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119 lines
3.3 KiB
C++
119 lines
3.3 KiB
C++
//ProjectEuler/C++/Source/Problem23.cpp
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//Matthew Ellison
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// Created: 11-09-18
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//Modified: 07-14-19
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//Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers
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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 <cinttypes>
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#include <algorithm>
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#include <string>
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#include <sstream>
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#include "Stopwatch.hpp"
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#include "Algorithms.hpp"
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#include "../Headers/Problem23.hpp"
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int Problem23::MAX_NUM = 28123;
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Problem23::Problem23() : Problem("Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers"), sum(0){
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//This makes sure the vector is the correct size
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divisorSums.reserve(MAX_NUM);
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divisorSums.resize(MAX_NUM);
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}
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bool Problem23::isSum(const std::vector<int>& abund, int num){
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int64_t sum = 0;
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//Pick a number for the first part of the sum
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for(unsigned int firstNum = 0;firstNum < abund.size();++firstNum){
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//Pick a number for the second part of the sum
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for(unsigned int secondNum = firstNum;secondNum < abund.size();++secondNum){
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sum = abund.at(firstNum) + abund.at(secondNum);
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if(sum == num){
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return true;
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}
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else if(sum > num){
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break;
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}
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}
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}
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//If you have run through the entire list and did not find a sum then it is false
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return false;
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}
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void Problem23::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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//Get the sum of the divisors of all numbers < MAX_NUM
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for(int cnt = 1;cnt < MAX_NUM;++cnt){
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std::vector<int> div = mee::getDivisors(cnt);
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if(div.size() > 1){
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div.pop_back(); //Remove the last element, which is the number itself. This gives us the propper divisors
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}
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divisorSums.at(cnt) = mee::getSum(div);
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}
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//Get the abundant numbers
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std::vector<int> abund;
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for(unsigned int cnt = 0;cnt < divisorSums.size();++cnt){
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if(divisorSums.at(cnt) > cnt){
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abund.push_back(cnt);
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}
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}
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//Check if each number can be the sum of 2 abundant numbers and add to the sum if no
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for(int cnt = 1;cnt < MAX_NUM;++cnt){
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if(!isSum(abund, cnt)){
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sum += cnt;
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}
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}
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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 Problem23::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 answer is " << sum;
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return results.str();
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}
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uint64_t Problem23::getSum() 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 sum;
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}
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