結果

問題 No.2180 Comprehensive Line Segments
コンテスト
ユーザー MasKoaTS
提出日時 2022-09-11 17:56:41
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
MLE  
(最新)
AC  
(最初)
実行時間 -
コード長 5,616 bytes
コンパイル時間 3,168 ms
コンパイル使用メモリ 240,908 KB
最終ジャッジ日時 2025-02-07 04:21:49
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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 * 2 MLE * 2
other AC * 13 WA * 1 TLE * 2 MLE * 9
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>
#define rep(i, l, n) for (int i = (l); i < (n); i++)
#define abs(x) (((x) < 0) ? -(x) : (x))
#define inf 1000000000
#define INF Fraction(1000000000ll, 1ll)
using namespace std;
using ll = long long;
template <class T>	using V = vector<T>;

inline ll gcd(ll x, ll y) {
	x = abs(x);	y = abs(y);
	while (y != 0) {
		ll r = x % y;
		x = y;
		y = r;
	}
	return x;
}

inline ll lcm(ll x, ll y) {
	ll g = gcd(x, y);
	return x / g * y;
}

struct Fraction {
	ll num;
	ll den;

	Fraction(void) {
		num = 0ll;
		den = 1ll;
	}

	Fraction(ll num, ll den) {
		assert(den != 0);
		ll g = gcd(num, den);
		num /= g;
		den /= g;
		if (den < 0) {
			num = -num;
			den = -den;
		}
		this->num = num;
		this->den = den;
	}

	Fraction operator+(const Fraction other) const {
		ll l = lcm(this->den, other.den);
		ll a = l / this->den;
		ll b = l / other.den;
		ll nnum = this->num * a + other.num * b;
		ll nden = l;
		return Fraction(nnum, nden);
	}

	Fraction operator-(const Fraction other) const {
		Fraction f = Fraction(-other.num, other.den);
		return (*this) + f;
	}

	Fraction operator*(const Fraction other) const {
		ll nnum = this->num * other.num;
		ll nden = this->den * other.den;
		return Fraction(nnum, nden);
	}

	Fraction operator/(const Fraction other) const {
		Fraction f = Fraction(other.den, other.num);
		return (*this) * f;
	}

	bool operator<(const Fraction other) const {
		ll l = lcm(this->den, other.den);
		ll a = l / this->den;
		ll b = l / other.den;
		return (this->num * a < other.num * b);
	}

	bool operator==(const Fraction other) const {
		ll l = lcm(this->den, other.den);
		ll a = l / this->den;
		ll b = l / other.den;
		return (this->num * a == other.num* b);
	}
};


struct Point {
	Fraction x;
	Fraction y;

	Point(void) {
		x = Fraction();
		y = Fraction();
	}

	Point(Fraction x, Fraction y) {
		this->x = x;
		this->y = y;
	}

	bool operator<(const Point other) const {
		return tie(this->x, this->y) < tie(other.x, other.y);
	}

	bool isNull(void) {
		return (this->x == INF and this->y == INF);
	}
};

struct Line {
	Fraction a;
	Fraction b;
	Fraction c;

	Line(void) {
		a = Fraction();
		b = Fraction();
		c = Fraction();
	}

	Line(Fraction a, Fraction b, Fraction c) {
		this->a = a;
		this->b = b;
		this->c = c;
	}

	bool operator<(const Line other) const {
		return tie(this->a, this->b, this->c) < tie(other.a, other.b, other.c);
	}

	bool operator==(const Line other) const {
		return tie(this->a, this->b, this->c) == tie(other.a, other.b, other.c);
	}
};

Line calcLine(Point one, Point other) {
	Fraction x1 = one.x, y1 = one.y;
	Fraction x2 = other.x, y2 = other.y;
	if (x1 == x2) {
		return Line(Fraction(1ll, 1ll), Fraction(0ll, 1ll), x1);
	}
	Fraction a = (y1 - y2) / (x1 - x2);
	Fraction c = y1 - a * x1;
	return Line(Fraction() - a, Fraction(1ll, 1ll), c);
}

Point intersection(Line one, Line other) {
	Fraction p = one.a * other.b - other.a * one.b;
	if (p == Fraction()) {
		return Point(INF, INF);
	}
	Fraction q = other.b * one.c - one.b * other.c;
	Fraction x = q / p;
	Fraction y = (one.b == Fraction()) ? ((other.c - other.a * x) / other.b) : ((one.c - one.a * x) / one.b);
	return Point(x, y);
}


/*
* Main Code
*/

int main(void) {
	int N;	cin >> N;
	V<Point> P(N);
	rep(i, 0, N) {
		ll x, y;	cin >> x >> y;
		P[i] = { Fraction(x,1ll),Fraction(y,1ll) };
	}

	if (N == 1) {
		cout << 1 << endl;
		return 0;
	}

	map<Point, int> ph = {};
	int pt_id = 0;
	for (Point p : P) {
		ph[p] = pt_id;
		pt_id++;
	}

	int ln_id = 0;
	map<Line, int> lh = {};
	V<Line> vec = {};
	rep(i, 0, N - 1) {
		rep(j, i + 1, N) {
			Point p1 = P[i], p2 = P[j];
			Line l = calcLine(p1, p2);
			if (lh.find(l) != lh.end()) {
				continue;
			}
			lh[l] = ln_id;
			ln_id++;
			vec.push_back(l);
		}
	}

	rep(i, 0, ln_id - 1) {
		rep(j, i + 1, ln_id) {
			Line l1 = vec[i], l2 = vec[j];
			Point p = intersection(l1, l2);
			if (p.isNull() or ph.find(p) != ph.end()) {
				continue;
			}
			//cout << p.x.num << '/' << p.x.den << ' ' << p.y.num << '/' << p.y.den << endl;
			P.push_back(p);
			ph[p] = pt_id;
			pt_id++;
		}
	}

	//cout << ln_id << ' ' << pt_id << endl;

	V<V<pair<int, int> > > dir_lis(pt_id, V<pair<int, int> >(pt_id, pair<int, int>({ inf,0 })));
	rep(i, 0, pt_id - 1) {
		rep(j, i + 1, pt_id) {
			Point p1 = P[i], p2 = P[j];
			Line l = calcLine(p1, p2);
			if (lh.find(l) == lh.end()) {
				continue;
			}
			dir_lis[i][j] = { lh[l], (p1 < p2) };
			dir_lis[j][i] = { lh[l], (p2 < p1) };
		}
	}

	//cout << ln_id << ' ' << pt_id << endl;

	V<V<V<V<int> > > > dp(1 << N, V<V<V<int> > >(pt_id, V<V<int> >(ln_id + 1, V<int>(2, inf))));
	deque<V<int> > que = {};
	rep(i, 0, N) {
		que.push_back({ 0, 1 << i, i, ln_id, 0 });
		dp[1 << i][i][ln_id][0] = 0;
	}
	int goal = (1 << N) - 1;
	int ans = inf;
	int cnt = 0;
	while (que.empty() == false) {
		V<int> vec = que.front();	que.pop_front();
		int c = vec[0], b = vec[1], v = vec[2], l = vec[3], a = vec[4];
		//cout << c << ' ' << b << ' ' << v << ' ' << l << ' ' << a << endl;
		if (l != ln_id and c > dp[b][v][l][a]) {
			continue;
		}
		if (b == goal) {
			ans = c;
			break;
		}
		rep(nv, 0, pt_id) {
			int nb = (nv < N) ? (b | (1 << nv)) : b;
			if (dir_lis[v][nv].first == inf) {
				continue;
			}
			int nl = dir_lis[v][nv].first, na = dir_lis[v][nv].second;
			int nc = c;
			if (l == ln_id or l != nl or a != na) {
				nc++;
			}
			if (nc >= dp[nb][nv][nl][na]) {
				continue;
			}
			dp[nb][nv][nl][na] = nc;
			if (nc == c) {
				que.push_front({ nc, nb, nv, nl, na });
			}
			else {
				que.push_back({ nc, nb, nv, nl, na });
			}
		}
	}
	cout << ans << endl;

	return 0;
}
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