USACO 1.4 Arithmetic Progressions (ariprog)

/*
ID: haolink1
PROG: ariprog
LANG: C++
*/

//#include <iostream>
#include <fstream>
#include <vector>
#include <algorithm>    // std::sort
//#include <time.h>
using namespace std;
typedef unsigned int u_int;

class Solution{
public:
int begin_;
int diff_;
Solution(int begin,int diff):
begin_(begin),diff_(diff){}
};

bool CompareDiff(Solution first, Solution second){
if(first.diff_ < second.diff_)
return true;
else if(first.diff_ == second.diff_ && first.begin_ < second.begin_)
return true;
else return false;
}

bool CheckValid(bool* bisquares,int begin,int diff,int prog_len){
for(int i = 1; i < prog_len; i++){
//This is the most direct way to check the existence of the arithmetic progression
if(bisquares[begin + diff*i] == false)
return false;
}
return true;
}
int main(){
//    time_t timer_begin;
//    time(&timer_begin);
//    ofstream fout_log("logfile");
ifstream fin("ariprog.in");
int prog_len = 0;
int upper_bound = 0;
fin >> prog_len;
fin >> upper_bound;
vector<int> squares;
for(int i = 0; i <= upper_bound; i++)
squares.push_back(i*i);
//Note: comsume more memory to trade for speed, very important
const int  max_size = 125001;
bool bisquares_array[max_size]={false};
for(int i = 0; i <= upper_bound; i++){
for(int j = 0; j <= upper_bound; j++){
bisquares_array[squares[i]+squares[j]] = true;
}
}
vector<Solution> solutions;
int max_bisquare = upper_bound*upper_bound*2;
//The enumerate all case, we need triple loop, so we must choose the
//most costless way by reducing unnecessary computation and indexing;
//Enumerate first term
for(int i=0; i < max_size; i++){
if(bisquares_array[i] == true){
//Enumerate tolerance
//Use i+diff*(prog_len-1) <= max_bisquare to reduce unnecessary computation
for(int diff = 1; i+diff*(prog_len-1) <= max_bisquare; diff++){
if(CheckValid(bisquares_array,i,diff,prog_len))
solutions.push_back(Solution(i,diff));
}
}
}
sort(solutions.begin(),solutions.end(),CompareDiff);
ofstream fout("ariprog.out");
int size = solutions.size();
if(size == 0){
fout<<"NONE"<<endl;
return 0;
}
for(int i = 0; i < size; i++){
fout<<solutions[i].begin_<<" "<<solutions[i].diff_<<endl;
}
//    time_t timer_end;
//    time(&timer_end);
//    cout<<endl<<"Comsume time: "<<timer_end -timer_begin<<endl;
return 0;
}