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ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
---|---|---|---|---|---|---|---|---|---|
#519336 | #7730. Convex Checker | TJUHuangTao | WA | 38ms | 13272kb | C++20 | 5.1kb | 2024-08-14 18:49:10 | 2024-08-14 18:49:11 |
Judging History
answer
#include <bits/stdc++.h>
// #define int long long
#define inf 0x3f3f3f3f
#define ll long long
#define pii pair<int, int>
#define tii tuple<int, int, int>
#define db double
#define all(a) a.begin(), a.end()
using namespace std;
const int maxn = 1e5 + 10;
const int mod = 998244353;
const db eps = 1e-8; // 根据题目精度要求进行修改
const db PI = acos(-1.0); // pai, 3.1415916....
int sgn(db x) { // 进行判断, 提高精度
if (fabs(x) < eps)
return 0; // x == 0, 精度范围内的近似相等
return x > 0 ? 1 : -1; // 返回正负
}
typedef struct Point {
db x, y;
Point(db x = 0, db y = 0) : x(x), y(y) {} // 构造函数, 初始值为 0
// 重载运算符
// 点 - 点 = 向量(向量AB = B - A)
Point operator-(const Point& B) const { return Point(x - B.x, y - B.y); }
// 点 + 点 = 点, 点 + 向量 = 向量, 向量 + 向量 = 向量
Point operator+(const Point& B) const { return Point(x + B.x, y + B.y); }
// 向量 × 向量 (叉积)
db operator^(const Point& B) const { return x * B.y - y * B.x; }
// 向量 · 向量 (点积)
db operator*(const Point& B) const { return x * B.x + y * B.y; }
// 点 * 数 = 点, 向量 * 数 = 向量
Point operator*(const db& B) const { return Point(x * B, y * B); }
// 点 / 数 = 点, 向量 / 数 = 向量
Point operator/(const db& B) const { return Point(x / B, y / B); }
// 判断大小, 一般用于排序
bool operator<(const Point& B) const {
return x < B.x || (x == B.x && y < B.y);
}
// 判断相等, 点 == 点, 向量 == 向量, 一般用于判断和去重
bool operator==(const Point& B) const {
return sgn(x - B.x) == 0 && sgn(y - B.y) == 0;
}
// 判断不相等, 点 != 点, 向量 != 向量
bool operator!=(const Point& B) const {
return sgn(x - B.x) || sgn(y - B.y);
}
} Vector;
using Points = vector<Point>;
// 判断点在直线的哪边
// Need: (-, ^), sgn()
// 点在直线上, 返回 0 (三点共线)
// 点在直线的逆时针方向, 返回 1
// 点在直线的顺时针方向, 返回 -1
// 点 a, b (向量ab) 所在的直线和点 c
// 使用的时候要注意 a 和 b 的顺序, 有时顺序不同, 结果不同
int Cross(Point a, Point b, Point c) {
return sgn((b - a) ^ (c - a));
}
// 判断多边形poly是否是凸多边形(前提是多边形)
// Need: Cross
struct Line {
Point s, e;
Line() {}
Line(Point x, Point y) : s(x), e(y) {}
};
struct Seg {
Point s, e;
Seg() {}
Seg(Point x, Point y) : s(x), e(y) {}
};
bool IsConvex(Points poly) {
int n = poly.size();
if (n < 3)
return false;
Line side = {poly[0], poly[1]};
// double rel = Cross(side.s, side.e, poly[2]);
int f1 = 1, f2 = 1;
for (int i = 0; i < n; i++) {
side.s = poly[i];
side.e = poly[(i + 1) % n];
if (Cross(side.s, side.e, poly[(i + 2) % n]) == -1)
f1 = 0;
if (Cross(side.s, side.e, poly[(i + 2) % n]) == 1)
f2 = 0;
}
return f1 | f2;
}
bool le(db a, db b) {
return a - b < eps;
} // <=
using Points = vector<Point>;
bool check(Point p, Point q, Point r) {
return le(0, (q - p) ^ (r - q));
}
vector<Point> Andrew(Points poly) { // 末尾额外塞了个头
int n = poly.size(), top = 0;
vector<int> stk(n + 2, 0), used(n + 2, 0);
sort(poly.begin(), poly.end());
stk[++top] = 0;
for (int i = 1; i < n; i++) {
while (top > 1 &&
sgn((poly[stk[top]] - poly[stk[top - 1]]) ^
(poly[i] - poly[stk[top]])) <= 0) // 去掉等号可以找共线的点
used[stk[top--]] = 0;
used[i] = 1;
stk[++top] = i;
}
int tmp = top;
for (int i = n - 2; i >= 0; i--) {
if (used[i])
continue;
while (top > tmp && sgn((poly[stk[top]] - poly[stk[top - 1]]) ^
(poly[i] - poly[stk[top]])) <= 0)
used[stk[top--]] = 0;
used[i] = 1;
stk[++top] = i;
}
vector<Point> a;
for (int i = 1; i <= top; i++)
a.push_back(poly[stk[i]]);
return a;
}
db convex_polygon_area(Points p) {
db area = 0;
int n = p.size();
for (int i = 1; i <= n - 2; ++i)
area += (p[i] - p[0]) ^ (p[i + 1] - p[0]);
// return area / 2;
return fabs(area / 2); // 不加的话求的是有向面积,逆时针为负,顺时针为正
}
signed main() {
// freopen("2.in", "r", stdin);
// freopen("2.out", "w", stdout);
ios::sync_with_stdio(false);
cin.tie(0), cout.tie(0);
int n;
cin >> n;
Points poly;
int flag = 1;
for (int i = 1; i <= n; i++) {
Point p;
cin >> p.x >> p.y;
poly.push_back(p);
}
Points tubao = Andrew(poly);
tubao.pop_back();
if (tubao.size() == n && IsConvex(tubao) &&
convex_polygon_area(poly) == convex_polygon_area(tubao))
cout << "Yes\n";
else
cout << "No\n";
return 0;
}
详细
Test #1:
score: 100
Accepted
time: 0ms
memory: 3724kb
input:
3 0 0 1 0 0 1
output:
Yes
result:
ok answer is YES
Test #2:
score: 0
Accepted
time: 1ms
memory: 3780kb
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: 4004kb
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: 3848kb
input:
3 0 0 0 0 0 0
output:
No
result:
ok answer is NO
Test #5:
score: 0
Accepted
time: 0ms
memory: 3972kb
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: 3724kb
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: 3900kb
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: 4008kb
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: 38ms
memory: 13272kb
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