USACO Section 1.4 Arithmetic Progressions

/*
ID: lucien23
PROG: ariprog
LANG: C++
*/

#include<iostream>
#include<fstream>
#include<set>
#include<vector>
#include<algorithm>
using namespace std;
typedef struct{
	int first;
	int different;
}ArithProgressions;

bool compProgressions(ArithProgressions item1,ArithProgressions item2)
{
	if(item1.different<item2.different)
		return true;
	else if(item1.different>item2.different)
		return false;
	else
	{
		if(item1.first<item2.first)
			return true;
		else
			return false;
	}
}

int main()
{
	ifstream infile("ariprog.in");
	ofstream outfile("ariprog.out");
	if(!infile || !outfile)
	{
		cout<<"file operation failure!"<<endl;
		return -1;
	}
	int N,M;
	infile>>N>>M;

	set<int> nums;
	vector<ArithProgressions> progressions;

	for (int i=0;i<=M;i++)
	{
		for (int j=0;j<=M;j++)
		{
			nums.insert(i*i+j*j);
		}
	}

	for (set<int>::iterator it=nums.begin();it!=nums.end();it++)
	{
		set<int>::iterator it1=it;
		while(++it1!=nums.end())
		{
			int diff=*it1-*it;
			if(*it+(N-1)*diff>2*M*M)
				break;
			int i;
			for (i=2;i<N;i++)//  i   0  ，     
			{
				int item=*it+i*diff;
				if(nums.find(item)==nums.end())
				{
					break;
				}
			}
			if(i==N)
			{
				ArithProgressions progression;
				progression.first=*it;
				progression.different=diff;
				progressions.push_back(progression);
			}
		}
	}

	sort(progressions.begin(),progressions.end(),compProgressions);

	if(progressions.size()==0)
		outfile<<"NONE"<<endl;
	else
	{
		for (vector<ArithProgressions>::iterator it=progressions.begin();it!=progressions.end();it++)
		{
			outfile<<it->first<<" "<<it->different<<endl;
		}
	}

	return 0;
}