結果

問題 No.2180 Comprehensive Line Segments
ユーザー heno239
提出日時 2023-01-06 23:23:24
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
(最新)
AC  
(最初)
実行時間 -
コード長 11,299 bytes
コンパイル時間 2,434 ms
コンパイル使用メモリ 177,324 KB
最終ジャッジ日時 2025-02-10 00:25:31
ジャッジサーバーID
（参考情報） 		judge3 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 23 WA * 2
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ソースコード

diff #
プレゼンテーションモードにする

#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<unordered_set>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
#include<array>
#include<chrono>
using namespace std;
//#define int long long
typedef long long ll;
typedef unsigned long long ul;
typedef unsigned int ui;
constexpr ll mod = 998244353;
//constexpr ll mod = 1000000007;
const ll INF = mod * mod;
typedef pair<int, int>P;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;
template<typename T>
void chmin(T& a, T b) {
    a = min(a, b);
}
template<typename T>
void chmax(T& a, T b) {
    a = max(a, b);
}
template<typename T>
void cinarray(vector<T>& v) {
    rep(i, v.size())cin >> v[i];
}
template<typename T>
void coutarray(vector<T>& v) {
    rep(i, v.size()) {
        if (i > 0)cout << " "; cout << v[i];
    }
    cout << "\n";
}
ll mod_pow(ll x, ll n, ll m = mod) {
    if (n < 0) {
        ll res = mod_pow(x, -n, m);
        return mod_pow(res, m - 2, m);
    }
    if (abs(x) >= m)x %= m;
    if (x < 0)x += m;
    //if (x == 0)return 0;
    ll res = 1;
    while (n) {
        if (n & 1)res = res * x % m;
        x = x * x % m; n >>= 1;
    }
    return res;
}
//mod should be <2^31
struct modint {
    int n;
    modint() :n(0) { ; }
    modint(ll m) {
        if (m < 0 || mod <= m) {
            m %= mod; if (m < 0)m += mod;
        }
        n = m;
    }
    operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
bool operator<(modint a, modint b) { return a.n < b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= (int)mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += (int)mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, ll n) {
    if (n == 0)return modint(1);
    modint res = (a * a) ^ (n / 2);
    if (n % 2)res = res * a;
    return res;
}
ll inv(ll a, ll p) {
    return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }
modint operator/=(modint& a, modint b) { a = a / b; return a; }
const int max_n = 1 << 20;
modint fact[max_n], factinv[max_n];
void init_f() {
    fact[0] = modint(1);
    for (int i = 0; i < max_n - 1; i++) {
        fact[i + 1] = fact[i] * modint(i + 1);
    }
    factinv[max_n - 1] = modint(1) / fact[max_n - 1];
    for (int i = max_n - 2; i >= 0; i--) {
        factinv[i] = factinv[i + 1] * modint(i + 1);
    }
}
modint comb(int a, int b) {
    if (a < 0 || b < 0 || a < b)return 0;
    return fact[a] * factinv[b] * factinv[a - b];
}
modint combP(int a, int b) {
    if (a < 0 || b < 0 || a < b)return 0;
    return fact[a] * factinv[a - b];
}
ll gcd(ll a, ll b) {
    a = abs(a); b = abs(b);
    if (a < b)swap(a, b);
    while (b) {
        ll r = a % b; a = b; b = r;
    }
    return a;
}
using ld = long double;
//typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-10;
const ld pi = acosl(-1.0);
template<typename T>
void addv(vector<T>& v, int loc, T val) {
    if (loc >= v.size())v.resize(loc + 1, 0);
    v[loc] += val;
}
/*const int mn = 2000005;
bool isp[mn];
vector<int> ps;
void init() {
    fill(isp + 2, isp + mn, true);
    for (int i = 2; i < mn; i++) {
        if (!isp[i])continue;
        ps.push_back(i);
        for (int j = 2 * i; j < mn; j += i) {
            isp[j] = false;
        }
    }
}*/
//[,val)
template<typename T>
auto prev_itr(set<T>& st, T val) {
    auto res = st.lower_bound(val);
    if (res == st.begin())return st.end();
    res--; return res;
}
//[val,)
template<typename T>
auto next_itr(set<T>& st, T val) {
    auto res = st.lower_bound(val);
    return res;
}
using mP = pair<modint, modint>;
mP operator+(mP a, mP b) {
    return { a.first + b.first,a.second + b.second };
}
mP operator+=(mP& a, mP b) {
    a = a + b; return a;
}
mP operator-(mP a, mP b) {
    return { a.first - b.first,a.second - b.second };
}
mP operator-=(mP& a, mP b) {
    a = a - b; return a;
}
LP operator+(LP a, LP b) {
    return { a.first + b.first,a.second + b.second };
}
LP operator+=(LP& a, LP b) {
    a = a + b; return a;
}
LP operator-(LP a, LP b) {
    return { a.first - b.first,a.second - b.second };
}
LP operator-=(LP& a, LP b) {
    a = a - b; return a;
}
mt19937 mt(time(0));
const string drul = "DRUL";
string senw = "SENW";
//DRUL,or SENW
int dx[4] = { 1,0,-1,0 };
int dy[4] = { 0,1,0,-1 };
//-----------------------------------------
typedef complex<ld> Point;
ld dot(Point a, Point b) { return real(conj(a) * b); }
ld cross(Point a, Point b) { return imag(conj(a) * b); }
namespace std {
    bool operator<(const Point& lhs, const Point& rhs) {
        return lhs.real() == rhs.real() ? lhs.imag() < rhs.imag() : lhs.real() < rhs.real();
    }
}
struct Line {
    Point a, b;
};
struct Circle {
    Point p; ld r;
};
int ccw(Point a, Point b, Point c) {
    b -= a; c -= a;
    if (cross(b, c) > eps)return 1;//counter clockwise
    if (cross(b, c) < -eps)return -1;//clock wise
    if (dot(b, c) < 0)return 2;//c--a--b on line
    if (norm(b) < norm(c))return -2;//a--b--c on line
    return 0; //a--c--b on line
}
bool eq(ld a, ld b) {
    return abs(a - b) < eps;
}
//2直線の交差判定
bool isis_ll(Line l, Line m) {
    return !eq(cross(l.b - l.a, m.b - m.a), 0);
}
//直線と線分の交差判定
bool isis_ls(Line l, Line s) {
    return (cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < eps);
}
//点が直線上に存在するか
bool isis_lp(Line l, Point p) {
    return (abs(cross(l.b - p, l.a - p)) < eps);
}
//点が線分上に存在するか
bool isis_sp(Line s, Point p) {
    //誤差がisis_lpに比べて大きいので、できるだけisis_lpを使う
    return (abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a) < eps);
}
//線分と線分の交差判定
//bool isis_ss(Line s, Line t) {
//  return(cross(s.b - s.a, t.a - s.a)*cross(s.b - s.a, t.b - s.a) < -eps && cross(t.b - t.a, s.a - t.a)*cross(t.b - t.a, s.b - t.a) < -eps);
//}
//線分と線分の交差判定2
//本当にそれは線分ですか？(check {(0,0),(2,0)},{(1,0),(1,0)})
bool isis_ss(Line s, Line t) {
    return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 && ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0;
}
//点から直線への垂線の足
Point proj(Line l, Point p) {
    ld t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
    return l.a + t * (l.a - l.b);
}
//直線と直線の交点
//平行な２直線に対しては使うな！！！！
Point is_ll(Line s, Line t) {
    Point sv = s.b - s.a; Point tv = t.b - t.a;
    return s.a + sv * cross(tv, t.a - s.a) / cross(tv, sv);
}
//直線と点の距離
ld dist_lp(Line l, Point p) {
    return abs(p - proj(l, p));
}
//直線と直線の距離
ld dist_ll(Line l, Line m) {
    return isis_ll(l, m) ? 0 : dist_lp(l, m.a);
}
//線分と直線の距離
ld dist_ls(Line l, Line s) {
    return isis_ls(l, s) ? 0 : min(dist_lp(l, s.a), dist_lp(l, s.b));
}
//線分と点の距離
ld dist_sp(Line s, Point p) {
    Point r = proj(s, p);
    return isis_sp(s, r) ? abs(p - r) : min(abs(p - s.a), abs(p - s.b));
}
//線分と線分の距離
ld dist_ss(Line s, Line t) {
    if (isis_ss(s, t))return 0;
    return min({ dist_sp(s,t.a),dist_sp(s,t.b),dist_sp(t,s.a),dist_sp(t,s.b) });
}
//線分と線分の交点、平行な場合は端点両方
vector<Point> is_ss(Line s1, Line s2) {
    if (!isis_ss(s1, s2))return {};
    vector<Point> res;
    if (abs(cross(s1.b - s1.a, s2.b - s2.a)) < eps) {
        if (isis_sp(s1, s2.a)) res.push_back(s2.a);
        if (isis_sp(s1, s2.b)) res.push_back(s2.b);
        if (isis_sp(s2, s1.a)) res.push_back(s1.a);
        if (isis_sp(s2, s1.b)) res.push_back(s1.b);
    }
    else {
        res.push_back(is_ll(s1, s2));
    }
    return res;
}
//2点の垂直二等分線
Line mid_line(Point a, Point b) {
    ld mx = (real(a) + real(b)) / 2.0, my = (imag(a) + imag(b)) / 2.0;
    ld dx = real(b) - real(a), dy = imag(b) - imag(a);
    swap(dx, dy); dx = -dx;
    Point le = { mx - dx,my - dy }, ri = { mx + dx,my + dy };
    //a,le,ri is counter clockwise
    return { le,ri };
}
//三角形の面積
ld area(Point a, Point b, Point c) {
    ld x1 = real(b) - real(a), y1 = imag(b) - imag(a);
    ld x2 = real(c) - real(a), y2 = imag(c) - imag(a);
    return abs(x1 * y2 - y1 * x2) / 2.0;
}
//直線lに幅dをつける
vector<Line> make_w(Line l, ld d) {
    Point dif = l.b - l.a;
    dif = dif * Point{ 0, 1 };
    dif = dif * (d / abs(dif));
    vector<Line> ret;
    for (int id = -1; id <= 1; id += 2) {
        Point a = l.a + dif * (ld)id;
        Point b = l.b + dif * (ld)id;
        ret.push_back({ a,b });
    }
    return ret;
}
//mid_line of two lines
vector<Line> mid_ll(Line l, Line m) {
    if (!isis_ll(l, m)) {
        ld u = dist_ll(l, m);
        Point d = l.b - l.a;
        Point md = d * exp(Point{ 0,pi / 2.0 });
        Line l_ = { l.a,l.a + md };
        Point ma = is_ll(l_, m);
        Point dif = ma - l.a;
        dif /= 2.0;
        Line res = { l.a + dif,(l.a + dif) + d };
        return { res };
    }
    else {
        Point p = is_ll(l, m);
        ld t1 = arg(l.b - l.a);
        ld t2 = arg(m.b - m.a);
        ld t = (t1 + t2) / 2.0;
        Point dif = { cos(t),sin(t) };
        Point np = p + dif;
        ld d1 = dist_lp(l, np);
        ld d2 = dist_lp(m, np);
        vector<Line> res;
        res.push_back({ p,p + dif });
        t += pi / 2.0;
        dif = { cos(t),sin(t) };
        res.push_back({ p,p + dif });
        return res;
    }
}
void solve() {
    int n; cin >> n;
    vector<int> x(n), y(n);
    rep(i, n)cin >> x[i] >> y[i];
    if (n == 1) {
        cout << 1 << "\n"; return;
    }
    vector<Point> p(n);
    rep(i, n) {
        p[i] = { (ld)x[i],(ld)y[i] };
    }
    vector<Point> vp = p;
    rep(i, n)Rep(j, i + 1, n) {
        rep(k, n)Rep(l, k+1, n) {
            if (P{ i,j } < P{ k,l }) {
                Line l1 = { p[i],p[j] };
                Line l2 = { p[k],p[l] };
                if (isis_ll(l1, l2)) {
                    Point c = is_ll(l1, l2);
                    bool valid = true;
                    for (auto pre : vp) {
                        if (abs(pre - c) < eps)valid = false;
                    }
                    if(valid)
                    vp.push_back(c);
                }
            }
        }
    }
    int sz = vp.size();
    //cout << sz << "\n";
    //rep(i, sz)cout << vp[i] << "\n";
    struct edge {
        int to, cost;
    };
    vector<vector<edge>> vs(sz);
    rep(i, sz)Rep(j, i + 1, sz) {
        Line l = { vp[i],vp[j] };
        int val = 0;
        int cnt = 0;
        rep(k, n) {
            if (isis_sp(l, p[k])) {
                val |= (1 << k); cnt++;
            }
        }
        if (cnt >= 2) {
            vs[i].push_back({ j,val });
            vs[j].push_back({ i,val });
        }
    }
    vector<vector<int>> dp(1<<n, vector<int>(sz,mod));
    rep(i, sz) {
        int val = 0;
        rep(j, n) {
            ld d = abs(vp[i] - p[j]);
            if (d < eps) {
                val |= (1 << j);
            }
        }
        dp[val][i] = 0;
    }
    rep(i, (1 << n)) {
        rep(j, sz) {
            if (dp[i][j] == mod)continue;
            for (edge e : vs[j]) {
                int ni = i | e.cost;
                chmin(dp[ni][e.to], dp[i][j] + 1);
            }
        }
    }
    int ans = mod;
    rep(i, sz)chmin(ans, dp[(1 << n) - 1][i]);
    cout << ans << "\n";
}
signed main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    //cout << fixed << setprecision(10);
    //init_f();
    //init();
    //expr();
    //while(true)
    //int t; cin >> t; rep(i, t)
    solve();
    return 0;
}
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