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Source/Problem18.cpp
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226
Source/Problem18.cpp
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//ProjectEuler/C++/Source/Problem18.hpp
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//Matthew Ellison
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// Created: 11-01-18
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//Modified: 07-14-19
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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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//Unless otherwise listed all non-standard includes are my own creation and available from https://bibucket.org/Mattrixwv/myClasses
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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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#include <vector>
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#include <list>
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#include <string>
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#include <sstream>
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#include "Stopwatch.hpp"
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#include "../Headers/Problem18.hpp"
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std::vector<int> Problem18::list[NUM_ROWS] =
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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, 9, 70, 98, 73, 93, 38, 53, 60, 04, 23}};
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Problem18::Problem18() : Problem("Find the maximum total from the top to the bottom of the pyramid."), actualTotal(0){
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//The method that I am using looks for the smallest numbers, so I need to invert the numbers in this list
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invert();
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//Now l[i][j] == 100 - l[i][j];
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//Add the top point because that is already the only path
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foundPoints.emplace_back(0, 0, list[0][0], false);
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//Add the second row as possible points
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possiblePoints.emplace_back(0, 1, (list[0][0] + list[1][0]), true);
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possiblePoints.emplace_back(1, 1, (list[0][0] + list[1][1]), false);
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}
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void Problem18::invert(){
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for(unsigned int rowCnt = 0;rowCnt < NUM_ROWS;++rowCnt){
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for(unsigned int colCnt = 0;colCnt < list[rowCnt].size();++colCnt){
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list[rowCnt][colCnt] = 100 - list[rowCnt][colCnt];
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}
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}
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}
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void Problem18::solve(){
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//If the problem has already been solved do nothing and end the function
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if(solved){
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return;
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}
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//Start the timer
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timer.start();
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bool 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(!foundBottom){
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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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location minLoc = possiblePoints.front();
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for(location loc : possiblePoints){
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if(loc.total < minLoc.total){
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minLoc = loc;
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}
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}
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//Remove it from the list of possible points
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possiblePoints.remove_if([minLoc](location loc){return (loc.xLocation == minLoc.xLocation) &&(loc.yLocation == minLoc.yLocation);});
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foundPoints.push_back(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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int xLoc = minLoc.xLocation;
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int yLoc = minLoc.yLocation + 1; //Add one because you will always be moving to the next row
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if(yLoc >= NUM_ROWS){
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foundBottom = true;
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}
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else{
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possiblePoints.emplace_back(xLoc, yLoc, minLoc.total + list[yLoc][xLoc], true);
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++xLoc; //Advance the x location to simulate going right
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possiblePoints.emplace_back(xLoc, yLoc, minLoc.total + list[yLoc][xLoc], false);
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}
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}
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actualTotal = ((100 * NUM_ROWS) - foundPoints.back().total); //Change the minimum to the maximum
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invert(); //Invert the list again so that it is back to it's original form
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//Stop the timer
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timer.stop();
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//Throw a flag to show the problem is solved
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solved = true;
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}
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std::string Problem18::getString() const{
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//If the problem hasn't been solved throw an exception
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if(!solved){
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throw unsolved();
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}
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std::stringstream results;
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results << "The value of the longest path is " << actualTotal;
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return results.str();
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}
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std::string Problem18::getPyramid(){
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//If the problem hasn't been solved throw an exception
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if(!solved){
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throw unsolved();
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}
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std::stringstream results;
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//Print the triangle list of numbers
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for(unsigned int rowCnt = 0;rowCnt < NUM_ROWS;++rowCnt){
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for(unsigned int colCnt = 0;colCnt < list[rowCnt].size();++colCnt){
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results << std::setw(2) << list[rowCnt][colCnt] << ' ';
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}
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}
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return results.str();
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}
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std::string Problem18::getTrail(){
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//If the problem hasn't been solved throw an exception
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if(!solved){
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throw unsolved();
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}
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std::stringstream results;
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//Print the trail the algorithm took
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std::list<location> trail;
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trail.push_front(foundPoints.back());
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bool top = false;
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while(!top){
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bool found = false;
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int loc = foundPoints.size() - 1;
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std::list<location>::iterator toAdd = foundPoints.begin();
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while(!found){
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if(loc < 0){
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results << "Error: Location < 0\n";
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exit(1);
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}
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std::list<location>::iterator it = foundPoints.begin();
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std::advance(it, loc);
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if(trail.front().fromRight){
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if((it->xLocation == trail.begin()->xLocation) && (it->yLocation == (trail.begin()->yLocation - 1))){
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found = true;
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toAdd = it;
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}
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else{
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--loc;
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}
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}
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else{
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if((it->xLocation == (trail.begin()->xLocation - 1)) && (it->yLocation == (trail.begin()->yLocation - 1))){
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found = true;
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toAdd = it;
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}
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else{
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--loc;
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}
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}
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}
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trail.push_front(*toAdd);
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if(trail.begin()->yLocation == 0){
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top = true;
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}
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}
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for(location loc : trail){
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results << list[loc.yLocation][loc.xLocation] << "->";
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}
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return results.str();
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}
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int Problem18::getTotal() const{
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//If the problem hasn't been solved throw an exception
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if(!solved){
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throw unsolved();
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}
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return actualTotal;
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}
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