//ProjectEuler/Java/Problem18.java
//Matthew Ellison
// Created: 03-11-19
//Modified: 03-28-18
//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/JavaClasses
/*
	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/>.
*/


import mattrixwv.Stopwatch;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.function.Predicate;


public class Problem18{
	//The number of rows in the array
	private static final Integer NUM_ROWS = 15;
	//Used to keep track of where the best location came from
	private static class location{
		public Integer xLocation;
		public Integer yLocation;
		public Integer total;
		public Boolean fromRight;
		location(Integer x, Integer y, Integer t, Boolean r){
			xLocation = x;
			yLocation = y;
			total = t;
			fromRight = r;
		}
	}
	//This function turns every number in the array into (100 - num) to allow you to find the largest numbers rather than the smallest
	private static void invert(ArrayList<ArrayList<Integer>> list){
		//Loop through every row in the list
		for(int rowCnt = 0;rowCnt < list.size();++rowCnt){
			//Loop through every column in the list
			for(int colCnt = 0;colCnt < list.get(rowCnt).size();++colCnt){
				//The current element gets the value of 100 - value
				list.get(rowCnt).set(colCnt, 100 - list.get(rowCnt).get(colCnt));
			}
		}
	}
	//This function helps by removing the element that is the same as the minimum location
	private static void removeHelper(ArrayList<location> possiblePoints, final location minLoc){
		possiblePoints.removeIf(loc -> ((loc.xLocation == minLoc.xLocation) && (loc.yLocation == minLoc.yLocation)));
	}
	public static void main(String[] argv){
		//Setup the timer
		Stopwatch timer = new Stopwatch();
		timer.start();

		//Setup the list you are trying to find a path through
		ArrayList<ArrayList<Integer>> list = new ArrayList<ArrayList<Integer>>();
		list.add(new ArrayList<Integer>(Arrays.asList(75)));
		list.add(new ArrayList<Integer>(Arrays.asList(95, 64)));
		list.add(new ArrayList<Integer>(Arrays.asList(17, 47, 82)));
		list.add(new ArrayList<Integer>(Arrays.asList(18, 35, 87, 10)));
		list.add(new ArrayList<Integer>(Arrays.asList(20, 04, 82, 47, 65)));
		list.add(new ArrayList<Integer>(Arrays.asList(19, 01, 23, 75, 03, 34)));
		list.add(new ArrayList<Integer>(Arrays.asList(88, 02, 77, 73, 07, 63, 67)));
		list.add(new ArrayList<Integer>(Arrays.asList(99, 65, 04, 28, 06, 16, 70, 92)));
		list.add(new ArrayList<Integer>(Arrays.asList(41, 41, 26, 56, 83, 40, 80, 70, 33)));
		list.add(new ArrayList<Integer>(Arrays.asList(41, 48, 72, 33, 47, 32, 37, 16, 94, 29)));
		list.add(new ArrayList<Integer>(Arrays.asList(53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14)));
		list.add(new ArrayList<Integer>(Arrays.asList(70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57)));
		list.add(new ArrayList<Integer>(Arrays.asList(91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48)));
		list.add(new ArrayList<Integer>(Arrays.asList(63, 66, 04, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31)));
		list.add(new ArrayList<Integer>(Arrays.asList(04, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 04, 23)));

		//Invert the list
		invert(list);

		ArrayList<location> foundPoints = new ArrayList<location>();	//For the points that I have already found the shortest distance to
		foundPoints.add(new location(0, 0, list.get(0).get(0), false));	//Add the first row as a found point because you have to go through the tip
		ArrayList<location> possiblePoints = new ArrayList<location>();	//For the locations you are checking this round
		//Add the second row as possible points
		possiblePoints.add(new location(0, 1, (list.get(0).get(0) + list.get(1).get(0)), true));
		possiblePoints.add(new location(1, 1, (list.get(0).get(0) + list.get(1).get(1)), false));
		Boolean foundBottom = false;	//Used when you find a point at the bottom of the list

		//Loop until you find the bottom of the list
		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.get(0);
			for(location loc : possiblePoints){
				if(loc.total < minLoc.total){
					minLoc = loc;
				}
			}

			//Remove it from the list of possible points
			removeHelper(possiblePoints, minLoc);

			//Add that point to the list of found points
			foundPoints.add(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
			Integer xLoc = minLoc.xLocation;
			Integer yLoc = minLoc.yLocation + 1;	//Add one because you will always be moving to the next row
			if(yLoc >= NUM_ROWS){
				foundBottom = true;
			}
			else{
				possiblePoints.add(new location(xLoc, yLoc, minLoc.total + list.get(yLoc).get(xLoc), true));
				++xLoc;	//Advance the x location to simulate going right
				//Check if x is out of bounds
				if(xLoc < list.get(yLoc).size()){
					possiblePoints.add( new location(xLoc, yLoc, minLoc.total + list.get(yLoc).get(xLoc), false));
				}
			}
		}

		//Stop the timer
		timer.stop();

		//Print the results
		//Get the correct total which will be the inversion of the current one
		Integer actualTotal = ((100 * NUM_ROWS) - foundPoints.get(foundPoints.size() - 1).total);

		System.out.println("The value of the longest path is " + actualTotal.toString());
		System.out.println("It took " + timer.getStr() + " to run this algorithm");
	}
}

/* Results:
The value of the longest path is 1074
It took 5.146 milliseconds to run this algorithm
*/