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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#267201#5106. Islands from the SkyjuampiAC ✓485ms82008kbJava85.6kb2023-11-27 01:46:122023-11-27 01:46:12

Judging History

你现在查看的是最新测评结果

  • [2023-11-27 01:46:12]
  • 评测
  • 测评结果:AC
  • 用时:485ms
  • 内存:82008kb
  • [2023-11-27 01:46:12]
  • 提交

answer

// Arup Guha
// 11/16/2022
// Solution to 2021 WF Problem F: Islands from the Sky

import java.util.*;

public class F {

	final public static double NOCOVER = 1000.0;

	public static int nIslands;
	public static int nFlights;
	public static pt[][] islands;
	public static lineseg[] flights;
	
	public static double[][] angleCover;

	public static void main(String[] args) {
	
		Scanner stdin = new Scanner(System.in);
		nIslands = stdin.nextInt();
		islands = new pt[nIslands][];
		nFlights = stdin.nextInt();
		flights = new lineseg[nFlights];
		
		// Read each island.
		for (int i=0; i<nIslands; i++) {
			int nPts = stdin.nextInt();
			islands[i] = new pt[nPts];
			
			// Read each pt.
			for (int j=0; j<nPts; j++) {
				long x = stdin.nextLong();
				long y = stdin.nextLong();
				islands[i][j] = new pt(x, y);
			}
		}
		
		// Read in each flight.
		for (int i=0; i<nFlights; i++) {
			pt[] tmp = new pt[2];
			for (int j=0; j<2; j++) {
				double x = stdin.nextDouble();
				double y = stdin.nextDouble();
				double z = stdin.nextDouble();
				tmp[j] = new pt(x, y, z);			
			}
			flights[i] = new lineseg(tmp[0], tmp[1]);
		}
		
		// angleCover[i][j] will equal the angle at which flight i can completely
		// survey island j. NOCOVER means it's impossible.
		angleCover = new double[nFlights][nIslands];
		for (int i=0; i<nFlights; i++) Arrays.fill(angleCover[i], NOCOVER);
		
		ArrayList<Double> allAngles = new ArrayList<Double>();
		
		// Fill this all in.
		for (int i=0; i<nFlights; i++) {
			for (int j=0; j<nIslands; j++) {
				angleCover[i][j] = solve(i, j);
				if (Math.abs(angleCover[i][j]-NOCOVER) > 1e-9)
					allAngles.add(angleCover[i][j]);
			}
		}
		
		// Get all possible answers and sort them.
		int sz = allAngles.size();
		Collections.sort(allAngles);
		
		// In this case, it can't be done.
		if (sz == 0 || !canDo(allAngles.get(sz-1)))
			System.out.println("impossible");
		
		// Binary search the answer.
		else
			System.out.println(binsearch(allAngles));
	}
	
	// Returns true iff angle works to cover all islands.
	public static boolean canDo(double angle) {
		
		// Try each islands.
		for (int j=0; j<nIslands; j++) {
			
			// See if at least one flight covers this island.
			boolean covered = false;
			for (int i=0; i<nFlights; i++) {
				if (angleCover[i][j] < angle+1e-8) {
					covered = true;
					break;
				}
			}
			
			// Oops, no one covered this island.
			if (!covered) return false;
		}
				
		// Woo hoo, we covered the island.
		return true;
	}
	
	// Binary searches which angle in angles is the smallest that works.
	public static double binsearch(ArrayList<Double> angles) {
		
		// Initial bounds.
		int low = 0, high = angles.size()-1;
		
		// Usual binary search.
		while (low < high) {
			
			// Go halfway.
			int mid = (low+high)/2;
			
			// Answer can't be bigger than mid.
			if (canDo(angles.get(mid)))
				high = mid;
			
			// Answer must be greater than mid.
			else
				low = mid+1;
		}
		
		// Here is our answer!
		return angles.get(low);
	}
	
	// Returns the minimum angle necessary for flight i to cover island j.
	public static double solve(int i, int j) {
		
		// Set up flight and island.
		lineseg flight = flights[i];
		pt[] island = islands[j];
		pt perp = new pt(flights[i].d.y, -flights[i].d.x);
		
		// Will update this.
		double max = 0;
		
		for (pt p: island) {
			
			// Line from island point to line segment.
			line mine = new line(p, perp);
			
			// See if this line, perp to segment, hits the segment.
			double[] info = mine.getD2D(flight);
			double dist = info[0];
			double beta = info[1];
			
			// If you can't cover all the points, you can't cover the polygon.
			if (dist < 0) return NOCOVER;
			
			// How high up the plane is...
			double myZ = flight.p.z + flight.d.z*beta;
			
			double angle = Math.atan2(dist, myZ);
			max = Math.max(angle, max);
		}
		
		// If we get here, this is what we want.
		return Math.toDegrees(max);
	}
}

class pt {

	public double x;
	public double y;
	public double z;
	
	public pt(double myx, double myy) {
		x = myx;
		y = myy;
		z = 0;
	}
	
	public pt(double myx, double myy, double myz) {
		x = myx;
		y = myy;
		z = myz;
	}	
	
	public pt sub(pt other) {
		return new pt(this.x-other.x, this.y-other.y, this.z-other.z);
	}
	
	public double mag2D() {
		return Math.sqrt(x*x+y*y);
	}
}

class lineseg {
	
	public pt p;
	public pt q;
	public pt d;
	
	public lineseg(pt start, pt end) {
		p = start;
		q = end;
		d = q.sub(p);
	}
}

class line {
	
	public pt p;
	public pt d;
	
	public line(pt start, pt dir) {
		p = start;
		d = dir;
	}
	
	// Returns the perpendicular distance from this object to L. If the perpendicular
	// doesn't hit L, then -1 is returned to indicate this.
	public double[] getD2D(lineseg L) {
		
		// p.x + lambda(d.x) = L.p.x + beta(L.d.x)
		// p.y + lambda(d.y) = L.p.y + beta(L.d.y)
		// lamb(d.x) - beta(L.d.x) = L.p.x-p.x
		// lamb(d.y) - beta(L.d.y) = L.p.y-p.y
		
		double det = -d.x*L.d.y + d.y*L.d.x;
		
		// For me, these cases will never "count"
		if (Math.abs(det) < 1e-9) return new double[]{-1,-1};
		
		double betaNum = d.x*(L.p.y-p.y) - d.y*(L.p.x-p.x);
		double beta = betaNum/det;
		
		// There's an intersection, but not with the segment.
		if (beta > 1+1e-9 || beta < -1e-9) return new double[]{-1,-1};
		
		// Get lambda.
		double lambNum = -(L.p.x-p.x)*L.d.y + (L.p.y-p.y)*L.d.x;
		double lambda = lambNum/det;
		
		// This is the distance to the line segment.
		return new double[]{Math.abs(d.mag2D()*lambda), beta};
	}
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 61ms
memory: 40664kb

input:

1 1
3
-5 0
5 0
0 5
-10 10 10 10 10 10

output:

45.0

result:

ok 

Test #2:

score: 0
Accepted
time: 62ms
memory: 41936kb

input:

1 1
3
-5 0
5 0
0 5
-10 0 10 10 0 10

output:

26.56505117707799

result:

ok 

Test #3:

score: 0
Accepted
time: 68ms
memory: 40804kb

input:

1 1
3
-5 0
5 0
0 5
0 10 10 10 0 10

output:

46.68614334171696

result:

ok 

Test #4:

score: 0
Accepted
time: 71ms
memory: 40780kb

input:

1 1
3
-5 0
5 0
0 5
0 10 5 10 0 10

output:

59.4910411337972

result:

ok 

Test #5:

score: 0
Accepted
time: 65ms
memory: 41432kb

input:

1 1
3
-5 0
5 0
0 5
0 10 20 -10 0 10

output:

31.219698447368387

result:

ok 

Test #6:

score: 0
Accepted
time: 75ms
memory: 40980kb

input:

1 3
3
-5 0
5 0
0 5
-10 0 25 10 0 20
-5 10 10 10 -5 20
-4 1 100 5 10 100

output:

12.528807709151511

result:

ok 

Test #7:

score: 0
Accepted
time: 65ms
memory: 39904kb

input:

1 2
4
0 0
20 0
20 40
0 40
-10 30 30 30 30 30
-10 10 30 30 10 30

output:

45.0

result:

ok 

Test #8:

score: 0
Accepted
time: 70ms
memory: 40664kb

input:

1 4
4
0 0
20 0
20 40
0 40
-10 30 30 30 30 30
-10 20 30 30 20 30
-10 10 30 30 10 30
10 -10 30 10 50 30

output:

18.43494882292201

result:

ok 

Test #9:

score: 0
Accepted
time: 69ms
memory: 39368kb

input:

1 2
4
0 0
40 0
40 40
0 40
10 10 10 20 20 20
30 10 10 10 30 20

output:

impossible

result:

ok 

Test #10:

score: 0
Accepted
time: 63ms
memory: 39832kb

input:

1 3
4
0 0
20 0
20 40
0 40
-10 30 30 15 30 30
5 30 30 30 30 30
1 50 30 21 50 30

output:

impossible

result:

ok 

Test #11:

score: 0
Accepted
time: 60ms
memory: 39972kb

input:

1 1
4
0 0
40 0
40 40
0 40
-100 -100 20 100 100 10

output:

63.66575215314687

result:

ok 

Test #12:

score: 0
Accepted
time: 58ms
memory: 40060kb

input:

1 4
4
-10 -10
10 -10
10 10
-10 10
-100 0 10 100 0 10
0 100 10 0 -100 10
50 50 15 -50 -50 15
-50 50 15 50 -50 15

output:

43.31385665828304

result:

ok 

Test #13:

score: 0
Accepted
time: 136ms
memory: 42720kb

input:

1 100
100
822286 0
856789 53904
986567 124632
629039 119995
732157 187986
691605 224716
728650 288493
591087 278144
801573 440668
425257 269876
614456 446428
424157 350893
645680 606334
406524 432904
545628 659551
359831 495265
367048 578376
251435 457360
319990 680014
336526 849968
214009 658652
23...

output:

53.790638431072466

result:

ok 

Test #14:

score: 0
Accepted
time: 199ms
memory: 60040kb

input:

100 1
100
461002 481444
460618 481480
460584 481512
460833 481595
460670 481605
460545 481607
460942 481801
460526 481672
460912 481923
460765 481903
460505 481781
460430 481766
460589 481959
460593 482032
460477 481972
460440 481994
460510 482183
460285 481888
460387 482179
460246 481963
460303 482...

output:

impossible

result:

ok 

Test #15:

score: 0
Accepted
time: 226ms
memory: 62416kb

input:

100 1
100
461002 481444
460618 481480
460584 481512
460833 481595
460670 481605
460545 481607
460942 481801
460526 481672
460912 481923
460765 481903
460505 481781
460430 481766
460589 481959
460593 482032
460477 481972
460440 481994
460510 482183
460285 481888
460387 482179
460246 481963
460303 482...

output:

33.69079560972086

result:

ok 

Test #16:

score: 0
Accepted
time: 222ms
memory: 62160kb

input:

100 1
100
461002 481444
460618 481480
460584 481512
460833 481595
460670 481605
460545 481607
460942 481801
460526 481672
460912 481923
460765 481903
460505 481781
460430 481766
460589 481959
460593 482032
460477 481972
460440 481994
460510 482183
460285 481888
460387 482179
460246 481963
460303 482...

output:

66.40279664206592

result:

ok 

Test #17:

score: 0
Accepted
time: 485ms
memory: 82008kb

input:

100 100
100
461002 481444
460618 481480
460584 481512
460833 481595
460670 481605
460545 481607
460942 481801
460526 481672
460912 481923
460765 481903
460505 481781
460430 481766
460589 481959
460593 482032
460477 481972
460440 481994
460510 482183
460285 481888
460387 482179
460246 481963
460303 4...

output:

4.1890016471314375

result:

ok 

Test #18:

score: 0
Accepted
time: 266ms
memory: 67140kb

input:

100 11
100
461002 481444
460618 481480
460584 481512
460833 481595
460670 481605
460545 481607
460942 481801
460526 481672
460912 481923
460765 481903
460505 481781
460430 481766
460589 481959
460593 482032
460477 481972
460440 481994
460510 482183
460285 481888
460387 482179
460246 481963
460303 48...

output:

32.41192847717416

result:

ok 

Test #19:

score: 0
Accepted
time: 420ms
memory: 81216kb

input:

100 90
100
461002 481444
460618 481480
460584 481512
460833 481595
460670 481605
460545 481607
460942 481801
460526 481672
460912 481923
460765 481903
460505 481781
460430 481766
460589 481959
460593 482032
460477 481972
460440 481994
460510 482183
460285 481888
460387 482179
460246 481963
460303 48...

output:

5.575448935978947

result:

ok 

Extra Test:

score: 0
Extra Test Passed