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Source/Problem21.cpp

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+//ProjectEuler/C++/Source/Problem21.cpp
+//Matthew Ellison
+// Created: 11-08-18
+//Modified: 07-14-19
+//Evaluate the sum of all the amicable numbers under 10000
+//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 <cinttypes>
+#include <vector>
+#include <string>
+#include <sstream>
+#include "Algorithms.hpp"
+#include "Stopwatch.hpp"
+#include "../Headers/Problem21.hpp"
+
+
+int Problem21::LIMIT = 10000;	//The top number that will be evaluated
+
+Problem21::Problem21() : Problem("Evaluate the sum of all the amicable numbers under 10000"){
+	divisorSum.reserve(LIMIT);	//Reserving it now makes it faster later
+	divisorSum.resize(LIMIT);	//Make sure there are enough spaces
+}
+
+void Problem21::solve(){
+	//If the problem has already been solved do nothing and end the function
+	if(solved){
+		return;
+	}
+
+	//Start the timer
+	timer.start();
+
+	//Generate the divisors of all the numbers < 10000, get their sum, and add it to the list
+	for(int cnt = 1;cnt < LIMIT;++cnt){
+		std::vector<int> divisors = mee::getDivisors(cnt);	//Get all the divisors of a number
+		if(divisors.size() > 1){
+			divisors.pop_back();	//Remove the last entry because it will be the number itself
+		}
+		divisorSum.at(cnt) = mee::getSum(divisors);	//Add the sum of the divisors to the vector
+	}
+	//Check every sum of divisors in the list for a matching sum
+	for(uint64_t cnt = 1;cnt < divisorSum.size();++cnt){
+		uint64_t sum = divisorSum.at(cnt);
+		//If the sum is greater than the number of divisors then it is impossible to be amicable. Skip the number and continue
+		if(sum >= divisorSum.size()){
+			continue;
+		}
+		//We know that divisorSum.at(cnt) == sum, so if divisorSum.at(sum) == cnt we found an amicable number
+		if(divisorSum.at(sum) == cnt){
+			//A number can't be amicable with itself
+			if(sum == cnt){
+				continue;
+			}
+			//Add the number to the amicable vector
+			amicable.push_back(cnt);
+		}
+	}
+
+	//Sort the vector for neatness
+	std::sort(amicable.begin(), amicable.end());
+
+	//Stop the timer
+	timer.stop();
+
+	//Throw a flag to show the problem is solved
+	solved = true;
+}
+
+std::string Problem21::getString() const{
+	//If the problem hasn't been solved throw an exception
+	if(!solved){
+		throw unsolved();
+	}
+
+	std::stringstream results;
+	results << "All amicable numbers less than 10000 are\n";
+	for(unsigned int cnt = 0;cnt < amicable.size();++cnt){
+		results << amicable.at(cnt) << '\n';
+	}
+	results << "The sum of all of these amicable numbers is " << mee::getSum(amicable);
+	return results.str();
+}
+
+std::vector<uint64_t> Problem21::getAmicable() const{
+	//If the problem hasn't been solved throw an exception
+	if(!solved){
+		throw unsolved();
+	}
+	return amicable;
+}
+
+uint64_t Problem21::getSum() const{
+	//If the problem hasn't been solved throw an exception
+	if(!solved){
+		throw unsolved();
+	}
+	return mee::getSum(amicable);
+}