LightOJ 1203 Guarding Bananas (凸包最小顶角)

Posted 2022-11-25 synapse7

http://lightoj.com/volume_showproblem.php?problem=1203

/*0.164s,6512KB*/

#include<bits/stdc++.h>
using namespace std;
#define sqr(x) ((x)*(x))
const double INF = 1e100;
const double pi = acos(-1.0);
const double eps = 1e-9;

struct POINT

	double x, y;
 temp[100000 + 7], ch[100000 + 7], s[100000 + 7];

double dist(POINT a, POINT b)

	return sqrt(sqr(a.x - b.x) + sqr(a.y - b.y));


double findArea(POINT o, POINT a, POINT b)

	return (a.x - o.x) * (b.y - o.y) - (b.x - o.x) * (a.y - o.y);


bool cmp_position(POINT a, POINT b)

	return a.y < b.y || (a.y == b.y && a.x < b.x);


double findAngle(POINT a, POINT b, POINT c)

	double A = sqrt(sqr(b.x - c.x) + sqr(b.y - c.y));
	double B = sqrt(sqr(a.x - c.x) + sqr(a.y - c.y));
	double C = sqrt(sqr(a.x - b.x) + sqr(a.y - b.y));
	if (2 * A * C == 0) return INF;
	double ang = acos((A * A + C * C - B * B) / (2 * A * C));
	return (ang * 180) / pi;


bool cmp_angle(POINT a, POINT b)

	double temp = findArea(ch[0], a, b);
	if (!temp) return (dist(a, ch[0]) + eps < dist(b, ch[0]));
	else return temp > -eps;


void print(POINT a[], int N)

	double MIN = INF;
	for (int i = 0; i < N - 2; i++) MIN = min(MIN, findAngle(a[i], a[i + 1], a[i + 2]));
	MIN = min(MIN, findAngle(a[N - 2], a[N - 1], a[0]));
	MIN = min(MIN, findAngle(a[N - 1], a[0], a[1]));
	if (MIN == INF) MIN = 0;
	printf("%.7f\\n", MIN + eps);


int main()

	int P, cs = 0;
	scanf("%d", &P);
	while (P--)
	
		int N;
		scanf("%d", &N);
		for (int i = 0; i < N; i++) scanf("%lf%lf", &temp[i].x, &temp[i].y);
		printf("Case %d: ", ++cs);
		if (N < 3)  printf("0\\n"); continue; 
		sort(temp, temp + N, cmp_position);
		ch[0] = temp[0];
		int K = N;
		N = 1;
		for (int i = 1; i < K; i++)
		
			if (temp[i].x == temp[i - 1].x && temp[i].y == temp[i - 1].y) continue;
			ch[N++] = temp[i];
		
		sort(ch + 1, ch + N, cmp_angle);
		ch[N] = ch[0];
		int top = 2;
		s[0] = ch[0];
		s[1] = ch[1];
		for (int i = 2; i <= N; i++)
		
			double A;
			while (top >= 2 && (A = findArea(s[top - 2], s[top - 1], ch[i])) < 0) top--;
			s[top++] = ch[i];
		
		top--;
		print(s, top);
	
	return 0;