//myClasses/Algorithms.hpp
//Matthew Ellison
// Created: 11-8-18
//Modified: 11-8-18
//This file contains the declarations to several algoritms that I have found useful

#ifndef MEE_ALGORITHMS_HPP
#define MEE_ALGORITHMS_HPP

#include <vector>
#include <cinttypes>
#include <algorithm>
#include <string>
#include <gmp.h>	//This is necessary for the getFib function for numbers larger than a normal int can hold. It can be commented out if needed

namespace mee{


//A list of functions in the file
//Also works as a declaration
//This is a function that returns all the primes <= goalNumber and returns a vector with those prime numbers
template<class T>
std::vector<T> getPrimes(T goalNumber);
//This is a function that gets all the divisors of num and returns a vector containing the divisors
template<class T>
std::vector<T> getDivisors(T num);
//This is a function that gets the sum of all elements in a vector and returns the number
template <class T>
T getSum(std::vector<T> numbers);
//This is a function that searches a vecter for an element. Returns true if num is found in list
template<class T>
bool isFound(T num, std::vector<T> list);
//This is a function that creates all permutations of a string and returns a vector of those permutations.
//It is meant to have only the string passed into it from the calling function. num is used for recursion purposes
//It can however be used with num if you want the first num characters to be stationary
std::vector<std::string> getPermutations(std::string master, int num = 0);
//These functions return the numth Fibonacci number
uint64_t getFib(uint64_t num);
void getFib(mpz_t fibNum, uint64_t num);


template<class T>
std::vector<T> getPrimes(T goalNumber){
	std::vector<T> primes;
	bool foundFactor = false;

	//If the number is 0 or a negative number return an empty vector
	if(goalNumber < 1){
		return primes;
	}

	//1 divides everything
	primes.push_back(1);
	//If the number is even 2 is a factor
	if((goalNumber % 2) == 0){
		primes.push_back(2);
	}
	//We can now start at 3 and skip all of the even numbers
	for(T possiblePrime = 3;possiblePrime <= goalNumber;possiblePrime += 2){
		//Step through every element in the current primes. If you don't find anything that divides it, it must be a prime itself
		for(uint64_t cnt = 0;(cnt < primes.size()) && ((primes.at(cnt) * primes.at(cnt)) < goalNumber);++cnt){
			if((possiblePrime % primes.at(cnt)) == 0){
				foundFactor = true;
				break;
			}
		}
		//If you didn't find a factor then it must be prime
		if(!foundFactor){
			primes.push_back(possiblePrime);
		}
		//If you did find a factor you need to reset the flag
		else{
			foundFactor = false;
		}
	}
	std::sort(primes.begin(), primes.end());
	return primes;
}

template<class T>
std::vector<T> getDivisors(T num){
	std::vector<T> divisors;	//Holds the number of divisors
	//You only need to go to sqrt(number). cnt * cnt is faster than sqrt()
	for(int cnt = 1;cnt * cnt <= num;++cnt){
		//Check if the counter evenly divides the number
		//If it does the counter and the other number are both divisors
		if((num % cnt) == 0){
			if(!isFound(cnt, divisors)){
				divisors.push_back(cnt);
			}
			if(!isFound(num/cnt, divisors)){
				divisors.push_back(num / cnt);
			}
		}
	}
	std::sort(divisors.begin(), divisors.end());
	return divisors;
}

template <class T>
T getSum(std::vector<T> numbers){
	T sum = 0;
	for(unsigned int cnt = 0;cnt < numbers.size();++cnt){
		sum += numbers.at(cnt);
	}
	return sum;
}

template<class T>
bool isFound(T num, std::vector<T> list){
	for(int cnt = 0;cnt < list.size();++cnt){
		if(list.at(cnt) == num){
			return true;
		}
	}
	return false;
}

std::vector<std::string> getPermutations(std::string master, int num){
	std::vector<std::string> perms;
	//Check if the number is out of bounds
	if((num >= master.size()) || (num < 0)){
		return perms;
	}
	//If this is the last possible recurse just return the current string
	else if(num == (master.size() - 1)){
		perms.push_back(master);
		return perms;
	}
	//If there are more possible recurses, recurse with the current permutation
	std::vector<std::string> temp;
	temp = getPermutations(master, num + 1);
	perms.insert(perms.end(), temp.begin(), temp.end());
	//You need to swap the current letter with every possible letter after it
	//The ones needed to swap before will happen automatically when the function recurses
	for(int cnt = 1;(num + cnt) < master.size();++cnt){
		std::swap(master[num], master[num + cnt]);
		temp = getPermutations(master, num + 1);
		perms.insert(perms.end(), temp.begin(), temp.end());
		std::swap(master[num], master[num + cnt]);
	}

	//The array is not necessarily in alpha-numeric order. So if this is the full array sort it before returning
	if(num == 0){
		std::sort(perms.begin(), perms.end());
	}
	return perms;
}

uint64_t getFib(uint64_t num){
	//Make sure the number is within bounds
	if(num <= 2){
		return 1;
	}
	//Setup the variables
	uint64_t fib = 0;
	uint64_t tempNums[3];
	tempNums[0] = tempNums[2] = 1;

	//Do the calculation
	uint64_t cnt = 2;
	uint64_t location = 1;
	while(cnt < num){
		tempNums[location] = tempNums[(location + 1) % 3] + tempNums[(location + 2) % 3];
		location = (location + 1) % 3;
		++cnt;
	}
	fib = tempNums[(num + 1) % 3];	//Transfer the answer to permanent variable
	return fib;
}

void getFib(mpz_t fibNum, uint64_t num){
	//Make sure the number is within bounds
	if(num <= 0){
		mpz_set_ui(fibNum, 0);
		return;
	}
	else if(num <= 2){
		mpz_set_ui(fibNum, 1);
		return;
	}
	mpz_t tempNums[3];
	//Initialize the variables
	mpz_init(tempNums[0]);
	mpz_init(tempNums[1]);
	mpz_init(tempNums[2]);
	//Set the variables correctly
	mpz_set_ui(tempNums[0], 1);
	mpz_set_ui(tempNums[2], 1);

	//Do the calculation
	uint64_t cnt = 2;
	uint64_t location = 1;
	while(cnt < num){
		mpz_add(tempNums[location], tempNums[(location + 1) % 3], tempNums[(location + 2) % 3]);
		location = (location + 1) % 3;
		++cnt;
	}
	mpz_set(fibNum, tempNums[(num + 1) % 3]);	//Transfer the answer to the permanent variable

	//Clear the variables
	mpz_clear(tempNums[0]);
	mpz_clear(tempNums[1]);
	mpz_clear(tempNums[2]);
}

}


#endif //MEE_ALGORITHMS_HPP