//myClasses/Algorithms.hpp
//Matthew Ellison
// Created: 11-08-18
//Modified: 02-28-19
//This file contains the declarations and implementations to several algoritms that I have found useful
/*
	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/>.
*/

#ifndef MEE_ALGORITHMS_HPP
#define MEE_ALGORITHMS_HPP

#include <vector>
#include <cinttypes>
#include <algorithm>
#include <string>
#include <cmath>

namespace mee{


//A list of functions in the file
//Also works as prototypes with general information
//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 function returns a vector with a specific number of primes
template <class T>
std::vector<T> getNumPrimes(T numberOfPrimes);
//This function returns all prime factors of a number
template <class T>
std::vector<T> getFactors(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 returns the sum of all elements in a vector
template <class T>
T getSum(const std::vector<T>& numbers);
//This is a function that returns the product of all elements in a vector
template <class T>
T getProduct(const std::vector<T>& nums);
//This is a function that searches a vecter for an element. Returns true if the key is found in list
template <class T>
bool isFound(std::vector<T> ary, T key);
//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
template <class T>
T getFib(const T num);
//This function returns a vector that includes all Fibonacci numbers <= num
template <class T>
std::vector<T> getAllFib(const T num);
//This is a function that performs a bubble sort on a vector
template <class T>
void bubbleSort(std::vector<T>& ary);
//This is a function that makes quick sort easier to start
template <class T>
void quickSort(std::vector<T>& ary);
//This is the function that actually performs the quick sort on the vector
template <class T>
void quickSort(std::vector<T>& ary, int64_t bottom, int64_t top);
//This is a helper function for quickSort. It chooses a pivot element and sorts everything to larger or smaller than the pivot. Returns location of pivot
template <class T>
int64_t partition(std::vector<T>& ary, int64_t bottom, int64_t top);
//This is a function that performs a search on a vector and returns the subscript of the item being searched for (-1 if not found)
template <class T>
int64_t search(const std::vector<T>& ary, T num);
//This function finds the smallest element in a vector
template <class T>
T findMin(const std::vector<T>& ary);
//This function finds the largest element in a vector
template <class T>
T findMax(const std::vector<T>& ary);


//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){
	std::vector<T> primes;
	bool foundFactor = false;

	//If the number is 1, 0, or a negative number return an empty vector
	if(goalNumber <= 1){
		return primes;
	}
	else{
		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
		uint64_t topPossibleFactor = ceil(sqrt(possiblePrime));
		for(uint64_t cnt = 0;(cnt < primes.size()) && (primes.at(cnt) <= topPossibleFactor);++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;
}

//This function returns a vector with a specific number of primes
template <class T>
std::vector<T> getNumPrimes(T numberOfPrimes){
	std::vector<T> primes;
	primes.reserve(numberOfPrimes);	//Saves cycles later
	bool foundFactor = false;

	//If the number is 1, 0, or a negative number return an empty vector
	if(numberOfPrimes <= 1){
		return primes;
	}
	//Otherwise 2 is the first prime number
	else{
		primes.push_back(2);
	}

	//Loop through every odd number starting at 3 until we find the requisite number of primes
	//Using possiblePrime >= 3 to make sure it doesn't loop back around in an overflow error and create an infinite loop
	for(T possiblePrime = 3;(primes.size() < numberOfPrimes) && (possiblePrime >= 3);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
		uint64_t topPossibleFactor = ceil(sqrt(possiblePrime));
		for(uint64_t cnt = 0;(cnt < primes.size()) && (primes.at(cnt) <= topPossibleFactor);++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;
		}
	}

	//The numbers should be in order, but sort them anyway just in case
	std::sort(primes.begin(), primes.end());
	return primes;
}

//This function returns all prime factors of a number
template <class T>
std::vector<T> getFactors(T goalNumber){
	//Get all the prime numbers up to sqrt(number). If there is a prime < goalNumber it will have to be <= sqrt(goalNumber)
	std::vector<T> primes = getPrimes((T)ceil(sqrt(goalNumber)));	//Make sure you are getting a vector of the correct type
	std::vector<T> factors;

	//Need to step through each prime and see if it is a factor of the number
	for(int cnt = 0;cnt < primes.size();){
		if((goalNumber % primes[cnt]) == 0){
			factors.push_back(primes[cnt]);
			goalNumber /= primes[cnt];
		}
		else{
			++cnt;
		}
	}

	//If it didn't find any factors in the primes the number itself must be prime
	if(factors.size() == 0){
		factors.push_back(goalNumber);
		goalNumber /= goalNumber;
	}

	///Should add some kind of error throwing inc ase the number != 1 after searching for all prime factors

	return factors;
}

//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){
	std::vector<T> divisors;	//Holds the number of divisors
	//Ensure the parameter is a valid number
	if(num <= 0){
		return divisors;
	}
	else if(num == 1){
		divisors.push_back(1);
		return divisors;
	}
	//You only need to check up to sqrt(num)
	T topPossibleDivisor = ceil(sqrt(num));
	for(uint64_t possibleDivisor = 1;possibleDivisor <= topPossibleDivisor;++possibleDivisor){
		//Check if the counter evenly divides the number
		//If it does the counter and the other number are both divisors
		if((num % possibleDivisor) == 0){
			//We don't need to check if the number already exists because we are only checking numbers <= sqrt(num), so there can be no duplicates
			divisors.push_back(possibleDivisor);
			//We still need to account for sqrt(num) being a divisor
			if(possibleDivisor != topPossibleDivisor){
				divisors.push_back(num / possibleDivisor);
			}
			//Take care of a few occations where a number was added twice
			if(divisors.at(divisors.size() - 1) == (possibleDivisor + 1)){
				++possibleDivisor;
			}
		}
	}
	//Sort the vector for neatness
	std::sort(divisors.begin(), divisors.end());
	//Return the vector of divisors
	return divisors;
}

//This is a function that returns the sum of all elements in a vector
template <class T>
T getSum(const std::vector<T>& ary){
	T sum = 0;
	for(unsigned int cnt = 0;cnt < ary.size();++cnt){
		sum += ary.at(cnt);
	}
	return sum;
}

//This is a function that returns the product of all elmements in a vector
template <class T>
T getProduct(const std::vector<T>& ary){
	//Make sure there is something in the array
	if(ary.size() == 0){
		return 0;
	}

	//Multiply all elements in the array together
	T prod = 1;
	for(T cnt = 0;cnt < ary.size();++cnt){
		prod *= ary.at(cnt);
	}
	return prod;
}

//This is a function that searches a vecter for an element. Returns true if they key is found in list
template <class T>
bool isFound(std::vector<T> ary, T key){
	for(int cnt = 0;cnt < ary.size();++cnt){
		if(ary.at(cnt) == key){
			return true;
		}
	}
	return false;
}

//This is a function that creates all permutations of a string and returns a vector of those permutations.
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;
}

//These functions return the numth Fibonacci number
template <class T>
T getFib(const T num){
	//Make sure the number is within bounds
	if(num <= 2){
		return 1;
	}
	//Setup the variables
	T fib = 0;
	T tempNums[3];
	tempNums[0] = tempNums[1] = 1;

	//Do the calculation
	unsigned int cnt;
	for(cnt = 2;(cnt < num) && (tempNums[(cnt - 1) % 3] >= tempNums[(cnt - 2) % 3]);++cnt){
		tempNums[cnt % 3] = tempNums[(cnt + 1) % 3] + tempNums[(cnt + 2) % 3];
	}
	fib = tempNums[(cnt - 1) % 3];	//Transfer the answer to permanent variable. -1 to account for the offset of starting at 0

	return fib;
}

//This function returns a vector that includes all Fibonacci numbers <= num
template <class T>
std::vector<T> getAllFib(const T num){
	std::vector<T> fibList;
	//Make sure the number is within bounds
	if(num <= 1){
		fibList.push_back(1);
		return fibList;
	}
	else{	//Make sure to add the first 2 elements
		fibList.push_back(1);
		fibList.push_back(1);
	}

	//Setup the variables
	T fib = 0;
	T tempNums[3];
	tempNums[0] = tempNums[1] = 1;

	//Do the calculation and add each number to the vector
	for(T cnt = 2;(tempNums[(cnt - 1) % 3] < num) && (tempNums[(cnt - 1) % 3] >= tempNums[(cnt - 2) % 3]);++cnt){
		tempNums[cnt % 3] = tempNums[(cnt + 1) % 3] + tempNums[(cnt + 2) % 3];
		fibList.push_back(tempNums[cnt % 3]);
	}

	//If you triggered the exit statement you have one more element than you need
	fibList.pop_back();

	//Return the vector that contains all of the Fibonacci numbers
	return fibList;
}

//This is a function that performs a bubble sort on a vector
template <class T>
void bubbleSort(std::vector<T>& ary){
	bool notFinished = true;	//A flag to determine if the loop is finished
	for(int numLoops = 0;numLoops < ary.size();++numLoops){	//Loop until you finish
		notFinished = false;	//Assume you are finished until you find an element out of order	
		//Loop through every element in the vector, moving the largest one to the end
		for(int cnt = 1;cnt < (ary.size() - numLoops);++cnt){	//use size - 1 to make sure you don't go out of bounds
			if(ary.at(cnt) < ary.at(cnt - 1)){
				std::swap(ary.at(cnt), ary.at(cnt - 1));
				notFinished = true;
			}
		}
	}
}

//This is a function that makes quick sort easier to start
template <class T>
void quickSort(std::vector<T>& ary){
	//Call the other quickSort function with all the necessary info
	quickSort(ary, 0, ary.size() - 1);
}

//This is the function that actually performs the quick sort on the vector
template <class T>
void quickSort(std::vector<T>& ary, int64_t bottom, int64_t top){
	//Make sure you have a valid slice of the vector
	if(bottom < top){
		//Get the pivot location
		int64_t pivot = partition(ary, bottom, top);

		//Sort all element less than the pivot
		quickSort(ary, bottom, pivot - 1);
		//Sort all element greater than the pivot
		quickSort(ary, pivot + 1, top);
	}
}

//This is a helper function for quickSort. It chooses a pivot element and sorts everything to larger or smaller than the pivot. Returns location of pivot
template <class T>
int64_t partition(std::vector<T>& ary, int64_t bottom, int64_t top){
	int64_t pivot = ary.at(top);	//Pick a pivot element
	int64_t smaller = bottom - 1;	//Keep track of where all elements are smaller than the pivot

	//Loop through every element in the vector testing if it is smaller than pivot
	for(int64_t cnt = bottom;cnt < top;++cnt){
		//If the element is smaller than pivot move it to the correct location
		if(ary.at(cnt) < pivot){
			//Increment the tracker for elements smaller than pivot
			++smaller;
			//Swap the current element to the correct location for being smaller than the pivot
			std::swap(ary.at(smaller), ary.at(cnt));
		}
	}

	//Move the pivot element to the correct location
	++smaller;
	std::swap(ary.at(top), ary.at(smaller));

	//Return the pivot element
	return smaller;
}

//This is a function that performs a search on a vector and returns the subscript of the item being searched for
template <class T>
int64_t search(const std::vector<T>& ary, T num){
	int64_t subscript = 0;	//Start with the subscript at 0
	//Step through every element in the vector and return the subscript if you find the correct element
	while(subscript < ary.size()){
		if(ary.at(subscript) == num){
			return subscript;
		}
		else{
			++subscript;
		}
	}
	//If you cannot find the element return -1
	return -1;
}

//This function finds the smallest element in a vector
template <class T>
T findMin(const std::vector<T>& ary){
	T min;	//For the smallest element

	//Make sure the vector is not empty
	if(ary.size() > 0){
		//Use the first element as the smallest element
		min = ary.at(0);
		//Run through every element in the vector, checking it against the current minimum
		for(int cnt = 1;cnt < ary.size();++cnt){
			//If the current element is smaller than the minimum, make it the new minimum
			if(ary.at(cnt) < min){
				min = ary.at(cnt);
			}
		}
	}

	//Return the element
	return min;
}

//This function finds the largest element in a vector
template <class T>
T findMax(const std::vector<T>& ary){
	T max;	//For the largest element

	//Make sure the vector is not empty
	if(ary.size() > 0){
		//Use the first element as the largest element
		max = ary.at(0);
		//Run through every element in the vector, checking it against the current minimum
		for(int cnt = 1;cnt < ary.size();++cnt){
			//If the current element is larger than the maximum, make it the new maximum
			if(ary.at(cnt) > max){
				max = ary.at(cnt);
			}
		}
	}

	//Return the element
	return max;
}

}


#endif //MEE_ALGORITHMS_HPP