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
| #include <bits/stdc++.h>
#pragma optimization_level 3
#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math,O3")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx")
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimization ("unroll-loops")
#define MAX_N 505
#define INF 987654321
#define ll long long
#define pll pair<ll, ll>
#define vpll vector<pll>
#define vall3 vector<array<ll,3>>
#define all5 array<ll,5>
#define vall5 vector<all5>
#define vll vector<ll>
#define vs vector<string>
#define usll unordered_set<ll>
#define vvs vector<vs>
#define vvll vector<vll>
#define all(a) begin(a), end(a)
using namespace std;
struct Point {
ll x, y;
bool operator ==(const Point& other) const {
return x == other.x and y == other.y;
}
Point operator -(const Point& other) const {
return {x - other.x, y - other.y};
}
bool operator <(const Point& other) const {
if(x == other.x) return y < other.y;
return x < other.x;
}
ll norm() { return x * x + y * y; }
};
ll dot(Point a, Point b) {
return a.x * b.x + a.y * b.y;
}
double abs(Point a) {
return sqrt(a.norm());
}
double angle(Point a, Point b) {
return acos(dot(a, b) / abs(a) / abs(b));
}
ll euclideanDistance(Point& a, Point& b) {
return (a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y);
}
ll n;
vector<Point> p;
ll ccw(Point &a, Point &b, Point &c) {
ll res = a.x * b.y + b.x * c.y + c.x * a.y;
res -= (a.x * c.y + b.x * a.y + c.x * b.y);
return res;
}
bool cmp(Point& a, Point& b) {
ll c=ccw(p[0], a, b);
if(c) return c > 0;
return euclideanDistance(p[0], a) < euclideanDistance(p[0], b);
}
vector<Point> convexHull() {
swap(p[0], *min_element(all(p)));
sort(begin(p) + 1, end(p), cmp);
vector<Point> st;
for(auto& pt: p) {
while(st.size() >= 2 and ccw(pt, st[st.size() - 2], st[st.size() - 1]) <= 0)
st.pop_back();
st.push_back(pt);
}
return st;
}
bool inside(vector<Point>& hull, Point& o) {
auto CCW = [&](Point& a, Point& b, Point& o) {
ll cw = ccw(a, b, o);
if(cw > 0) return 1;
if(cw == 0) return 0;
return -1;
};
ll cw = CCW(hull[0], hull[1], o), n = hull.size();
for(ll i = 1; i < n; i++) {
if(cw != CCW(hull[i], hull[(i + 1) % n], o))
return false;
}
return true;
}
ll solve(Point& o) {
ll res = 0;
while(p.size() >= 3) {
auto hull = convexHull();
if(!inside(hull, o)) break;
vector<Point> next;
for(ll hi = 0, pi = 0; pi < p.size();pi++) {
if(hi < hull.size() and hull[hi] == p[pi]) {
hi++;
} else {
next.push_back(p[pi]);
}
}
p = next;
res++;
}
return res;
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.setf(ios::fixed);
cout.precision(8);
ll n, x, y;
cin>>n>>x>>y;
Point o{x,y};
for(ll i = 0; i < n; i++) {
cin>>x>>y;
p.push_back({x,y});
}
cout<<solve(o);
return 0;
}
|
