#include <string>
#include <vector>
#include <numeric>
#include <fstream>
#include <iterator>
#include <iostream>
#include <utility>
#include <iomanip>
#include <ctime>
#include <boost/math/special_functions.hpp>
#include <boost/lexical_cast.hpp>
#include <boost/algorithm/string/replace.hpp>

#include <stdio.h>
#include <math.h>
#include <algorithm>    // std::find
#include <map>
#include <iterator>
using namespace std;


struct compare {
    bool operator()(const std::string& first, const std::string& second) {
    	if(first.size() == second.size())
    		return first < second;
    	else
    		return first.size() < second.size();
    }
};

string int_to_str(int num)
{
    stringstream ss;

    ss << num;

    return ss.str();
};


int str_to_int(string st)
{
    int result;

    stringstream(st) >> result;

    return result;
};

bool compareI(const pair<string, double>&i, const pair<string, double>&j)
{
    return i.second < j.second;
}

bool compareD(const pair<string, double>&i, const pair<string, double>&j)
{
    return i.second > j.second;
}

bool compareIn(const pair<double, string>&i, const pair<double, string>&j)
{
    return i.first < j.first;
}

bool compareDe(const pair<double, string>&i, const pair<double, string>&j)
{
    return i.first > j.first;
}

double logAB (double x, double y)
{
	double result;
	double maxVal = max(x,y);

	if(maxVal == x)
	{
		result = maxVal + log(1+exp(y-maxVal));
	}
	else
	{
		result = maxVal + log(1+exp(x-maxVal));
	}
	return result;
}

double persentageXofY (double newS, double oldS)
{
	double result;
	result = exp(oldS-newS)*100;
	return result;
}

void findAndReplaceAll(std::string & data, std::string toSearch, std::string replaceStr)
{
	// Get the first occurrence
	size_t pos = data.find(toSearch);

	// Repeat till end is reached
	while( pos != std::string::npos)
	{
		// Replace this occurrence of Sub String
		data.replace(pos, toSearch.size(), replaceStr);
		// Get the next occurrence from the current position
		pos =data.find(toSearch, pos + toSearch.size());
	}
}

int main() {
	/*
	//TEMPORARY INPUT FILE
	vector< vector<int> > DAT;
	vector <int> temp, temp2, temp3, temp4, temp5, temp6, temp7, temp8, temp9, temp10, temp11, temp12, temp13, temp14, temp15, temp16;
	//Filling up some of the test variables needed for the data set
	temp.push_back(0);
	temp.push_back(0);
	temp.push_back(1);
	//set 2
	temp2.push_back(0);
	temp2.push_back(1);
	temp2.push_back(0);
	//set3
	temp3.push_back(0);
	temp3.push_back(1);
	temp3.push_back(1);
	//set4
	temp4.push_back(1);
	temp4.push_back(0);
	temp4.push_back(0);
	//set5
	temp5.push_back(1);
	temp5.push_back(1);
	temp5.push_back(1);
	//set6
	temp6.push_back(1);
	temp6.push_back(1);
	temp6.push_back(0);
	//set7
	temp7.push_back(1);
	temp7.push_back(0);
	temp7.push_back(1);
	//set8
	temp8.push_back(1);
	temp8.push_back(0);
	temp8.push_back(1);
	//set9
	temp9.push_back(1);
	temp9.push_back(0);
	temp9.push_back(1);
	//set10
	temp10.push_back(1);
	temp10.push_back(0);
	temp10.push_back(1);
	//set11
	temp11.push_back(1);
	temp11.push_back(1);
	temp11.push_back(1);
	//set12
	temp12.push_back(1);
	temp12.push_back(0);
	temp12.push_back(1);
	//set13
	temp13.push_back(1);
	temp13.push_back(0);
	temp13.push_back(1);
	//set14
	temp14.push_back(1);
	temp14.push_back(1);
	temp14.push_back(0);
	//set15
	temp15.push_back(0);
	temp15.push_back(1);
	temp15.push_back(1);
	//set16
	temp16.push_back(1);
	temp16.push_back(0);
	temp16.push_back(1);
	std::cout << endl;
	//Filling up test DATASET
	DAT.push_back(temp);
	DAT.push_back(temp2);
	DAT.push_back(temp3);
	DAT.push_back(temp4);
	DAT.push_back(temp5);
	DAT.push_back(temp6);
	DAT.push_back(temp7);
	DAT.push_back(temp8);
	DAT.push_back(temp9);
	DAT.push_back(temp10);
	DAT.push_back(temp11);
	DAT.push_back(temp12);
	DAT.push_back(temp13);
	DAT.push_back(temp14);
	DAT.push_back(temp15);
	DAT.push_back(temp16);
	std::cout << endl;
	size_t totvars = DAT[1].size();
	size_t tottuples = DAT.size();
	*/
	//Time before user input
	time_t now = time(0);
	char* dt = ctime(&now);
	std::cout << "The local date and time is: " << dt << std::endl;
	string FILENAME;
	std::cout << "What is the name of your file?: ";
	std::cin >> FILENAME;
	// Variable declarations
	fstream file;
	int COLS;
	std::cout << "How many variables in your data file?: ";
	std::cin >> COLS;
	std::cout << endl;
	vector < vector <int> > DAT; // 2d array as a vector of vectors
	vector <int> rowVector(COLS); // vector to add into 'array' (represents a row)
	int row = 0; // Row counter

				 // Read file
	file.open(FILENAME.c_str(), ios::in); // Open file
	if (file.is_open()) { // If file has correctly opened...
						  // Output debug message
		cout << "File correctly opened" << endl;

		// Dynamically store data into array
		while (file.good()) { // ... and while there are no errors,
			DAT.push_back(rowVector); // add a new row,
			for (int col = 0; col<COLS; col++) {
				file >> DAT[row][col]; // fill the row with col elements
			}
			row++; // Keep track of actual row 
		}
	}
	else cout << "Unable to open file" << endl;
	file.close();

	size_t totvars = DAT[1].size();	//column number
	size_t tottuples = DAT.size();//row number
	



	//Ask User for the order they would like to test Order starts at 0 e.g. 0,1,2 is valid order for three variables
	int order_i;
	vector <int> order;
	std::cout << "Which is the order you would like to test?: ";
	for (int i = 0; i < totvars;++i) {
		std::cin >> order_i;
		order.push_back(order_i);
	}
	std::cout << endl;
	//Ask user for max value and min value of each variable being inputed
	vector <int> max_cat;
	vector <int> min_cat;
	int max_cat_input;
	int min_cat_input;

	std::cout << "What is the maximum categorical value of each variable?: ";
	for (int i = 0; i < totvars; ++i) {
		std::cin >> max_cat_input;
		max_cat.push_back(max_cat_input);
	}
	for (size_t i = 0; i < max_cat.size();++i) {
		std::cout << max_cat[i] << " ";
	}
	std::cout << endl;
	std::cout << endl;
	std::cout << "What is the minimum categorical value of each variable?: ";
	for (int i = 0; i < totvars; ++i) {
		std::cin >> min_cat_input;
		min_cat.push_back(min_cat_input);
	}
	for (size_t i = 0; i < min_cat.size();++i) {
		std::cout << min_cat[i] << " ";
	}
	std::cout << endl;
	//Set the maximum for the amount of parents for any given variable
	unsigned int maxparents;
	std::cout << "What is the maximum amount of parents to be considered for any given variable?: ";
	std::cin >> maxparents;
	std::cout << endl;

	double PERCENT;
	std::cout << "What is the percentage (Please use the format of 98.99, not 0.9899)?: ";
	std::cin >> PERCENT;
	std::cout << endl;

	//Time that program begins
	time_t start = time(0);
	char* dt_start = ctime(&start);
	std::cout << "The local date and time is: " << dt_start << std::endl;


	//Lets convert to counts for every variable combination which would be 2^n in the case of binary variables starting with the minimum in each category:
	//categories in i
	vector <int> catsi;
	//total combinations of variables
	//int totcombos = 1;
	//how many catagori for every variable
	for ( int i = 0; i < totvars; ++i) {
		catsi.push_back((max_cat[i] - min_cat[i]) + 1);
		//totcombos = totcombos * ((max_cat[i] - min_cat[i]) + 1);
	}
	/*size_t mincatsi = 10000, mincatvar;
	for (size_t i = 0; i < catsi.size(); ++i) {
		if (catsi[i] < mincatsi) {
			mincatsi = catsi[i];
			mincatvar = i;
		}
	}*/
	//print out catsi
	for (size_t i = 0; i < catsi.size();++i) {
		std::cout << catsi[i] << " ";
	}
	std::cout << endl;

	//Total Families Ui,alpha for a particular variable in the order
	vector <unsigned long long> families;//is vector, first element is the number of parentset for the first variabel......
	for (unsigned int i = 0; i < totvars; ++i) {
		int numparents = i;
		if (numparents == 0) {
			families.push_back(1);
		}
		else {

			unsigned long long numfams = 0;
			for (unsigned int j = 0; j <= i; ++j) {
				if (j <= maxparents) {
					unsigned long long jFactorial = 1;
					unsigned long long ijFactorial = 1;
					unsigned long long iFactorial = 1;
					//Calculate j!
					for (unsigned int g = 0; g <= j; ++g) {
						if (g != 0) {
							jFactorial *= g;
						}
					}
					//Calculate i!
					for (unsigned int g = 0; g <= i; ++g) {
						if (g != 0) {
							iFactorial *= g;
						}
					}
					//Calculate (i-j)!
					for (unsigned int g = 0; g <= (i - j); ++g) {
						if (g != 0) {
							ijFactorial *= g;
						}
					}
					numfams += (iFactorial) / (jFactorial * ijFactorial);
				}
				else {
					break;
				}
			}
			families.push_back(numfams);
		}
	}

		
	//How many parent combinations for each step? As well as there counts
	vector< vector <int> > ParentCombos;
	vector< vector <int> > fullNijkvector;
	vector< vector <string> > indexofvar; // This is label or index for each variable.
	for (size_t i = 0; i < order.size(); ++i) {
		//i represents the order of the variable
		if (i == 0) {
			vector <int> tmp,Nijkovercombos1;
			vector <string> tempstring;
			tempstring.push_back("[0]");
			tmp.push_back(1);
			ParentCombos.push_back(tmp);
			//counting the amount of times that a value of the first variable in the order occurs
			//this starts with the maximum value for that variable
			for (int hello = max_cat[order[0]];hello >= min_cat[order[0]];--hello) {
				//hello cycles through the categories of the first variable in the order
				int Nijk1 = 0;
				//green cycles through tuples
				for (int green = 0; green < tottuples; ++green){
					if (DAT[green][order[0]] == hello) {
						Nijk1 += 1;
					}
				}
				Nijkovercombos1.push_back(Nijk1);
			}
			fullNijkvector.push_back(Nijkovercombos1);
			indexofvar.push_back(tempstring);

		}
		else {
			vector <int> tmp,Nijkovercombos1;
			vector <string> tempstring;
			string tempa = "[" + int_to_str(i) +"]";
			tempstring.push_back(tempa);
			tmp.push_back(1);
			int numparnts = i;
			//counting the amount of times that a value of the last variable in the current order size occurs
			//this starts with the maximum value for that variable
			for (int hello = max_cat[order[numparnts]];hello >= min_cat[order[numparnts]];--hello) {
				//hello cycles through the categories of the first variable in the order
				int Nijk1 = 0;
				//green cycles through tuples
				for (int green = 0; green < tottuples; ++green) {
					if (DAT[green][order[numparnts]] == hello) {
						Nijk1 += 1;
					}
				}
				Nijkovercombos1.push_back(Nijk1);
			}
			fullNijkvector.push_back(Nijkovercombos1);
			
			//j representing the number of parents
			for (int it = 1; it <= numparnts; ++it) {
				//(333)Creating a vector that uses the right combination
				double Nloopy = 0, NcolFactorial = 1, iFactorial = 1, NiFactorial = 1;
				/*std::cout << "This is for " << numparnts << " choose " << it << endl;
				std::cout << "The iteration number is: " << it << endl;*/
				//Accounting for the limit of parent quantity
				if (it > maxparents) {
					break;
				}
				else {
					vector <int> NewMat(numparnts, 0);
					for (int p = 0; p < it; ++p) {
						NewMat[p] = 1;
					}
					for (int g = 2; g <= numparnts; ++g) {
						NcolFactorial *= g;
					}
					for (int g = 2; g <= it; ++g) {
						iFactorial *= g;
					}
					for (int g = 2; g <= (numparnts - it); ++g) {
						NiFactorial *= g;
					}
					//Nloopy represents the result of numparnts choose i e.g. numparnts choose 1 equals numparnts
					Nloopy = NcolFactorial / (iFactorial * NiFactorial);
					for (int iNloopy = 0; iNloopy < Nloopy; ++iNloopy) {
						int combsparents = 1;
                        vector <int> parsetv;
                        for (int par = 0; par < NewMat.size(); ++par){
                        	if (NewMat[par] == 1){
                        		parsetv.push_back(par);
                        	}
                        }

                        string tempstring2;

                        for (int par2 = 0; par2 < parsetv.size(); ++par2){
                        	if(par2+1==parsetv.size()){
                        		tempstring2 = tempstring2 + int_to_str(parsetv[par2]);
                        		//tempstring2 = tempstring2 +","+"|" + int_to_str(i);
                        		tempstring2 = "[" + int_to_str(i)+"|"+tempstring2 +"]";
                        	}
                        	else{
                        		//tempstring2 = tempstring2 + int_to_str(parsetv[par2])+",";
                        		tempstring2 = tempstring2 + int_to_str(parsetv[par2])+":";
                        	}


                        }
                        tempstring.push_back(tempstring2);

						/*std::cout << "This is iNloopy: " << (iNloopy + 1) << endl;
						std::cout << "Here comes the NewMat:" << endl;*/
						//(444)This sets up the process for changing
						//PosOne tells me the position of the last one in the vector
						//We want to change when the position is the last position available in the vector
						int SumOnes = 0, PosOne = 0, SumOnes2 = 0, PosOne2, NxtOne = 0, FrstOne = 0;
						int SumOnes3 = 0, SumOnes4 = 0, SumY = 0;
						for (PosOne = (numparnts - 1); PosOne >= 0; --PosOne) {
							if (NewMat[PosOne] == 1) {
								break;
							}
						}
						for (int y = (numparnts - 1); y >= (numparnts - it); --y) {
							//SumOnes tells you the amount of ones in the last i columns
							//These are the last columns being considered
							SumOnes += NewMat[y];
						}
						for (PosOne2 = (numparnts - 1); PosOne2 >= 0; --PosOne2) {
							//SumOnes2 tells you the amount of ones before you reach the next zero
							//PosOne2 keeps track of the position of the coming zero
							SumOnes2 += NewMat[PosOne2];
							if ((SumOnes2 > 0) & (NewMat[PosOne2] == 0)) {
								break;
							}
						}
						for (FrstOne = 0; FrstOne < numparnts; ++FrstOne) {
							//FrstOne tells you the position of the first number 1 starting from the left hand side
							if (NewMat[FrstOne] == 1) {
								break;
							}
						}
						for (int x = (numparnts - 1); x >= (numparnts - it + 1); --x) {
							//SumOnes4 helps keep track of the sum of all ones located in the last i - 1 positions
							SumOnes4 += NewMat[x];
						}
						//Prints out NewMat
						/*for (int u = 0; u < numparnts; ++u) {
							std::cout << NewMat[u] << " ";
						}
						std::cout << endl;*/


						//Adding in the code that will allow counts parent combinations for this particular variable
						for (int q = 0; q < i; ++q) {
							if (NewMat[q] == 1) {
								combsparents *= catsi[order[q]];
							}
						}
						tmp.push_back(combsparents);//made the whole parentset configure for a variable
						/*std::cout << "This is combsparents: " << combsparents << endl;
						std::cout << endl;*/
						vector <int> hvect;
						//hvect tells us which variables are being considered always the last variable is being considered
						//e.g if ABC is our order and we are on i equals 1 then we are looking at relationships between A and B only
						//continued: A is the only one that is either a parent or isn't a parent so hvect will be < 0 1 > 
						//for A C hvect will be < 0 2 >
						for (int h = 0; h < i; ++h) {
							if (NewMat[h] == 1) {
								hvect.push_back(h);
							}
						}
						hvect.push_back(numparnts);
						size_t shvect = hvect.size();
						//Prints out hvect
						/*for (int u = 0; u < shvect; ++u) {
							std::cout << hvect[u] << " ";
						}*/
						//std::cout << endl;
						//Counting the amount of values in the data that have that particular parent combination
						vector <int> Nijkovercombos;
						for (int last = min_cat[order[numparnts]]; last <= max_cat[order[numparnts]]; ++last) {
							//(333)Creating a vector that uses the right combination
							/*std::cout << "This is for " << i << " place in the order with value of variable equal to" << last << endl;*/
							vector <int> Test(shvect, last), maxtest;
							for (int p = 0; p < (shvect-1); ++p) {
								Test[p] = max_cat[order[hvect[p]]];
							}
							maxtest = Test;
							for (int i2Nloopy = 0; i2Nloopy < combsparents; ++i2Nloopy) {
								//std::cout << endl;
								/*std::cout << endl;
								std::cout << "This is i2Nloopy: " << (i2Nloopy + 1) << endl;
								std::cout << "Here comes the Test:" << endl;*/
								//(444)This sets up the process for changing
								//NMpos tells me the position of the last non minimum value in the vector
								//We want to change when the position is the last position available in the vector
								int NMpos = 0, minpos = 0;
								for (NMpos = (shvect - 2); NMpos >= 0; --NMpos) {
									if (Test[NMpos] != min_cat[order[hvect[NMpos]]]) {
										break;
									}
								}
								for (minpos = (shvect - 2); minpos >= 0; --minpos) {
									//minpos tells you the position of the last minimum value
									if (Test[minpos] == min_cat[order[hvect[minpos]]]) {
										break;
									}
								}
								//Prints out Test
								/*for (int u = 0; u < shvect; ++u) {
									std::cout << Test[u] << " ";
								}
								std::cout << endl;
								std::cout << endl;
								std::cout << endl;*/
								//Count how many occurrences of the value are present in the data
								int Nijk = 0;
								for (int num2size = 0; num2size < tottuples; ++num2size) {
									int countcorrect = 0;
									for (size_t g = 0; g < Test.size(); ++g) {
										//num2size cycles through tuples
										//order[hvect[g]] represents the variable in the order that we are considering as a parent
										if (DAT[num2size][order[hvect[g]]] == Test[g]) {
											countcorrect += 1;
										}
									}
									if (countcorrect == Test.size()) {
										Nijk += 1;
									}
								}
								//Nijkovercombos displays data as follows
								//it starts with the smallest value for the last variable in hvect
								//and the largest values in the first n-1 variables in hvect
								//max,max-1,max-2,max-3 e.g. 2, 1, 0, 2, 1, 0  
								//count,count,count,count e.g. 13, 2, 2, 3, 4, 10
								Nijkovercombos.push_back(Nijk);
								//(666)Now that the values have been calculated find out what the next combination of variables should be
								if ((NMpos == -1) & (minpos == (shvect - 2))) {
									//break when the 1st non minimum does not exist and the first minimum is found in the last position e.g. 0000
									break;
								}
								if (minpos < NMpos) {
									Test[NMpos] = Test[NMpos] - 1;
								}
								else if (NMpos < minpos) {
									Test[NMpos] = Test[NMpos] - 1;
									for (int filler = NMpos + 1; filler < (shvect - 1); ++filler) {
										Test[filler] = maxtest[filler];
									}
								}
							}
						}
						fullNijkvector.push_back(Nijkovercombos);
						//(666)Now that the unique values have been calculated find out what the next combination of variables should be
						if ((PosOne == (numparnts - 1)) & (SumOnes == it)) {
							break;
						}
						else if ((PosOne == (numparnts - 1)) & (SumOnes != it)) {
							for (NxtOne = (numparnts - 1); NxtOne >= 0; --NxtOne) {
								//NxtOne tells you the position of the next closest number 1 that we would
								//like to change the position of (we will call it the important number one)
								//SumOnes3 helps keep track of the sum of all ones between now and the next important number one
								SumOnes3 += NewMat[NxtOne];
								if (SumOnes3 == (SumOnes2 + 1)) {
									break;
								}
							}
							if (SumOnes4 == (it - 1)) {
								//If all except one of the 1's are found in the last it - 1 columns
								for (int x = 0; x < numparnts; ++x) {
									if (((x <= (NxtOne + SumOnes3)) & (x > NxtOne)) | (x == (FrstOne + 1))) {
										//If 
										NewMat[x] = 1;
									}
									else {
										NewMat[x] = 0;
									}
								}
							}
							else {
								for (int x = 0; x < numparnts; ++x) {
									if (((x <= (NxtOne + SumOnes3)) & (x > NxtOne)) | (x == FrstOne)) {
										//If the position is that of the first 1 or it falls between the changed number one and the total 
										//amount of ones that are on that side of the zero 10111
										NewMat[x] = 1;
									}
									else if ((x != FrstOne) & (x != NxtOne) & (NewMat[x] == 1) & (x < PosOne2)) {
										//If it is not the position of the first 1 and it is not the position of the 1 whose position we are interested in changing
										//and the previous value at this position was 1 and the postion is below the value of the first zero spotted from the right
										NewMat[x] = 1;
									}
									else {
										NewMat[x] = 0;
									}
								}
							}
						}
						else if ((PosOne != (numparnts - 1)) & (SumOnes != it)) {
							for (NxtOne = (numparnts - 1); NxtOne >= 0; --NxtOne) {
								//NxtOne tells you the position of the next closest number 1 that we would
								//like to change the position of (we will call it the important number one)
								//SumOnes3 helps keep track of the sum of all ones between now and the next important number one
								SumOnes3 += NewMat[NxtOne];
								if (SumOnes3 == 1) {
									break;
								}
							}
							if (it != 1) {
								for (int x = 0; x < numparnts; ++x) {
									if (x == (NxtOne + 1)) {
										NewMat[x] = 1;
									}
									else if (x == NxtOne) {
										NewMat[x] = 0;
									}
									else if ((NewMat[x] == 1) & (x != NxtOne)) {
										NewMat[x] = 1;
									}
									else {
										NewMat[x] = 0;
									}
								}
							}
							else {
								for (int x = 0; x < numparnts; ++x) {
									if ((x == (NxtOne + 1))) {
										NewMat[x] = 1;
									}
									else {
										NewMat[x] = 0;
									}
								}
							}
						}
					}

				}
			}
			ParentCombos.push_back(tmp);
			indexofvar.push_back(tempstring);
		}

	}
	//std::cout << endl;
	std::cout << endl;
	//printing out the ParentCombos matrix just created above
	/*for (size_t i = 0; i < ParentCombos.size(); ++i) {
		for (size_t j = 0; j < ParentCombos[i].size(); ++j) {
			std::cout << ParentCombos[i][j] << " ";
		}
		std::cout << endl;
	}*/
	std::cout << endl;
	//printing out the fullNijkvector matrix just created above
	/*for (size_t i = 0; i < fullNijkvector.size(); ++i) {
		for (size_t j = 0; j < fullNijkvector[i].size(); ++j) {
			std::cout << fullNijkvector[i][j] << " ";
		}
		std::cout << endl;
	}
	std::cout << endl;*/
	//Print out Data
	/*for (int i = 0; i < DAT.size(); ++i) {
		for (int j = 0; j < DAT[i].size(); ++j) {
			std::cout << DAT[i][j] << " ";
		}
		std::cout << endl;
	}*/
	//Print out the families size
	/*for (size_t i = 0; i < families.size(); ++i) {
		std::cout << families[i] << " ";
	}*/

	//Obtaining the actual score from this information
	//varinorder cycles through families (the amount of parent families that should be considered for the variable with a particular order starting
	//the first variable in the order)
	//keeping track of the position within the fullNijkvector associated with the varinorder and the qi_Uialpha
	int posinfull = 0;
	//finlogscore is the final score in natural log format
	long double finlogscore = 0.0;
	vector< vector <double> > vecvarparset;
	for (size_t varinorder = 0; varinorder < families.size(); ++varinorder) {
		//sumovUialpha is the the sum over all parent sets for a particular variable
		long double sumovUialpha = 0.0;
		//vector of all values of seclastgamma
		vector <double> vec2ndlastgamma;
		long double maxseclastgamma;
		//Uialpha cycles through all the parent sets for a particular family
		for (int Uialpha = 0; Uialpha < families[varinorder]; ++Uialpha) {
			// nijkprime represents the value of 1/(ri * qi)
			long double nijkprime, nijprime;
			long double rij = catsi[order[varinorder]], PCs = ParentCombos[varinorder][Uialpha];

			nijprime = 1.0 / (PCs);
			nijkprime = 1.0 / (rij * PCs);
			//seclastgamma is the sum over all combinations for the parents in a set sum because it is logarithmic
			long double seclastgamma = 0.0;
			//qi_Uialpha cycles through the combinations for the parents in a set
			for (int qi_Uialpha = 0; qi_Uialpha < ParentCombos[varinorder][Uialpha];++qi_Uialpha) {
				long double lastgamma = 0.0;
				long double nij = 0.0;
				//countijk cycles through the categories of the variable with a particular order
				//catsi is in the order that data is input and so one must use the order[varinorder] to first obtain the variable that we are referring to
				//and then find the categories for it
				for (int countijk = 0; countijk < catsi[order[varinorder]]; ++countijk) {
					long double topy;
					//rightcol lets you find the right column/position of the value that you need for a particular category within the
					int rightcol = qi_Uialpha + (countijk * ParentCombos[varinorder][Uialpha]);
					nij += fullNijkvector[posinfull][rightcol];
					topy = (nijkprime + fullNijkvector[posinfull][rightcol]);

					//Using boost lgamma function for the product over categories and parent combinations
					lastgamma += boost::math::lgamma(topy) - boost::math::lgamma(nijkprime);

				}
				long double boty = nij + nijprime;
				seclastgamma += lastgamma + boost::math::lgamma(nijprime) - boost::math::lgamma(boty);

			}
			vec2ndlastgamma.push_back(seclastgamma);



			//Calculate sumovUialpha based on the logsumexp concept
			if (Uialpha + 1 == families[varinorder]) {
				
				for (size_t que = 0; que < vec2ndlastgamma.size(); ++que) {
					//change the value of maxseclastgamma if new value is larger than the previous value
					if (que == 0) {
						maxseclastgamma = vec2ndlastgamma[0];
					}
					else {
						if (maxseclastgamma < vec2ndlastgamma[que]) {
							maxseclastgamma = vec2ndlastgamma[que];
						}
					}
				}
				for (size_t what = 0; what < vec2ndlastgamma.size(); ++what) {
					sumovUialpha += exp(vec2ndlastgamma[what] - maxseclastgamma);
				}
				//add info on parent set scores for each variable to this vector of vectors
				vecvarparset.push_back(vec2ndlastgamma);
			}
			
			/*std::cout << endl;
			std::cout << seclastgamma;
			std::cout << endl;*/
			posinfull += 1;
			//std::cout << posinfull << endl;
		}
		finlogscore += log(sumovUialpha) + maxseclastgamma;
	}

	vector < vector<string> > parSet;
	vector< map <double, string, greater <double> > > parSetScoreSorted;
	vector< map <double, string, greater <double> > > strucScore;


//Below is another way to match the index or label sets with the scores sets, and store the (score, label) into a map vector. And for each vector element the map is a sorted map.

	for (unsigned i = 0; i < indexofvar.size(); ++i){

		map <double, string, greater <double> > tempMap;
		for (unsigned j=0; j< indexofvar[i].size(); ++j){
		    tempMap.insert(make_pair(vecvarparset[i][j], indexofvar[i][j]));
		   }
		parSetScoreSorted.push_back(tempMap);

	}


	pair <double, string> bestStrScore;
	double bestScore = 0;
	string bestLable;


	for (unsigned i = 0; i < parSetScoreSorted.size(); ++i){
		map <double, string> :: iterator itr;
		itr = parSetScoreSorted[i].begin();
		bestScore = bestScore + (itr->first);
		bestLable = bestLable +(itr->second);
	}

	bestStrScore = make_pair(bestScore, bestLable);//This is the best score.

	vector < pair <double, string> > sortedStru;//This store all the structures in the percentage.
	vector < vector < pair <double, string > > > deltaC;

	for (unsigned l = 1; l< parSetScoreSorted.size(); ++l){
		map <double, string> :: iterator itr0, itr1;
		vector < pair <double, string > > tempDelta;
		double tempDeltaS;
		string tempDeltaL;
		itr0 = parSetScoreSorted[l].begin();
		itr1 = parSetScoreSorted[l].begin();
		double tem1=exp(itr1->first), tem2 = exp(itr1->first);
		for (unsigned m = 1; m< parSetScoreSorted[l].size(); ++m){
			tem1 = tem2;
			itr1 = ++itr1;
			tem2 = tem1 + exp(itr1->first);
			double tem = (tem1/tem2)*100;
			if(tem <= PERCENT){
				tempDeltaS = (itr1->first)-(itr0->first);
				tempDeltaL = itr1->second;
				tempDelta.push_back(make_pair(tempDeltaS, tempDeltaL));
			}
		}

		deltaC.push_back( tempDelta);
	}


	for(unsigned i=0; i< deltaC.size(); ++i){
		for (unsigned j=0; j< deltaC[i].size(); ++j)
		{
			double score = bestStrScore.first + deltaC[i][j].first;
			string lab = bestStrScore.second;
			findAndReplaceAll(lab, parSetScoreSorted[i+1].begin()->second, deltaC[i][j].second);
			sortedStru.push_back(make_pair(score, lab));
		}
	}

	sort(sortedStru.begin(),sortedStru.end(),compareDe);



/*	for (unsigned l = 1; l< parSetScoreSorted.size(); ++l){ //l means each variable
		for (unsigned m = contl; m < parSetScoreSorted[l].size(); ++m){ //m means the number of parents sets
			contl =m;
			vector < pair <string, double > > delta; // store the different of the highest score and the second highest score
			for (unsigned i = l; i < parSetScoreSorted.size(); ++i){
				map <double, string> :: iterator itr0, itr1;
				double tempDeltaS;
				string tempDeltaL;
				itr0 = parSetScoreSorted[i].begin();
				itr1 = itr0;
				for (int kr = 0; kr < contl; ++kr){
					itr1 = itr0++;
				}
				tempDeltaS = (itr1->first)-(itr0->first);
				tempDeltaL = int_to_str(i);
				delta.push_back(make_pair(tempDeltaL, tempDeltaS));
			}

			sort(delta.begin(),delta.end(),compareI);

            double const stopLimit = PERCENT;
			double tempbeforeS = bestStrScore.first, temafterS;

			for (unsigned i = 0; i < delta.size(); ++i){
				pair <double, string > temppair;
			    double tempLime;
			    int ind = str_to_int(delta[i].first);
			    string s = parSetScoreSorted[ind].begin()->second;
				string sRep = (++parSetScoreSorted[ind].begin())->second;
				temppair = bestStrScore;
				findAndReplaceAll(temppair.second, s, sRep);
				temppair.first = temppair.first - delta[i].second;

				temafterS = logAB(tempbeforeS, temppair.first);

				tempLime = persentageXofY(temafterS, tempbeforeS) ;

				tempbeforeS = temafterS;

				if(tempLime > stopLimit){
					goto finish;
			}

				sortedStru.push_back(temppair);

					//		std::cout << ind << "    "<< s << "     "<< sRep << "     "<< temppair.first  << "    " << temppair.second <<endl;
					//		std::cout << temppair.first  << "    " << temppair.second <<endl;
					//		std::cout << std::endl;

			}

		}

	}

	finish:*/


	std::cout << std::endl;
	std::cout << "Total Score: "<< boost::lexical_cast<string>(finlogscore) << std::endl;
	std::cout << std::endl;


	cout << "Best several structures are:" << endl;
	cout  << bestScore << " : " << bestLable << endl;

	for (unsigned i=0; i< sortedStru.size(); ++i )
	{
		cout  << sortedStru[i].first << " : " << sortedStru[i].second << endl;
	}

	std::cout << std::endl;
	std::cout << std::endl;

	for(unsigned i=0; i< parSetScoreSorted.size(); ++i){
		map <double, string> :: iterator itr;
		std::cout << "For variable "<<  i <<":"<< endl;
		for (itr = parSetScoreSorted[i].begin(); itr != parSetScoreSorted[i].end(); ++itr)
		{
			cout  << itr->second << " : " << itr->first << ";   ";
		}
		cout << endl;
		cout << endl;

	}


/*	ofstream myfile;
	myfile.open("/home/zgong001/Documents/SprinklerDataset/bestStructure.txt");
	if (myfile.is_open())
	{
		myfile << bestLable << " : " << bestScore << sortedStru.size();
		myfile << "\n";

		for(unsigned i=0; i< sortedStru.size(); ++i){
			myfile  << sortedStru[i].second << " : " << sortedStru[i].first;
            myfile << "\n";
		}
	 }
	 else cout << "Unable to open file";
	 myfile.close();*/


	//time after completion
	time_t later = time(0);
	char* dt_later = ctime(&later);
	std::cout << "The local date and time is: " << dt_later << std::endl;

	std::cout << std::endl;
	std::cout << std::endl;


	std::cin.clear();
	std::cin.ignore();
	std::cin.get();
	return 0;
}