oj.uz

Submission #379579

# Submission time Handle Problem Language Result Execution time Memory
379579 2021-03-18T16:40:36 Z pit4h Fences (JOI18_fences) C++14
100 / 100
 896 ms 5944 KB 
#include<bits/stdc++.h>
#define st first
#define nd second
#define mp make_pair
using namespace std;
using ld = long double;
using pii = pair<int, int>;
const ld INF = 1e16+1, MAX_X = 201, eps = 1e-9;
const int MAXN = 205;
int n, S, m;

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

struct Segment;
struct Point {
	ld x, y;
	Point() {} Point(ld _x, ld _y) { x = _x, y = _y; }
	Point operator-(const Point& o) const { return Point(x - o.x, y - o.y); }
	bool operator==(const Point& o) const { return (abs(x-o.x)<eps && abs(y-o.y)<eps); }
	
	ld cross(Point o) { return x*o.y - o.x*y; }
	ld cross(Point p1, Point p2) { return (p1 - *this).cross(p2 - *this); }
	ld dot(Point o) { return x * o.x + y * o.y; }
	ld dot(Point p1, Point p2) { return (p1 - *this).dot(p2 - *this); }

	ld dist(Point o) { return (ld)sqrt((x-o.x)*(x-o.x) + (y-o.y)*(y-o.y)); }
	ld dist(Segment* seg, Point& p2);
};
bool inter1d(ld a, ld b, ld c, ld d) {
	if(a > b) swap(a, b);
	if(c > d) swap(c, d);
	return max(a, c)-eps <= min(b, d);
}
struct Segment {
	Point a, b;
	Segment() {} Segment(ld _a, ld _b, ld _c, ld _d) { a = Point(_a, _b), b = Point(_c, _d); }
	Segment(Point _a, Point _b) { a = _a, b = _b; }
	bool operator!=(const Segment& o) const {
		return !((a==o.a && b==o.b) || (a==o.b && b==o.a));
	}
	ld length() { return a.dist(b); }
	ld dist(Segment o, Point& p1, Point& p2) {
		p1 = a;
		if(a == b && o.a == o.b) {
			p2 = o.a;
			return a.dist(o.a);
		}
		if(a==b) {
			return a.dist(&o, p2);
		}
		if(o.a==o.b) {
			p2 = o.a;
			return (o.a).dist(this, p1);
		}
		ld min_dist = a.dist(&o, p2);
		Point pp;
		if(b.dist(&o, pp) < min_dist) {
			p1 = b, min_dist = b.dist(&o, p2);
		}
		if((o.a).dist(this, pp) < min_dist) {
			p2 = o.a, min_dist = (o.a).dist(this, p1);
		}
		if((o.b).dist(this, pp) < min_dist) {
			p2 = o.b, min_dist = (o.b).dist(this, p1);
		}
		return min_dist;
	}
	bool intersect(Segment o) {
		//if(a == o.a || a == o.b || b == o.a || b == o.b) return false;
		if((o.a).cross(a, o.b)==0 && (o.a).cross(b, o.b)==0) {
			return inter1d(a.x, b.x, o.a.x, o.b.x) && inter1d(a.y, b.y, o.a.y, o.b.y);	
			//return false;
		}
		return sgn(a.cross(b, o.a)) != sgn(a.cross(b, o.b)) && sgn((o.a).cross(o.b, a)) != sgn((o.a).cross(o.b, b));
	}
};
ld Point::dist(Segment* seg, Point& p2) {
	ld height = abs(cross(seg->a, seg->b)) / (seg->length());
	if((seg->a).dot(*this, seg->b) < (ld)0 || (seg->b).dot(*this, seg->a) < (ld)0) {
		if(dist(seg->a) < dist(seg->b)) p2 = seg->a;
		else p2 = seg->b;
		return min(dist(seg->a), dist(seg->b));
	}
	p2.x = seg->a.x + (seg->a).dot(*this, seg->b) / seg->length() * (seg->b.x - seg->a.x) / seg->length();			
	p2.y = seg->a.y + (seg->a).dot(*this, seg->b) / seg->length() * (seg->b.y - seg->a.y) / seg->length();
	return height;
}

bool half_change(Point p1, Point p2) {
	if(Segment(p1, p2).intersect(Segment(-S, S-eps, -S, MAX_X)) && ((p1.x <= -S && p2.x > -S) || (p1.x > -S && p2.x <= -S))) {
		return true;
	}
	return false;
}

ld w[2*MAXN][2*MAXN];
pair<Point, Point> edge_points[2*MAXN][2*MAXN];
inline void init();
int main() {
	ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
	cin>>n>>S;
	init();
	vector<Segment> fence(n+4);
	vector<Point> pts;
	for(int i=0; i<n; ++i) {
		cin>>fence[i].a.x>>fence[i].a.y>>fence[i].b.x>>fence[i].b.y;
	}
	fence[n] = Segment(S, S, S, S);
	fence[n+1] = Segment(S, -S, S, -S);
	fence[n+2] = Segment(-S, S, -S, S);
	fence[n+3] = Segment(-S, -S, -S, -S);
	n = n+4;	

	for(int i=0; i<n; ++i) {
		pts.push_back(fence[i].a);
		pts.push_back(fence[i].b);
	}
	m = pts.size(); assert(m==2*n);

	for(int i=0; i<n; ++i) {
		for(int j=0; j<n; ++j) {
			Point p1, p2;
			ld dist = fence[i].dist(fence[j], p1, p2);
			Segment edge(p1.x, p1.y, p2.x, p2.y);
			if(Segment(p1, p2) != Segment(-S, -S, -S, S) && Segment(p1, p2) != Segment(-S, -S, S, -S) && Segment(p1, p2) != Segment(-S, S, S, S) && Segment(p1, p2) != Segment(S, -S, S, S)) {
				int cnt_inter = 0;
				if(edge.intersect(Segment(-S, -S, -S, S))) {
					cnt_inter++;
				}
				if(edge.intersect(Segment(-S, -S, S, -S))) {
					cnt_inter++;
				}
				if(edge.intersect(Segment(-S, S, S, S))) {
					cnt_inter++;
				}
				if(edge.intersect(Segment(S, -S, S, S))) {
					cnt_inter++;
				}
				if(cnt_inter > 0 && (cnt_inter != 2 || ((abs(p1.x) != S || abs(p1.y) != S) && (abs(p2.x) != S || abs(p2.y) != S)))) {
					continue;	
				}
			}
			w[2*i][2*j] = w[2*i+1][2*j] = w[2*i][2*j+1] = w[2*i+1][2*j+1] = dist;
			if(i!=j) {
				edge_points[2*i][2*j] = edge_points[2*i+1][2*j] = edge_points[2*i][2*j+1] = edge_points[2*i+1][2*j+1] = mp(p1, p2);
			}
			else {
				edge_points[2*i][2*j] = mp(fence[i].a, fence[i].a);
				edge_points[2*i+1][2*j+1] = mp(fence[i].b, fence[i].b);
				edge_points[2*i][2*j+1] = mp(fence[i].a, fence[i].b);
				edge_points[2*i+1][2*j] = mp(fence[i].b, fence[i].a);
			}
		}
	}

	ld ans = INF;	
	for(int it=0; it<n; ++it) {
		int i = -1;
		if(pts[it*2].x <= -S) i = it*2;
		if(pts[it*2+1].x <= -S) i = it*2+1;
		if(i==-1) continue;
		vector<vector<ld>> dist(m, vector<ld>(2, INF));
		vector<vector<bool>> vis(m, vector<bool>(2));
		dist[i][0] = 0;
		priority_queue<pair<ld, pii>> pq;
		pq.push(mp(0, mp(i, 0)));
		
		while(pq.size()) {
			pii cur = pq.top().nd;
			pq.pop();
			if(vis[cur.st][cur.nd]) continue;	
			vis[cur.st][cur.nd] = 1;
			for(int j=0; j<m; ++j) {
				bool side = cur.nd;	
				if(half_change(pts[cur.st], edge_points[cur.st][j].st)) {
					side = !side;
				}
				if(half_change(edge_points[cur.st][j].st, edge_points[cur.st][j].nd)) {
					side = !side;
				}
				if(half_change(edge_points[cur.st][j].nd, pts[j])) {
					side = !side;
				}
				if(dist[j][side]-eps > dist[cur.st][cur.nd] + w[cur.st][j]) {
					dist[j][side] = dist[cur.st][cur.nd] + w[cur.st][j];
					pq.push(mp(-dist[j][side], mp(j, side)));
				}
			}
		}
		
		ans = min(ans, dist[i][1]);
	}
	cout<<fixed<<setprecision(3)<<ans<<'\n';
}

inline void init() {
	for(int i=0; i<2*(n+4); ++i) {
		for(int j=0; j<2*(n+4); ++j) {
			w[i][j] = INF;
		}
	}
}

Subtask #1
18.0 / 18.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 492 KB Output is correct
2 Correct 1 ms 492 KB Output is correct
3 Correct 1 ms 492 KB Output is correct
4 Correct 1 ms 492 KB Output is correct
5 Correct 1 ms 512 KB Output is correct
6 Correct 1 ms 492 KB Output is correct
7 Correct 1 ms 492 KB Output is correct
8 Correct 1 ms 492 KB Output is correct
9 Correct 1 ms 492 KB Output is correct
10 Correct 1 ms 492 KB Output is correct
11 Correct 1 ms 492 KB Output is correct
12 Correct 1 ms 492 KB Output is correct
13 Correct 1 ms 492 KB Output is correct
14 Correct 1 ms 492 KB Output is correct
15 Correct 1 ms 492 KB Output is correct
16 Correct 1 ms 492 KB Output is correct
17 Correct 2 ms 492 KB Output is correct
18 Correct 1 ms 492 KB Output is correct
19 Correct 1 ms 492 KB Output is correct
20 Correct 1 ms 492 KB Output is correct

Subtask #2
33.0 / 33.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 492 KB Output is correct
2 Correct 1 ms 492 KB Output is correct
3 Correct 1 ms 492 KB Output is correct
4 Correct 1 ms 492 KB Output is correct
5 Correct 1 ms 512 KB Output is correct
6 Correct 1 ms 492 KB Output is correct
7 Correct 1 ms 492 KB Output is correct
8 Correct 1 ms 492 KB Output is correct
9 Correct 1 ms 492 KB Output is correct
10 Correct 1 ms 492 KB Output is correct
11 Correct 1 ms 492 KB Output is correct
12 Correct 1 ms 492 KB Output is correct
13 Correct 1 ms 492 KB Output is correct
14 Correct 1 ms 492 KB Output is correct
15 Correct 1 ms 492 KB Output is correct
16 Correct 1 ms 492 KB Output is correct
17 Correct 2 ms 492 KB Output is correct
18 Correct 1 ms 492 KB Output is correct
19 Correct 1 ms 492 KB Output is correct
20 Correct 1 ms 492 KB Output is correct
21 Correct 1 ms 492 KB Output is correct
22 Correct 1 ms 492 KB Output is correct
23 Correct 1 ms 492 KB Output is correct
24 Correct 1 ms 492 KB Output is correct
25 Correct 1 ms 492 KB Output is correct
26 Correct 1 ms 492 KB Output is correct
27 Correct 1 ms 492 KB Output is correct
28 Correct 1 ms 492 KB Output is correct
29 Correct 1 ms 492 KB Output is correct
30 Correct 1 ms 492 KB Output is correct
31 Correct 1 ms 492 KB Output is correct
32 Correct 1 ms 492 KB Output is correct
33 Correct 1 ms 492 KB Output is correct
34 Correct 1 ms 492 KB Output is correct
35 Correct 1 ms 492 KB Output is correct
36 Correct 1 ms 492 KB Output is correct
37 Correct 1 ms 492 KB Output is correct
38 Correct 1 ms 492 KB Output is correct
39 Correct 1 ms 492 KB Output is correct
40 Correct 1 ms 492 KB Output is correct
41 Correct 1 ms 492 KB Output is correct
42 Correct 1 ms 492 KB Output is correct
43 Correct 1 ms 492 KB Output is correct

Subtask #3
49.0 / 49.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 492 KB Output is correct
2 Correct 1 ms 492 KB Output is correct
3 Correct 1 ms 492 KB Output is correct
4 Correct 1 ms 492 KB Output is correct
5 Correct 1 ms 512 KB Output is correct
6 Correct 1 ms 492 KB Output is correct
7 Correct 1 ms 492 KB Output is correct
8 Correct 1 ms 492 KB Output is correct
9 Correct 1 ms 492 KB Output is correct
10 Correct 1 ms 492 KB Output is correct
11 Correct 1 ms 492 KB Output is correct
12 Correct 1 ms 492 KB Output is correct
13 Correct 1 ms 492 KB Output is correct
14 Correct 1 ms 492 KB Output is correct
15 Correct 1 ms 492 KB Output is correct
16 Correct 1 ms 492 KB Output is correct
17 Correct 2 ms 492 KB Output is correct
18 Correct 1 ms 492 KB Output is correct
19 Correct 1 ms 492 KB Output is correct
20 Correct 1 ms 492 KB Output is correct
21 Correct 1 ms 492 KB Output is correct
22 Correct 1 ms 492 KB Output is correct
23 Correct 1 ms 492 KB Output is correct
24 Correct 1 ms 492 KB Output is correct
25 Correct 1 ms 492 KB Output is correct
26 Correct 1 ms 492 KB Output is correct
27 Correct 1 ms 492 KB Output is correct
28 Correct 1 ms 492 KB Output is correct
29 Correct 1 ms 492 KB Output is correct
30 Correct 1 ms 492 KB Output is correct
31 Correct 1 ms 492 KB Output is correct
32 Correct 1 ms 492 KB Output is correct
33 Correct 1 ms 492 KB Output is correct
34 Correct 1 ms 492 KB Output is correct
35 Correct 1 ms 492 KB Output is correct
36 Correct 1 ms 492 KB Output is correct
37 Correct 1 ms 492 KB Output is correct
38 Correct 1 ms 492 KB Output is correct
39 Correct 1 ms 492 KB Output is correct
40 Correct 1 ms 492 KB Output is correct
41 Correct 1 ms 492 KB Output is correct
42 Correct 1 ms 492 KB Output is correct
43 Correct 1 ms 492 KB Output is correct
44 Correct 766 ms 5596 KB Output is correct
45 Correct 682 ms 5748 KB Output is correct
46 Correct 558 ms 5404 KB Output is correct
47 Correct 501 ms 5476 KB Output is correct
48 Correct 836 ms 5844 KB Output is correct
49 Correct 729 ms 5944 KB Output is correct
50 Correct 519 ms 5384 KB Output is correct
51 Correct 508 ms 5648 KB Output is correct
52 Correct 534 ms 5564 KB Output is correct
53 Correct 549 ms 5592 KB Output is correct
54 Correct 554 ms 5472 KB Output is correct
55 Correct 620 ms 5492 KB Output is correct
56 Correct 683 ms 5496 KB Output is correct
57 Correct 512 ms 5400 KB Output is correct
58 Correct 616 ms 5516 KB Output is correct
59 Correct 649 ms 5716 KB Output is correct
60 Correct 685 ms 5548 KB Output is correct
61 Correct 620 ms 5876 KB Output is correct
62 Correct 3 ms 620 KB Output is correct
63 Correct 3 ms 620 KB Output is correct
64 Correct 240 ms 5524 KB Output is correct
65 Correct 509 ms 5484 KB Output is correct
66 Correct 374 ms 4780 KB Output is correct
67 Correct 856 ms 5380 KB Output is correct
68 Correct 896 ms 5496 KB Output is correct
69 Correct 636 ms 5560 KB Output is correct
70 Correct 550 ms 5128 KB Output is correct
71 Correct 652 ms 5468 KB Output is correct
72 Correct 462 ms 5228 KB Output is correct