-
Notifications
You must be signed in to change notification settings - Fork 0
/
ao.py
50 lines (39 loc) · 1.19 KB
/
ao.py
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
import sys
from math import gcd
input = sys.stdin.readline
def cross(a, b):
return a[0] * b[1] - a[1] * b[0]
def convex_hull(ps):
ps.sort()
res = []
for p in ps:
while len(res) > 1 and cross((res[-1][0] - res[-2][0], res[-1][1] - res[-2][1]),
(p[0] - res[-1][0], p[1] - res[-1][1])) <= 0:
res.pop()
res.append(p)
t = len(res)
for p in ps[-2::-1]:
while len(res) > t and cross((res[-1][0] - res[-2][0], res[-1][1] - res[-2][1]),
(p[0] - res[-1][0], p[1] - res[-1][1])) <= 0:
res.pop()
res.append(p)
res.pop()
return res
def area2(ps):
n = len(ps)
return sum(cross(ps[i], ps[i + 1 - n]) for i in range(n))
def main():
n = int(input())
ps = [tuple(map(int, input().split())) for _ in range(n)]
ch = convex_hull(ps)
m = len(ch)
bound_cnt = 0
for i in range(m):
p, q = ch[i], ch[i + 1 - m]
dx = abs(q[0] - p[0])
dy = abs(q[1] - p[1])
bound_cnt += gcd(dx, dy)
inner_cnt = (area2(ch) - bound_cnt + 2) // 2
print(bound_cnt + inner_cnt - n)
if __name__ == "__main__":
main()