USACO-T016: Arithmetic Progressions

/*
ID: mickyta1
TASK: ariprog
LANG: C++
*/

#include <bits/stdc++.h>
using namespace std;

typedef pair<int, int> pii;

const int N = 125000 + 5;

vector<pii> ans;
vector<int> bisq;
bool isBisq[N];

bool comp(const pii &lhs, const pii &rhs){
    if(lhs.second != rhs.second){
        return lhs.second < rhs.second;
    }
    return lhs.first < rhs.first;
}

int main(){
    freopen("ariprog.in", "r", stdin);
    freopen("ariprog.out", "w", stdout);

    int n, limBisq;
    scanf("%d%d", &n, &limBisq);
    for(int i = 0; i <= limBisq; ++i){
        for(int j = i; j <= limBisq; ++j){
            int x = i * i + j * j;
            bisq.push_back(x);
            isBisq[x] = true;
        }
    }
    sort(bisq.begin(), bisq.end());
    bisq.resize(unique(bisq.begin(), bisq.end()) - bisq.begin());
    for(int i = 0; i < (int)bisq.size() - 1; ++i){
        for(int j = i + 1; j < bisq.size(); ++j){
            int a = bisq[i];
            int d = bisq[j] - bisq[i];
            if(a + (n - 1) * d > bisq.back()){
                break;
            }
            bool ok = true;
            for(int k = 1; k <= n; ++k){
                if(!isBisq[a + (k - 1) * d]){
                    ok = false;
                    break;
                }
            }
            if(ok){
                ans.emplace_back(a, d);
            }
        }
    }
    sort(ans.begin(), ans.end(), comp);
    if(ans.empty()){
        cout << "NONE\n";
    }
    for(pii p : ans){
        cout << p.first << ' ' << p.second << '\n';
    }

    fclose(stdin);
    fclose(stdout);
    return 0;
}