Cod sursa(job #3358943)

Utilizator alexdumitrascuDumitrascu Stefan-Alexandru alexdumitrascu Data 22 iunie 2026 10:30:36
Problema Infasuratoare convexa Scor 20
Compilator cpp-64 Status done
Runda Arhiva educationala Marime 1.37 kb
#include <iostream>
#include <fstream>
#include <algorithm>
#include <cmath>

using namespace std;
ifstream fin("infasuratoare.in");
ofstream fout("infasuratoare.out");

long double x[120005], y[120005];
int id[120005];
int stk[120005];

long double cross(int O, int A, int B) {
    return (x[A]-x[O]) * (y[B]-y[O]) - (y[A]-y[O]) * (x[B]-x[O]);
}

bool cmp(int a, int b) {
    long double cr = cross(0, a, b);
    if (fabsl(cr) > 1e-12) return cr > 0;
    long double da = (x[a]-x[0])*(x[a]-x[0]) + (y[a]-y[0])*(y[a]-y[0]);
    long double db = (x[b]-x[0])*(x[b]-x[0]) + (y[b]-y[0])*(y[b]-y[0]);
    return da<db;
}

int main()
{
    int n, sz=0;
    fin.tie(0);
    fin.sync_with_stdio(false);

    fin>>n;
    for (int i=1; i<=n; i++) 
        fin>>x[i]>>y[i];

    int pi=1;
    for (int i=2; i<=n; i++) {
        if (y[i]<y[pi] || (y[i]==y[pi] && x[i]<x[pi])) {
            pi=i;
        }
    }

    swap(x[1], x[pi]); swap(y[1], y[pi]);
    for (int i=0; i<n; i++) { 
        x[i]=x[i+1]; 
        y[i]=y[i+1]; 
    }
    for (int i=1; i<n; i++) id[i]=i;
    sort(id+1, id+n, cmp);

    stk[0]=0; stk[1]=id[1]; sz=2;
    for (int i=2; i<n; i++) {
        while (sz >= 2 && cross(stk[sz-2], stk[sz-1], id[i]) <= 0) {
            sz--;
        }
        stk[sz++]=id[i];
    }

    fout<<sz<<"\n";
    for (int i=0; i<sz; i++) {
        fout<<x[stk[i]]<<" "<<y[stk[i]]<<"\n";
    }
    return 0;
}