//ProjectEuler/C++/Source/Problem18.hpp
//Matthew Ellison
// Created: 11-01-18
//Modified: 07-14-19
//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
//Unless otherwise listed all non-standard includes are my own creation and available from https://bibucket.org/Mattrixwv/myClasses
/*
	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/>.
*/


#include <vector>
#include <list>
#include <string>
#include <sstream>
#include "Stopwatch.hpp"
#include "../Headers/Problem18.hpp"


std::vector<int> Problem18::list[NUM_ROWS] =
		{{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,  9, 70, 98, 73, 93, 38, 53, 60, 04, 23}};

Problem18::Problem18() : Problem("Find the maximum total from the top to the bottom of the pyramid."), actualTotal(0){
}

void Problem18::invert(){
	for(unsigned int rowCnt = 0;rowCnt < NUM_ROWS;++rowCnt){
		for(unsigned int colCnt = 0;colCnt < list[rowCnt].size();++colCnt){
			list[rowCnt][colCnt] = 100 - list[rowCnt][colCnt];
		}
	}
}

void Problem18::solve(){
	//If the problem has already been solved do nothing and end the function
	if(solved){
		return;
	}

	//Start the timer
	timer.start();

	//The method that I am using looks for the smallest numbers, so I need to invert the numbers in this list
	invert();
	//Now l[i][j] == 100 - l[i][j];
	//Add the top point because that is already the only path
	foundPoints.emplace_back(0, 0, list[0][0], false);
	//Add the second row as possible points
	possiblePoints.emplace_back(0, 1, (list[0][0] + list[1][0]), true);
	possiblePoints.emplace_back(1, 1, (list[0][0] + list[1][1]), false);

	bool foundBottom = false;	//Used when you find a point at the bottom

	//Loop until you find the bottom
	while(!foundBottom){
		//Check which possible point gives us the lowest number. If more than one has the same number simply keep the first one
		location minLoc = possiblePoints.front();
		for(location loc : possiblePoints){
			if(loc.total < minLoc.total){
				minLoc = loc;
			}
		}

		//Remove it from the list of possible points
		possiblePoints.remove_if([minLoc](location loc){return (loc.xLocation == minLoc.xLocation) &&(loc.yLocation == minLoc.yLocation);});

		foundPoints.push_back(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
		int xLoc = minLoc.xLocation;
		int yLoc = minLoc.yLocation + 1;	//Add one because you will always be moving to the next row
		if(yLoc >= NUM_ROWS){
			foundBottom = true;
		}
		else{
			possiblePoints.emplace_back(xLoc, yLoc, minLoc.total + list[yLoc][xLoc], true);
			++xLoc;	//Advance the x location to simulate going right
			possiblePoints.emplace_back(xLoc, yLoc, minLoc.total + list[yLoc][xLoc], false);
		}
	}

	actualTotal = ((100 * NUM_ROWS) - foundPoints.back().total);	//Change the minimum to the maximum
	invert();	//Invert the list again so that it is back to it's original form

	//Stop the timer
	timer.stop();

	//Throw a flag to show the problem is solved
	solved = true;
}

std::string Problem18::getString() const{
	//If the problem hasn't been solved throw an exception
	if(!solved){
		throw unsolved();
	}

	std::stringstream results;
	results << "The value of the longest path is " << actualTotal;
	return results.str();
}

std::string Problem18::getPyramid(){
	//If the problem hasn't been solved throw an exception
	if(!solved){
		throw unsolved();
	}
	std::stringstream results;
		
	//Print the triangle list of numbers
	for(unsigned int rowCnt = 0;rowCnt < NUM_ROWS;++rowCnt){
		for(unsigned int colCnt = 0;colCnt < list[rowCnt].size();++colCnt){
			results << std::setw(2) << list[rowCnt][colCnt] << ' ';
		}
	}
	return results.str();
}

std::string Problem18::getTrail(){
	//If the problem hasn't been solved throw an exception
	if(!solved){
		throw unsolved();
	}

	std::stringstream results;
	//Print the trail the algorithm took
	std::list<location> trail;
	trail.push_front(foundPoints.back());
	bool top = false;
	while(!top){
		bool found = false;
		int loc = foundPoints.size() - 1;
		std::list<location>::iterator toAdd = foundPoints.begin();
		while(!found){
			if(loc < 0){
				results << "Error: Location < 0\n";
				exit(1);
			}
			std::list<location>::iterator it = foundPoints.begin();
			std::advance(it, loc);
			if(trail.front().fromRight){
				if((it->xLocation == trail.begin()->xLocation) && (it->yLocation == (trail.begin()->yLocation - 1))){
					found = true;
					toAdd = it;
				}
				else{
					--loc;
				}
			}
			else{
				if((it->xLocation == (trail.begin()->xLocation - 1)) && (it->yLocation == (trail.begin()->yLocation - 1))){
					found = true;
					toAdd = it;
				}
				else{
					--loc;
				}
			}
		}

			
		trail.push_front(*toAdd);

		if(trail.begin()->yLocation == 0){
			top = true;
		}
	}

	for(location loc : trail){
		results << list[loc.yLocation][loc.xLocation] << "->";
	}
	return results.str();
}

int Problem18::getTotal() const{
	//If the problem hasn't been solved throw an exception
	if(!solved){
		throw unsolved();
	}
	return actualTotal;
}

void Problem18::reset(){
	Problem::reset();
	foundPoints.clear();
	possiblePoints.clear();
	actualTotal = 0;
}