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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#463369 | #7730. Convex Checker | Qingyu | WA | 11ms | 4600kb | C++17 | 2.3kb | 2024-07-04 19:09:54 | 2024-07-04 19:09:54 |
Judging History
answer
#include <stdio.h>
#include <math.h>
#include <vector>
typedef long long i64;
const double PI = acos(-1.0);
const double eps = 1e-8;
int rd()
{
int k = 0, f = 1;
char c = getchar();
while (c < '0' || c > '9')
{
if (c == '-')
f = 0;
c = getchar();
}
while (c >= '0' && c <= '9')
{
k = (k << 1) + (k << 3) + (c ^ '0');
c = getchar();
}
return f ? k : -k;
}
struct point
{
int x, y;
int idx;
point(int _x = 0, int _y = 0, int id = 0) : x(_x), y(_y), idx(id) {}
void input() { x = rd(), y = rd(); }
point operator-(const point &o) const { return point(x - o.x, y - o.y); }
double len() const { return sqrt(1ll * x * x + 1ll * y * y); }
// point product of vector
i64 operator*(const point &o) const { return 1ll * x * o.x + 1ll * y * o.y; }
// cross product of vector
i64 operator^(const point &o) const { return 1ll * x * o.y - 1ll * y * o.x; }
bool operator<(const point &o) const { return (x ^ o.x) ? (x < o.x) : (y < o.y); }
bool operator==(const point &o) const { return (x == o.x) && (y == o.y); }
};
// using point as vector
double angle(const point &a, const point &b) { return acos(1.0 * (a * b) / (a.len() * b.len())); }
bool isconvex(const std::vector<point> &pts)
{
int n = (int)pts.size();
if (n <= 2)
return false;
double exterior_angle = 0.0;
i64 cross = (pts[0] - pts[n - 1]) ^ (pts[n - 1] - pts[n - 2]);
if (cross == 0)
return false;
bool dir = cross > 0;
exterior_angle += angle(pts[0] - pts[n - 1], pts[n - 1] - pts[n - 2]);
cross = (pts[1] - pts[0]) ^ (pts[0] - pts[n - 1]);
if ((cross == 0) || ((cross > 0) != dir))
return false;
exterior_angle += angle(pts[1] - pts[0], pts[0] - pts[n - 1]);
for (int i = 2; i < n; ++i)
{
cross = (pts[i] - pts[i - 1]) ^ (pts[i - 1] - pts[i - 2]);
if ((cross == 0) || ((cross > 0) != dir))
return false;
exterior_angle += angle(pts[i] - pts[i - 1], pts[i - 1] - pts[i - 2]);
}
return fabs(exterior_angle - 2 * PI) < eps;
}
int main()
{
int n = rd();
std::vector<point> pts(n);
for (int i = 0; i < n; ++i)
pts[i].x = rd(), pts[i].y = rd();
puts(isconvex(pts) ? "Yes" : "No");
}
Details
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Test #1:
score: 100
Accepted
time: 0ms
memory: 3844kb
input:
3 0 0 1 0 0 1
output:
Yes
result:
ok answer is YES
Test #2:
score: 0
Accepted
time: 0ms
memory: 3912kb
input:
4 0 0 0 1 1 1 1 0
output:
Yes
result:
ok answer is YES
Test #3:
score: 0
Accepted
time: 0ms
memory: 3708kb
input:
4 0 0 0 3 1 2 1 1
output:
Yes
result:
ok answer is YES
Test #4:
score: 0
Accepted
time: 0ms
memory: 3536kb
input:
3 0 0 0 0 0 0
output:
No
result:
ok answer is NO
Test #5:
score: 0
Accepted
time: 0ms
memory: 3912kb
input:
5 1 0 4 1 0 1 2 0 3 2
output:
No
result:
ok answer is NO
Test #6:
score: 0
Accepted
time: 0ms
memory: 3912kb
input:
5 0 0 1000000000 0 1000000000 500000000 1000000000 1000000000 0 1000000000
output:
No
result:
ok answer is NO
Test #7:
score: 0
Accepted
time: 0ms
memory: 3732kb
input:
5 0 0 1000000000 0 1000000000 499999999 1000000000 1000000000 0 1000000000
output:
No
result:
ok answer is NO
Test #8:
score: 0
Accepted
time: 0ms
memory: 3916kb
input:
5 0 0 999999999 0 1000000000 50000000 999999999 1000000000 0 1000000000
output:
Yes
result:
ok answer is YES
Test #9:
score: -100
Wrong Answer
time: 11ms
memory: 4600kb
input:
128312 5578014 410408218 5585076 410404717 5588011 410403262 5588473 410403033 5589740 410402405 5593295 410400643 5593751 410400417 5597248 410398684 5598935 410397848 5600618 410397014 5605185 410394751 5610514 410392111 5614281 410390245 5617263 410388768 5621142 410386847 5630840 410382045 56310...
output:
No
result:
wrong answer expected YES, found NO