This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include<bits/stdc++.h>
using namespace std;
#define int long long
#define F first
#define S second
#define all(x) x.begin(),x.end()
#define pii pair<int,int>
#define pb push_back
#define sz(x) (int)(x.size())
#define chmin(x,y) x=min(x,y)
#define chmax(x,y) x=max(x,y)
#define vi vector<int>
#define vp vector<pii>
#define vvi vector<vi>
#define ykh mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count())
#define __lg(x) 63-__builtin_clzll(x)
#define pow2(x) (1LL<<x)
void __print(int x) {cerr << x;}
void __print(float x) {cerr << x;}
void __print(double x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(char x) {cerr << '\'' << x << '\'';}
void __print(const char *x) {cerr << '\"' << x << '\"';}
void __print(const string &x) {cerr << '\"' << x << '\"';}
void __print(bool x) {cerr << (x ? "true" : "false");}
template<typename T, typename V>
void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ','; __print(x.second); cerr << '}';}
template<typename T>
void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? "," : ""), __print(i); cerr << "}";}
void _print() {cerr << "]\n";}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}
void setIO(string s) {
freopen((s + ".in").c_str(), "r", stdin);
freopen((s + ".out").c_str(), "w", stdout);
}
#ifdef local
void CHECK();
void setio(){
freopen("/Users/iantsai/cpp/input.txt","r",stdin);
freopen("/Users/iantsai/cpp/output.txt","w",stdout);
}
#define debug(x...) cerr << "[" << #x << "] = ["; _print(x)
#else
void setio(){}
#define debug(x...)
#endif
#define TOI_is_so_de ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);setio();
int cross(pii a, pii b){
return a.S*b.F-a.F*b.S;
}
tuple<int,int,int>exgcd(int a, int b){
if(b == 0)return {a, 1, 0};
auto [g, s, t] = exgcd(b, a%b);
return {g, t, s-a/b*t};
}
signed main(){
TOI_is_so_de;
int n;
cin >> n;
vector<pii>p(n+1);
int d[2][n];
memset(d, 0 ,sizeof(d));
for(int i=0;i<n;i++){
cin >> p[i].F >> p[i].S;
}
for(int i=0;i+1<n;i++){
d[0][i] = p[i+1].F-p[i].F;
d[1][i] = p[i+1].S-p[i].S;
}
for(int i=0;i+1<n;i++){
if(d[0][i]){
swap(d[0][i], d[0][0]);
swap(d[1][i], d[1][0]);
break;
}
}
if(d[0][0] == 0){
cout << -1 << '\n';
return 0;
}
int ans = 0;
for(int i=1;i+1<n;i++){
auto [g, s, t] = exgcd(d[0][0], d[0][i]);
//if(s == 0)swap(s,t);
int f = d[0][0]*s+d[0][i]*t;
int f2 = d[1][0]*s+d[1][i]*t;
//debug(s, t);
s = d[1][0]*(-d[0][i]/g)+d[1][i]*(d[0][0]/g);
d[0][0] = f;
//debug(d[1][0], d[1][i]*(d[0][0]/g));
//debug(d[0][0], d[1][0], d[0][i], d[1][i], g, s);
if(ans)d[1][0] = f2%ans;
else d[1][0] = f2;
//s = abs(d[1][i] - d[0][i]/g*d[1][0]);
//debug(d[0][0], d[1][0], d[0][i], d[1][i], g, s);
ans = gcd(ans, s);
}
ans = abs(ans*d[0][0]);
cout << (ans == 0 ? -1 : ans) << '\n';
#ifdef local
CHECK();
#endif
}
/*
input:
2 -1
0 2
*/
#ifdef local
void CHECK(){
cerr << "\n[Time]: " << 1000.0 * clock() / CLOCKS_PER_SEC << " ms.\n";
function<bool(string,string)> compareFiles = [](string p1, string p2)->bool {
std::ifstream file1(p1);
std::ifstream file2(p2);
if (!file1.is_open() || !file2.is_open())return false;
std::string line1, line2;
while (getline(file1, line1) && getline(file2, line2)) {
if (line1 != line2)return false;
}
int cnta=0,cntb=0;
while(getline(file1,line1))cnta++;
while(getline(file2,line2))cntb++;
return cntb-cnta<=1;
};
bool check = compareFiles("output.txt","expected.txt");
if (check) cerr<<"ACCEPTED\n";
else cerr<<"WRONG ANSWER!\n";
}
#else
#endif
Compilation message (stderr)
Main.cpp: In function 'void setIO(std::string)':
Main.cpp:35:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
35 | freopen((s + ".in").c_str(), "r", stdin);
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Main.cpp:36:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
36 | freopen((s + ".out").c_str(), "w", stdout);
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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