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;
}
