1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
| #include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <sstream>
#include <cstring>
#include <queue>
#include <set>
#include <map>
#include <cmath>
#define REP(i,k,n) for(int i=k;i<n;i++)
#define rep(i,n) for(int i=0;i<n;i++)
#define EPS 1e-9
#define INF 1<<30
using namespace std;
typedef long long ll;
struct Point {
double x, y;
Point(double x=0, double y=0) : x(x), y(y) {}
Point operator+(const Point &o) const { return Point(x+o.x, y+o.y); }
Point operator-(const Point &o) const { return Point(x-o.x, y-o.y); }
Point operator*(const double m) const { return Point(x*m, y*m); }
Point operator/(const double d) const { return Point(x/d, y/d); }
bool operator<(const Point &o) const { return x != o.x ? x < o.x : y < o.y; }
bool operator==(const Point &o) const { return fabs(x-o.x) < EPS && fabs(y-o.y) < EPS; }
double cross(const Point &o) const { return x * o.y - y * o.x; }
double dot(const Point &o) const { return x * o.x + y * o.y; }
double atan() const { return atan2(y, x); }
double norm() const { return sqrt(dot(*this)); }
double distance(const Point &o) const { return (o - (*this)).norm(); }
double area(const Point &a,const Point &b) {
Point p = a - (*this), p2 = b - (*this);
return p.cross(p2);
}
double area_abs(const Point &a,const Point &b) const {
Point p = a - (*this), p2 = b - (*this);
return fabs(p.cross(p2)) / 2.0;
}
// //線分abが自身に含まれているのかどうか判断する
// int between(const Point &a,const Point &b) {
// if(area(a,b) != 0) return 0;
//
// if(a.x != b.x) return ((a.x <= x) && (x <= b.x) || (a.x >= x) && (x >= b.x));
// else return ((a.y <= y) && (y <= b.y) || (a.y >= y) && (y >= b.y));
// }
double distance_seg(const Point& a,const Point& b) {
if((b-a).dot(*this-a) < EPS) {
return (*this-a).norm();
}
if((a-b).dot(*this-b) < EPS) {
return (*this-b).norm();
}
return abs((b-a).cross(*this-a)) / (b-a).norm();
}
bool hitPolygon(const Point& a,const Point& b,const Point& c) {
double t = (b-a).cross(*this-b);
double t2 = (c-b).cross(*this-c);
double t3 = (a-c).cross(*this-a);
if((t > 0 && t2 > 0 && t3 > 0) || ( t < 0 && t2 < 0 && t3 < 0)) {
return true;
}
return false;
}
};
class Flee {
public:
double maximalSafetyLevel(vector <int> x, vector <int> y) {
int n = x.size();
vector<Point> v;
map<pair<int,int>,bool > m;
rep(i,n) {
pair<int,int> p = make_pair(x[i],y[i]);
if(m[p]) continue;
v.push_back(Point(x[i],y[i]));
m[p] = true;
}
double ans = 0;
if(v.size() == 1) {
ans = v[0].norm();
}
else if(v.size() == 2) {
ans = min(v[0].norm(),v[1].norm());
}else {
vector<int> d;
int res = INF;
rep(i,v.size()) {
res = min(res,(int)(v[i]*2).dot(v[i]*2));
}
d.push_back(res);
Point p(0,0);
if(p.hitPolygon(v[0],v[1],v[2])) {
rep(i,v.size()) {
rep(j,v.size()) {
if(i == j) continue;
Point p(v[i]-v[j]);
if(p.dot(p) < res) {
d.push_back(p.dot(p));
}
}
}
sort(d.begin(),d.end(),greater<double>());
d.erase(unique(d.begin(),d.end()),d.end());
rep(k,d.size()) {
int len = d[k];
bool flag = false;
Point p1(v[0].x-v[1].x, v[0].y-v[1].y);
Point p2(v[0].x-v[2].x, v[0].y-v[2].y);
Point p3(v[1].x-v[2].x, v[1].y-v[2].y);
int r = (int)p1.x*p1.x + p1.y*p1.y;
int r2 = (int)p2.x*p2.x + p2.y*p2.y;
int r3 = (int)p3.x*p3.x + p3.y*p3.y;
if(r >= len) {
flag = true;
}
if(r2 >= len) {
flag = true;
}
if(r3 >= len) {
flag = true;
}
if(flag) {
ans = sqrt(d[k])/2.0;
break;
}
}
}else {
sort(d.begin(),d.end());
ans = sqrt(d[0])/2.0;
}
}
return ans;
}
};
|
