Submission #62330

#	Time	Username	Problem	Language	Result	Execution time	Memory
62330		Benq	Fences (JOI18_fences)	C++11	100 / 100	438 ms	17388 KiB

fences

#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;
 
ld EPS = 1e-14;
 
template<class T> istream& operator>> (istream& is, complex<T>& p) {
    T value;
    is >> value; p.real(value);
    is >> value; p.imag(value);
    return is;
}
 
int N,S;
vector<pair<cd,cd>> p;
vector<vector<pair<int,pair<ld,int>>>> adj;
ld ans = INF;
 
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 bet(cd a, cd b, cd c) { return ((b-a)/(c-b)).real() > 0; }
 
cd closest(cd a, pair<cd,cd> b) {
    if (b.f == b.s) return b.f;
    auto x = proj(a,b.f,b.s);
    if (bet(b.f,x,b.s)) return x;
    return abs(a-b.f) < abs(a-b.s) ? b.f : b.s;
}
 
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); }
 
cd line(cd a, cd b, cd c, cd d) {
    ld x = area(a,b,c), y = area(a,b,d);
    return (x*d-y*c)/(x-y);
}
 
bool equiv(cd a, cd b) {
    return abs(1-abs(a/b)) <= EPS;
}
 
int inter(pair<cd,cd> bes) {
    F0R(i,4) {
        auto x = line({0,0},p[i].f,bes.f,bes.s);
        if (bet(bes.f,x,bes.s) && abs(x) < abs(p[i].f) && !equiv(p[i].f,x)) return MOD;
    }
    bool swa = 0;
    if (bes.f.imag() > bes.s.imag()) swa = 1, swap(bes.f,bes.s);
    if (bes.f.imag() < 0 && bes.s.imag() >= 0) {
        auto x = line({0,0},{1,0},bes.f,bes.s);
        if (x.real() < 0) return 0;
        if (swa == 0) return 1;
        return -1;
    }
    return 0;
}
 
pair<cd,cd> bet(pair<cd,cd> a, pair<cd,cd> b) {
     return (abs(a.f-a.s) < abs(b.f-b.s) ? a : b);
}
 
pair<ld,int> dis(pair<cd,cd> a, pair<cd,cd> b) {
    pair<cd,cd> bes = {{0,0},{INF,INF}};
    bes = bet(bes,{a.f,closest(a.f,b)});
    bes = bet(bes,{a.s,closest(a.s,b)});
    bes = bet(bes,{closest(b.f,a),b.f});
    bes = bet(bes,{closest(b.s,a),b.s});
    
    int x = inter(bes);
    
    if (x == MOD) return {INF,0};
    return {abs(bes.s-bes.f),x};
}
 
void input() {
    ios_base::sync_with_stdio(0); cin.tie(0);
    cin >> N >> S;
    p.pb({{S,S},{S,S}});
    p.pb({{S,-S},{S,-S}});
    p.pb({{-S,S},{-S,S}});
    p.pb({{-S,-S},{-S,-S}});
    F0R(i,N) {
        cd a,b; cin >> a >> b; a += cd(1e-9,1e-9); b += cd(1e-9,1e-9);
        if (a.imag() > b.imag()) swap(a,b);
        if (a.imag() < 0 && b.imag() >= 0) {
            auto x = line(a,b,{0,0},{1,0});
            if (x.real() > 0) {
                p.pb({a,x+EPS*(a-x)});
                p.pb({x,b});
                continue;
            }
        } 
        p.pb({a,b});
    }
}
 
ld dist[300][101];

void genDist(int x) {
    F0R(i,sz(p)) F0R(j,101) dist[i][j] = INF;
    priority_queue<pair<ld,pi>,vector<pair<ld,pi>>,greater<pair<ld,pi>>> p;
    p.push({dist[x][50] = 0, {x,0}});
    while (sz(p)) {
        auto a = p.top(); p.pop();
        if (a.f > dist[a.s.f][a.s.s+50]) continue;
        if (a.s.f == x && a.s.s != 0) {
            ans = min(ans,a.f);
            return;
        }
        for (auto x: adj[a.s.f]) {
            pi t = {x.f,a.s.s+x.s.s};
            if (abs(t.s) > 50) continue;
            if (x.s.f+a.f < dist[t.f][t.s+50]) {
                p.push({dist[t.f][t.s+50] = x.s.f+a.f,t});
            }
        }
    }
}
 
void genEdge() {
    // for (auto a: p) cout << a.f << " " << a.s << "\n";
    adj.resize(sz(p));
    F0R(i,sz(p)) {
        F0R(j,sz(p)) if (i != j) {
            auto a = dis(p[i],p[j]);
            if (a.f == INF) continue;
            // cout << i << " " << j << " " << a.f << " " << a.s << "\n";
            adj[i].pb({j,a});
        }
    }
}
 
int main() {
    input();
    genEdge();
    F0R(i,sz(p)) genDist(i);
    cout << fixed << setprecision(9) << ans;
}
 
/* Look for:
* the exact constraints (multiple sets are too slow for n=10^6 :( ) 
* special cases (n=1?)
* overflow (ll vs int?)
* array bounds
*/

Compilation message (stderr)

fences.cpp: In function 'void input()':
fences.cpp:117:23: warning: narrowing conversion of 'S' from 'int' to 'long double' inside { } [-Wnarrowing]
     p.pb({{S,S},{S,S}});
                       ^
fences.cpp:117:23: warning: narrowing conversion of 'S' from 'int' to 'long double' inside { } [-Wnarrowing]
fences.cpp:117:23: warning: narrowing conversion of 'S' from 'int' to 'long double' inside { } [-Wnarrowing]
fences.cpp:117:23: warning: narrowing conversion of 'S' from 'int' to 'long double' inside { } [-Wnarrowing]
fences.cpp:118:25: warning: narrowing conversion of 'S' from 'int' to 'long double' inside { } [-Wnarrowing]
     p.pb({{S,-S},{S,-S}});
                         ^
fences.cpp:118:14: warning: narrowing conversion of '- S' from 'int' to 'long double' inside { } [-Wnarrowing]
     p.pb({{S,-S},{S,-S}});
              ^~
fences.cpp:118:25: warning: narrowing conversion of 'S' from 'int' to 'long double' inside { } [-Wnarrowing]
     p.pb({{S,-S},{S,-S}});
                         ^
fences.cpp:118:21: warning: narrowing conversion of '- S' from 'int' to 'long double' inside { } [-Wnarrowing]
     p.pb({{S,-S},{S,-S}});
                     ^~
fences.cpp:119:12: warning: narrowing conversion of '- S' from 'int' to 'long double' inside { } [-Wnarrowing]
     p.pb({{-S,S},{-S,S}});
            ^~
fences.cpp:119:25: warning: narrowing conversion of 'S' from 'int' to 'long double' inside { } [-Wnarrowing]
     p.pb({{-S,S},{-S,S}});
                         ^
fences.cpp:119:19: warning: narrowing conversion of '- S' from 'int' to 'long double' inside { } [-Wnarrowing]
     p.pb({{-S,S},{-S,S}});
                   ^~
fences.cpp:119:25: warning: narrowing conversion of 'S' from 'int' to 'long double' inside { } [-Wnarrowing]
     p.pb({{-S,S},{-S,S}});
                         ^
fences.cpp:120:12: warning: narrowing conversion of '- S' from 'int' to 'long double' inside { } [-Wnarrowing]
     p.pb({{-S,-S},{-S,-S}});
            ^~
fences.cpp:120:15: warning: narrowing conversion of '- S' from 'int' to 'long double' inside { } [-Wnarrowing]
     p.pb({{-S,-S},{-S,-S}});
               ^~
fences.cpp:120:20: warning: narrowing conversion of '- S' from 'int' to 'long double' inside { } [-Wnarrowing]
     p.pb({{-S,-S},{-S,-S}});
                    ^~
fences.cpp:120:23: warning: narrowing conversion of '- S' from 'int' to 'long double' inside { } [-Wnarrowing]
     p.pb({{-S,-S},{-S,-S}});
                       ^~

• Subtask 1: 18 / 18
• Subtask 2: 33 / 33
• Subtask 3: 49 / 49