結果

問題 No.2180 Comprehensive Line Segments
ユーザー MasKoaTSMasKoaTS
提出日時 2022-10-12 21:52:43
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
MLE  
(最新)
AC  
(最初)
実行時間 -
コード長 5,966 bytes
コンパイル時間 3,635 ms
コンパイル使用メモリ 252,132 KB
実行使用メモリ 813,952 KB
最終ジャッジ日時 2024-04-28 10:34:41
合計ジャッジ時間 8,000 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 9 ms
6,812 KB
testcase_01 AC 2 ms
6,944 KB
testcase_02 AC 2 ms
6,944 KB
testcase_03 MLE -
testcase_04 -- -
testcase_05 -- -
testcase_06 -- -
testcase_07 -- -
testcase_08 -- -
testcase_09 -- -
testcase_10 -- -
testcase_11 -- -
testcase_12 -- -
testcase_13 -- -
testcase_14 -- -
testcase_15 -- -
testcase_16 -- -
testcase_17 -- -
testcase_18 -- -
testcase_19 -- -
testcase_20 -- -
testcase_21 -- -
testcase_22 -- -
testcase_23 -- -
testcase_24 -- -
testcase_25 -- -
testcase_26 -- -
testcase_27 -- -
testcase_28 -- -
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ソースコード

diff # 

#include <bits/stdc++.h>
#define rep(i, l, n) for (int i = (l); i < (n); i++)
#define inf 1000000000
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);
	}

	bool operator!=(const Fraction other) const {
		return (((*this) == other) == false);
	}
};
const Fraction zero = Fraction();
inline Fraction abs_frac(Fraction x) {
	return ((x < zero) ? zero - x : x);
}


struct Vector2 {
	Fraction x;
	Fraction y;

	Vector2(void) {
		x = zero;
		y = zero;
	}

	Vector2(Fraction x, Fraction y) {
		this->x = x;
		this->y = y;
	}

	Vector2 operator-(const Vector2 other) const {
		return Vector2(other.x - this->x, other.y - this->y);
	}

	bool operator<(const Vector2 other) const {
		return tie(this->x, this->y) < tie(other.x, other.y);
	}

	bool operator==(const Vector2 other) const {
		return tie(this->x, this->y) == tie(other.x, other.y);
	}

	bool operator!=(const Vector2 other) const {
		return tie(this->x, this->y) != tie(other.x, other.y);
	}
};
const Vector2 zero_vector = Vector2();


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

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

	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);
	}
};

Line calcLine(Vector2 one, Vector2 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(zero - a, Fraction(1ll, 1ll), c);
}

Vector2* calcIntersection(Line one, Line other) {
	Fraction p = one.a * other.b - other.a * one.b;
	if (p == zero) {
		return nullptr;
	}
	Fraction q = other.b * one.c - one.b * other.c;
	Fraction x = q / p;
	Fraction y = (one.b == zero) ? ((other.c - other.a * x) / other.b) : ((one.c - one.a * x) / one.b);
	return new Vector2(x, y);
}

Vector2 normalize_vector(Vector2 v) {
	assert(v.x != zero or v.y != zero);
	Fraction norm = v.x * v.x + v.y * v.y;
	return Vector2(v.x * abs_frac(v.x) / norm, v.y * abs_frac(v.y) / norm);
}


/*
* Main Code
*/

int main(void) {
	// 入力
	int N;	cin >> N;
	V<Vector2> P(N);
	rep(i, 0, N) {
		ll x, y;	cin >> x >> y;
		P[i] = { Fraction(x,1ll),Fraction(y,1ll) };
	}

	// 点が1個のときは必ず答え1
	if (N == 1) {
		cout << 1 << endl;
		return 0;
	}

	// 各点に番号付け
	map<Vector2, int> ph = {};
	int pt_id = 0;
	for (Vector2& p : P) {
		ph[p] = pt_id;
		pt_id++;
	}

	// 有り得る直線を調べて番号付け
	int ln_id = 0;
	map<Line, int> lh = {};
	V<Line> vec = {};
	rep(i, 0, N - 1) {
		rep(j, i + 1, N) {
			Vector2 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);
		}
	}

	// 有り得る交点を調べて番号付け
	rep(i, 0, ln_id - 1) {
		rep(j, i + 1, ln_id) {
			Line l1 = vec[i], l2 = vec[j];
			Vector2* p = calcIntersection(l1, l2);
			if (p == nullptr or ph.find(*p) != ph.end()) {
				continue;
			}
			P.push_back(*p);
			ph[*p] = pt_id;
			pt_id++;
		}
	}

	//任意の2点について、2点から構成されるベクトルを調べて正規化
	V<V<Vector2> > vectors(pt_id, V<Vector2>(pt_id, zero_vector));
	rep(i, 0, pt_id - 1) {
		rep(j, i + 1, pt_id) {
			if (lh.find(calcLine(P[i], P[j])) == lh.end()) {
				continue;
			}
			vectors[i][j] = normalize_vector(P[j] - P[i]);
			vectors[j][i] = normalize_vector(P[i] - P[j]);
		}
	}

	// グラフ探索
	V<V<V<int> > > dp(1 << N, V<V<int> >(pt_id, V<int>(pt_id, inf)));
	deque<V<int> > que = {};
	rep(i, 0, N) {
		que.push_back({ 0, 1 << i, i, i });
		dp[1 << i][i][i] = 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], lv = vec[2], v = vec[3];
		if (c > dp[b][lv][v]) {
			continue;
		}
		if (b == goal) {
			ans = c;
			break;
		}
		rep(nv, 0, pt_id) {
			if (v == nv or min(v,nv) >= N or vectors[v][nv] == zero_vector) {
				continue;
			}
			int nb = (nv < N) ? (b | (1 << nv)) : b;
			int nc = c;
			if (lv == v or vectors[lv][v] != vectors[v][nv]) {
				nc++;
			}
			if (nc >= dp[nb][v][nv]) {
				continue;
			}
			dp[nb][v][nv] = nc;
			if (nc == c) {
				que.push_front({ nc, nb, v, nv });
			}
			else {
				que.push_back({ nc, nb, v, nv });
			}
		}
	}
	cout << ans << endl;

	return 0;
}
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