Submission #59353

#	Time	Username	Problem	Language	Result	Execution time	Memory
59353		Benq	2circles (balkan11_2circles)	C++14	10 / 100	4051 ms	4468 KiB

twocircles

#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>

using namespace std;
using namespace __gnu_pbds;
 
typedef long long ll;
typedef long double ld;
typedef complex<ld> cd;

typedef pair<int, int> pi;
typedef pair<ll,ll> pl;
typedef pair<ld,ld> pd;

typedef vector<int> vi;
typedef vector<ld> vd;
typedef vector<ll> vl;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<cd> vcd;

template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update>;

#define FOR(i, a, b) for (int i=a; i<(b); i++)
#define F0R(i, a) for (int i=0; i<(a); i++)
#define FORd(i,a,b) for (int i = (b)-1; i >= a; i--)
#define F0Rd(i,a) for (int i = (a)-1; i >= 0; i--)

#define sz(x) (int)(x).size()
#define mp make_pair
#define pb push_back
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound
#define all(x) x.begin(), x.end()

const int MOD = 1000000007;
const ll INF = 1e18;
const int MX = 100001;

typedef pair<cd,ld> circ;

int N;
ld lo = 0, hi = 1e8;
cd p[50000];

bool overlap(circ a, circ b) {
    return abs(a.f-b.f) < a.s+b.s;
}

template<class T> istream& operator>> (istream& is, complex<T>& p) {
    T value;
    is >> value; p.real(value);
    is >> value; p.imag(value);
    return is;
}

cd reflect(cd p, cd a, cd b) { return a+conj((p-a)/(b-a))*(b-a); }
cd proj(cd p, cd a, cd b) { return (p+reflect(p,a,b))/(ld)2; }

bool obtuse(cd a, cd b, cd c) {
    cd z = (a-b)/(c-b);
    return z.real() < 0;
}

ld dist(cd a, cd b, cd c) {
    // cout << "A\n";
    if (obtuse(a,b,c)) return abs(a-b);
    // cout << "B " << a << " " << c << "\n";
    if (obtuse(a,c,b)) return abs(a-c);
    // cout << "C\n";
    return abs(a-proj(a,b,c));
}

ld cross(cd a, cd b) { return (conj(a)*b).imag(); }

ld area(cd a, cd b, cd c) { return cross(b-a,c-a); }

int sgn(ld x) {
    if (x > 0) return 1;
    if (x == 0) return 0;
    return -1;
}

ld side(cd a, cd b, cd c) { return sgn(area(a,b,c)); }
bool ok(circ x) {
    F0R(i,N) {
        if (side(x.f,p[i],p[(i+1)%N]) != side(p[(i+N-1)%N],p[i],p[(i+1)%N])) return 0;
        // cout << x.f << " " << p[i] << " " << p[(i+1)%N] << " " << dist(x.f,p[i],p[(i+1)%N]) << "\n";
        // cout << obtuse(x.f,p[i],p[(i+1)%N]) << "\n";
        if (dist(x.f,p[i],p[(i+1)%N]) < x.s-(1e-9)) return 0;
    }
    return 1;
}

circ genCirc(int i, ld rad) {
    ld a = arg(p[(i+1)%N]-p[i]);
    ld b = arg(p[(i+N-1)%N]-p[i]);
    
    cd offset;
    while (b <= a) b += 2*M_PIl;
    if (b > a+M_PIl) while (a <= b) a += M_PIl;
    offset = polar((ld)1,(a+b)/2);
    ld dis = abs(offset-proj(offset,cd(0,0),p[(i+N-1)%N]-p[i]));
    offset *= rad/dis;
    return {p[i]+offset,rad};
}

bool test(ld mid) {
    vector<circ> v;
    F0R(i,N) {
        circ x = genCirc(i,mid);
        if (ok(x)) {
            // cout << x.f.real() << " " << x.f.imag() << " " << x.s << "\n";
            v.pb(x);
        }
    }
    F0R(i,sz(v)) FOR(j,i+1,sz(v)) if (!overlap(v[i],v[j])) return 1;
    return 0;
}

int main() {
    ios_base::sync_with_stdio(0); cin.tie(0);
    cin >> N;
    F0R(i,N) cin >> p[i];
    while (hi-lo > (1e-4)) {
        ld mid = (lo+hi)/2;
        if (test(mid)) lo = mid;
        else hi = mid;
    }
    cout << fixed << setprecision(3) << (lo+hi)/2;
}

/* Look for:
* the exact constraints (multiple sets are too slow for n=10^6 :( ) 
* special cases (n=1?)
* overflow (ll vs int?)
* array bounds
*/

• Subtask 1: 10 / 100