/*
 * readdata.cpp, jonathan bober <jwb235@nyu.edu>, <bober@acm.cs.nyu.edu>
 * anyone is free to modify this program in anyway they want, and to do
 * whatever they want with it, so long as they do not claim that shoddy 
 * modifications were made by me.
 * if someone uses this for something useful, i would be happy to know.
 * 12/2002
 */

//this program reads in a file containing a list of primes
//and the longest increasing subsequences of the permutations
//they define.  it may also read in a list if numbers and
//means about those numbers, or can be modified to do various
//other things.
//mostly, this is a collection of functions that are used in different
//ways depending on some simple modifications of the main() function
#include <iostream>
#include <fstream>

#include <cmath>
#include <list>

using namespace std;

const int top = 50000010;  	//the largest prime that will be read in
int * len;	//array that will contain the lengths that will be read in

//takes a list of [sorted] numbers, (normally doubles) and creates a histogram 
//(probabiliy density graph) of them.  doesnt create an actual graph - simply 
//outputs to standard out a list of x and y coordinates which can be used by
//(for example) the graph program of gnu plotutils (search www.gnu.org for 
//plotutils for more info.)  can be easily modified to produce a probability
//distribution graph (not sure if i am using the right terms here.)
template<typename T>
void hist(std::list<T> input, int total = 0, double begin = -10, double inc = .02) {
	double area = 0;
        double ceiling = begin;
        //long total = input.count();
        //long total = 0;
        if(total==0) {
		for(std::list<T>::iterator i = input.begin(); i != input.end(); i++)
			total++;
	}

        long count = 0;
	T prev = begin;
        for(std::list<T>::iterator i = input.begin(); i != input.end(); i++) {
                if(*i > ceiling && prev < ceiling) {
                        std::cout << ceiling << "   " << (double)count/(total*inc)<< std::endl;
			area += ((double)count/total);
                        ceiling+=inc;
			count = 0;
                }
		else if (*i > ceiling) {
			while(*i > ceiling) ceiling+=inc;
			std::cout << ceiling - inc << "   " << 0 << std::endl;
		}
		prev = *i;
                count++;
        }
	cerr << area << endl;

}




//gets the mean of the lengths in an interval centered at N
double getmean(int N) {
	double l = log10((double)N);
	int A = (int)(300*(l * l)); 	// this is the interval length, which
					// can be changed easily

	int count = 0;
	int total = 0;
	for(int i = N - A; i < N + A; i++) {
		if(0 <= i && i <= top) {
			if(len[i] != -1) {
				count++;
				total += len[i];
			}
		}
	}
	cout << count << "    ";
	return total/(double)count;

}

//builds a list of data from the len array.  take an interval
//centered at N and builds a list of doubles, normalized somehow,
//depending on how the code is modified.
void buildList(int N, double mean, list<double> * o) {
	double l = log10((double)N);
	int A = (int)(300*(l*l*l));

	double two_twothird = pow(2, 2.0/3.0);
	double N_onesixth = pow(N, 1.0/6.0);

	double temp = two_twothird*N_onesixth;

	for(int i = N - A; i < N + A; i++) {
		if(0 <= i && i <= top) {
			if(len[i] != -1) {
//				cout << len[i] - mean << endl;
				o->push_back(((double)len[i] - (mean - 2 * sqrt(N) + 2 * sqrt(i)))/temp); 	//this can be modified to do various things
				//one modification simlpy inserts the lengths
				//and later the mean and variance of the list
				//is found and normalization uses this.
			}
		}
	}

	o->sort();

	//code can be inserted here to normalize the list to have
	//mean 0 and standard deviation 1
}

//prints out a list of a few stats of the distribution in the list o
//can (and normally should) be modified to return these stats instead
//of printing them out.
void getStats(list<double> * o) {
	
	int count = 0;
	double total = 0;
	
	double mean = 0;
	double mean_squared = 0;
	
	for(list<double>::iterator i = o->begin(); i!=o->end(); i++) {
		count++;
		mean += *i;
		mean_squared += (*i) * (*i);
	}

	mean = mean / count;
	mean_squared = mean_squared / count;

	double variance = mean_squared - mean*mean;
	double stddev = sqrt(variance);

	cout << "mean: " << mean << endl;
	cout << "variance: " << variance << endl;
	cout << "standard deviation: " << stddev  << endl;
	
}
				
				

//use depends on how this is put together.
//currently, this function reads in a list of primes and lengths and then
//computes some means and prints out some stuff about the lengths.  it is
//not too useful in its exact form.
//
//a good use modification i have made is to use this file to make a file
//full of values for means, and then read this file in with the file
//full of data, as computing many means can be time consuming.
int main(int argc, char * argv[]) {
	len = new int[top];
	for(int i = 0; i < top; i++) {
		len[i] = -1;
	}
	
	ifstream in(argv[1]);

	int prime;
	int curlen;

	in >> prime;
	in >> curlen;
	while(!in.eof()) {
		len[prime] = curlen;
		in >> prime;
		in >> curlen;
	}
	cerr << "got data" << endl;

	cout.precision(10);
	int N = 3000000;
	double mean = getmean(N);
//	for(int N = 1000000; N < 4500000; N+=10) 
		cout << N << (char)9 << mean << (char)9 << 2 * sqrt(N) << endl;
		
	list<double> l;
	
	buildList(N, mean, &l);

	for(list<double>::iterator i = l.begin(); i != l.end(); i++)
		cout << *i << endl;

	getStats(&l);

	hist(l);
	
	return 0;
}