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QOJ
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 |
---|---|---|---|---|---|---|---|---|---|
#647865 | #9434. Italian Cuisine | infCraft | WA | 13ms | 3652kb | C++14 | 10.6kb | 2024-10-17 15:58:53 | 2024-10-17 15:58:55 |
Judging History
answer
#include <bits/stdc++.h>
using namespace std;
#define endl '\n'
#define IOS ios::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define pb push_back
#define Yes cout << "Yes\n"
#define No cout << "No\n"
#define YES cout << "YES\n"
#define NO cout << "NO\n"
#define ff first
#define ss second
#define fori(x,y) for(int i=x;i<=(int)(y);++i)
#define forj(x,y) for(int j=x;j<=(int)(y);++j)
#define fork(x,y) for(int k=x;k<=(int)(y);++k)
#define debug(x) cerr << #x << " = " << x << endl
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
ll MOD = 998244353;
ll qpow(ll a,ll p) {ll res=1; while(p) {if (p&1) {res=res*a%MOD;} a=a*a%MOD; p>>=1;} return res;}
#define double long double
namespace Geometry {
const double PI = acos(-1);
const double eps = 1e-25;
int cmp(double x, double y) { // 比较两个浮点数的大小 x<y为-1,x>y为1
if (fabs(x-y)<eps) return 0;
else return x<y?-1:1;
}
int sgn(double x) { // 符号函数,大于0为1,小于0为-1
return cmp(x, 0);
}
struct Vector {
double x, y;
Vector(): x(0), y(0) {}
Vector(double x, double y): x(x), y(y) {}
Vector(pll pi): x(pi.first), y(pi.second) {}
bool zero() const {
return sgn(x) == 0&&sgn(y) == 0;
}
double distance2(const Vector& B) const {
return (x-B.x)*(x-B.x)+(y-B.y)*(y-B.y);
}
double distance(const Vector& B) const {
return sqrt(distance2(B));
}
double length2() const {
return x*x+y*y;
}
double length() const {
return sqrt(length2());
}
Vector normalize() const {
return Vector(x/length(), y/length());
}
Vector operator+(const Vector& B) const {
return Vector(x+B.x, y+B.y);
}
Vector operator-(const Vector& B) const {
return Vector(x-B.x, y-B.y);
}
Vector operator*(double k) const {
return Vector(x*k, y*k);
}
Vector operator/(double k) const {
return Vector(x/k, y/k);
}
double dot(const Vector& B) const {
return x*B.x+y*B.y;
}
double operator*(const Vector& B) const {
return dot(B);
}
bool operator==(const Vector& B) const {
return sgn(x-B.x) == 0&&sgn(y-B.y) == 0;
}
double cross(const Vector& B) const { // 从自身旋转到B的叉积(注意方向,逆时针正顺时针负)
return x*B.y-y*B.x;
}
// 从自身旋转到向量B的夹角(注意方向,逆时针正顺时针负)
// 180度算做PI而非-PI!!!
double angle(const Vector& B) const {
double co = acos(dot(B)/length()/B.length());
return sgn(co-PI) == 0? co: sgn(cross(B))*co;
}
bool parallel(const Vector& B) const { // 判断两个向量是否平行
return sgn(cross(B)) == 0;
}
};
struct Polygon { // 由向量构成的多边形
vector<Vector> points; // 尽量用逆时针排布
Polygon(): points(vector<Vector>()) {}
Polygon(vector<Vector> points): points(points) {}
/**
* 判断点是否在多边形内:
* 3:点在多边形顶点上
* 2:点在多边形的边上
* 1:点在多边形内部
* 0:点在多边形外部
*/
int isInPolygon(Vector point) const {
int n = points.size();
fori(0, n-1) {
if (point == points[i]) return 3;
}
fori(0, n-1) {
Vector v1 = points[i], v2 = points[(i+1)%n];
if ((point-v1).parallel(v2-v1)&&sgn((point-v1).dot(point-v2))<=0) return 2;
}
int num = 0;
fori(0, n-1) {
Vector v1 = points[i], v2 = points[(i+1)%n];
int c = sgn((point-v2).cross(v1-v2));
int u = sgn(v1.y-point.y);
int v = sgn(v2.y-point.y);
if (c>0&&u<0&&v>=0) num++;
if (c<0&&u>=0&&v<0) num--;
}
return num!=0;
}
/**
* 求多边形面积的两倍
* 但一定要注意!多边形得是逆时针排布!
*/
double area2() const {
double sum = 0;
int n = points.size();
fori(0, n-1) sum += points[i].cross(points[(i+1)%n]);
return sum;
}
double area() const { // 多边形面积
return area2()/2;
}
/**
* 求多边形的重心
*/
Vector gravityCenter() const {
Vector ans;
int n = points.size();
fori(0, n-1) {
Vector v1 = points[i], v2 = points[(i+1)%n];
ans = ans+(v1+v2)*v1.cross(v2);
}
ans = ans/area()/6;
return ans;
}
};
struct Line { // 直线
Vector p1, p2; // 两点确定一条直线
Line(Vector p1, Vector p2): p1(p1), p2(p2) {} // 基础构造方法
Line(Vector p, double angle) { // 斜率构造方法:一点+斜率,0<=angle<=pi
p1 = p;
if (sgn(angle-PI/2) == 0) {p2 = (p1+Vector(0, 1));}
else {p2 = (p1+Vector(1, tan(angle)));}
}
Line(double a, double b, double c) { // ax+by+c=0
if (sgn(a) == 0) {
p1 = Vector(0, -c/b);
p2 = Vector(1, -c/b);
}
else if (sgn(b) == 0) {
p1 = Vector(-c/a, 0);
p2 = Vector(-c/a, 1);
}
else {
p1 = Vector(0, -c/b);
p2 = Vector(1, -(c+a)/b);
}
}
// 判断一个点在直线上、左侧还是右侧
int pointLineRelation(Vector p) const {
int c = sgn((p-p1).cross(p2-p1));
if (c<0) return 1; // 1: 左侧
else if (c>0) return 2; // 2: 右侧
else return 0; // 0: 在直线上
}
// 计算点到直线的距离
double distanceToPoint(Vector p) const {
return fabs((p-p1).cross(p2-p1))/p1.distance(p2);
}
// 点在直线上的投影
Vector pointProj(Vector p) const {
double k = (p-p1).dot(p2-p1)/p1.distance2(p2);
return p1+(p2-p1)*k;
}
// 与另一条直线的位置关系
int lineRelation(const Line& B) const {
if (sgn((p2-p1).cross(B.p2-B.p1)) == 0) {
if (pointLineRelation(B.p1) == 0) return 1; // 1: 重合
else return 0; // 0: 平行
}
return 2; // 2: 相交
}
// 与另一条直线的交点(注意!两条直线必须相交!!!)
Vector crossPoint(const Line& B) const {
double s1 = (p2-p1).cross(B.p1-p1);
double s2 = (p2-p1).cross(B.p2-p1);
return Vector(B.p1.x*s2-B.p2.x*s1, B.p1.y*s2-B.p2.y*s1)/(s2-s1);
}
};
struct Circle {
Vector c; // 圆心
double r; // 半径
Circle(Vector c, double r): c(c), r(r) {}
Circle(const Vector& a, const Vector& b, const Vector& c) { // 三点定圆
double a1 = b.x-a.x, b1 = b.y-a.y, c1 = (a1*a1+b1*b1)/2;
double a2 = c.x-a.x, b2 = c.y-a.y, c2 = (a2*a2+b2*b2)/2;
double d = a1*b2-a2*b1;
Vector center(a.x+(c1*b2-c2*b1)/d, a.y+(a1*c2-a2*c1)/d);
this->c = center;
r = center.distance(a);
}
// 点和圆的位置关系
int pointCircleRelation(Vector p) const {
double d = p.distance(c);
if (sgn(d-r)<0) return 0; // 0: 点在圆内
else if (sgn(d-r)==0) return 1; // 1: 点在圆上
else return 2; // 2: 点在圆外
}
// 直线和圆的位置关系
int lineCircleRelation(const Line& line) const {
double d = line.distanceToPoint(c);
if (sgn(d-r)<0) return 0; // 0: 直线和圆相交
else if (sgn(d-r)==0) return 1; // 1: 直线和圆相切
else return 2; // 2: 直线在圆外
}
/**
* 求解直线和圆的交点
*
* @param line 直线
* @param p1 返回第一个交点
* @param p2 返回第二个交点
* @return 返回交点的个数
*/
int lineCrossCircle(const Line& line, Vector& p1, Vector& p2) const {
if (lineCircleRelation(line) == 2) return 0; // 没有交点
Vector pro = line.pointProj(c);
double d = line.distanceToPoint(c);
double k = sqrt(r*r-d*d);
if (sgn(k) == 0) {
p1 = pro, p2 = pro;
return 1; // 直线和圆相切,只有一个交点
}
Vector n = (line.p2-line.p1)/line.p2.distance(line.p1);
p1 = pro+n*k, p2 = pro-n*k;
return 2; // 两个交点
}
};
};
const int N = 2e5+7;
using namespace Geometry;
pll pt[N];
ll cross(ll x, ll y, ll Bx, ll By) { // 从自身旋转到B的叉积(注意方向,逆时针正顺时针负)
return x*By-y*Bx;
}
ll area(pll p1, pll p2, pll p3) {
return llabs(cross(p3.first-p1.first, p3.second-p1.second, p2.first-p1.first, p2.second-p1.second));
}
void solve() {
int n;
cin >> n;
ll x, y, r;
cin >> x >> y >> r;
Vector cen(x, y);
Circle cir(cen, r);
fori(1, n) cin >> pt[i].first >> pt[i].second;
fori(n+1, 2*n) pt[i] = pt[i-n];
ll ans = 0;
// 只算右半边
int l = 1;
ll tmp = 0; // 暂时的面积
fori(2, 2*n) {
// debug(Line(pt[l], pt[i]).pointLineRelation(cen));
// debug(cir.lineCircleRelation(Line(pt[l], pt[i])));
while (Line(pt[l], pt[i]).pointLineRelation(cen) != 1) {
tmp -= area(pt[i-1], pt[l], pt[l+1]);
l++;
}
while (cir.lineCircleRelation(Line(pt[l], pt[i])) != 2) {
tmp -= area(pt[i-1], pt[l], pt[l+1]);
l++;
}
tmp += area(pt[i], pt[i-1], pt[l]);
// debug(i);
// debug(l);
// debug(tmp);
// debug(area(pt[i], pt[i-1], pt[l]));
ans = max(ans, tmp);
}
cout << ans << endl;
}
signed main() {
IOS;
int t;
cin >> t;
while (t--) {
solve();
}
return 0;
}
详细
Test #1:
score: 100
Accepted
time: 1ms
memory: 3652kb
input:
3 5 1 1 1 0 0 1 0 5 0 3 3 0 5 6 2 4 1 2 0 4 0 6 3 4 6 2 6 0 3 4 3 3 1 3 0 6 3 3 6 0 3
output:
5 24 0
result:
ok 3 number(s): "5 24 0"
Test #2:
score: 0
Accepted
time: 0ms
memory: 3592kb
input:
1 6 0 0 499999993 197878055 -535013568 696616963 -535013568 696616963 40162440 696616963 499999993 -499999993 499999993 -499999993 -535013568
output:
0
result:
ok 1 number(s): "0"
Test #3:
score: -100
Wrong Answer
time: 13ms
memory: 3600kb
input:
6666 19 -142 -128 26 -172 -74 -188 -86 -199 -157 -200 -172 -199 -186 -195 -200 -175 -197 -161 -188 -144 -177 -127 -162 -107 -144 -90 -126 -87 -116 -86 -104 -89 -97 -108 -86 -125 -80 -142 -74 -162 -72 16 -161 -161 17 -165 -190 -157 -196 -154 -197 -144 -200 -132 -200 -128 -191 -120 -172 -123 -163 -138...
output:
5093 2862 2539 668 3535 7421 4883 5711 5624 1034 2479 3920 4372 2044 4996 5070 2251 4382 4175 1489 1154 3231 4038 1631 5086 14444 1692 6066 687 1512 4849 5456 2757 8341 8557 8235 1013 5203 10853 6042 6300 4480 2303 2728 1739 2187 3385 4266 6322 909 4334 1518 948 5036 1449 2376 3180 4810 1443 1786 47...
result:
wrong answer 2nd numbers differ - expected: '3086', found: '2862'