - 1))) then
|
||||
found = true;
|
||||
else
|
||||
location = location - 1;
|
||||
end
|
||||
else
|
||||
if((foundPoints[location].xLocation == (trail[1].xLocation) - 1) and (foundPoints[location].yLocation == (trail[1].yLocation - 1))) then
|
||||
found = true;
|
||||
else
|
||||
location = location - 1;
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
--Insert the location into the trail
|
||||
table.insert(trail, 1, foundPoints[location]);
|
||||
|
||||
--If the current location is 1 then we are at the top
|
||||
if(trail[1].yLocation == 1) then
|
||||
top = true;
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
--Print the trail
|
||||
for location=1,#trail do
|
||||
io.write(list[trail[location].yLocation][trail[location].xLocation] .. "->");
|
||||
end
|
||||
print("");
|
||||
]]
|
||||
|
||||
|
||||
--[[ Results:
|
||||
The value of the longest path is 1074
|
||||
It took 1.162 milliseconds to run this algorithm
|
||||
]]
|
||||
Reference in New Issue
Block a user