QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#278252 | #7906. Almost Convex | Jacka1 | TL | 1ms | 4800kb | C++17 | 3.8kb | 2023-12-07 14:15:56 | 2023-12-07 14:15:56 |
Judging History
answer
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int,int> PII;
const int N=4010;
int n;
namespace Geometry{
const double pi=acos(-1);
const double eps=1e-12;
struct Point{//点坐标
double x,y;
int flag;
Point(double x=0,double y=0):x(x),y(y) {}
//可用Point a(1,2);语句直接将值设置为x=1,y=2
//如果未设定初值则直接设置为x=0,y=0
bool operator==(const Point a) const{
return (fabs(x-a.x)<=eps&&fabs(y-a.y)<=eps);
}
bool operator<(const Point &b) const{//以横纵坐标从小到大排序
return x == b.x ? y < b.y : x < b.x;
}
};
typedef Point Vector;//向量
//简化向量运算
Vector operator +(Vector A,Vector B){
return Vector(A.x+B.x,A.y+B.y);
}
Vector operator -(Vector A,Vector B){
return Vector(A.x-B.x,A.y-B.y);
}
Vector operator *(Vector A,double p){
return Vector(A.x*p,A.y*p);
}
Vector operator /(Vector A,double p){
return Vector(A.x/p,A.y/p);
}
int sign(double x){//符号函数:精度为eps
if(fabs(x)<eps) return 0;//x为0
if(x<0) return -1;//x为负数
return 1;//x为正数
}
int cmp(double x,double y){//比较函数:精度为eps
if(fabs(x-y)<eps) return 0;//x与y相等
if(x<y) return -1;//x小于y
return 1;//x大于y
}
double cross(Point a,Point b){//向量叉积
return a.x*b.y-b.x*a.y;
}
double area(Point a,Point b,Point c){//A为顶点,向量AB与向量AC的叉积,即三角形ABC面积的2倍(有向)
return cross(b-a,c-a);
}
int stk[N];
Point q[N];
bool used[N];
int top;
void andrew(){//求凸包
sort(q,q+n);//以横纵坐标从小到大排序
for(int i=0;i<n;i++)
{
while(top>=2&&sign(area(q[stk[top-1]],q[stk[top]],q[i]))<=0)//
//不带等号:可以求出所有点都在一条直线上的情况
{
if(sign(area(q[stk[top-1]],q[stk[top]],q[i]))<0)
used[stk[top--]]=false;
else top--;
}
stk[++top]=i;
used[i]=true;
}
used[0]=false;
for(int i=n-1;i>=0;i--)
{
if(used[i]) continue;
while(top>=2&&sign(area(q[stk[top-1]],q[stk[top]],q[i]))<=0)//
top--;
stk[++top]=i;
}
//凸包上的点为1~top-1,q[top]与q[1]为同一点
//该遍历为逆时针顺序!!!
// for (int i = 1; i <= top; i ++ )
// cout << stk[i] << ' ';
// cout<<endl;
}
int cnt;
struct Line{//存储凸包上每条线段的起点和终点
Point st,ed;
double ang;
int flag;
}line[N];
Point pg[N],ans[N];
int l[N];
double line_get_angle(const Line& a){
return atan2(a.ed.y-a.st.y,a.ed.x-a.st.x);
}
bool line_cmp(const Line& a, const Line& b){
double A=line_get_angle(a),B=line_get_angle(b);
if (!cmp(A,B)) return area(a.st,a.ed,b.ed)<0;
return A<B;
}
}
using namespace Geometry;
void solve()//求半平面交
{
scanf("%d",&n);
for(int i=0;i<n;i++)
{
scanf("%lf%lf",&q[i].x,&q[i].y);//读入凸包上的所有点
q[i].flag=0;
}
andrew();
for(int i=1;i<=top;i++) q[stk[i]].flag=1;//flag==1在凸包上
// for(int i=1;i<=top;i++) cout<<q[stk[i]].x<<" "<<q[stk[i]].y<<endl;
int ans=0;
for(int i=0;i<n;i++)
{
if(q[i].flag) continue;
// cout<<q[i].x<<" "<<q[i].y<<endl;
int cnt=0,res=0;
for(int j=0;j<n;j++)
{
if(i==j) continue;
line[cnt++]={q[i],q[j]};
if(q[j].flag) line[cnt-1].flag=1;
else line[cnt-1].flag=0;
}
sort(line,line+cnt,line_cmp);
line[cnt++]=line[0];
// for(int j=0;j<cnt;j++) cout<<line[j].ed.x<<" "<<line[j].ed.y<<" "<<line[j].flag<<endl;
for(int j=1;j<cnt;j++)
{
if(line[j].flag&&line[j-1].flag) res++;
}
ans+=res;
// cout<<res<<endl;
}
printf("%d",ans+1);
}
int main()
{
int t = 1;
//cin>>t;
while(t--) solve();
return 0;
}
Details
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Test #1:
score: 100
Accepted
time: 0ms
memory: 4800kb
input:
7 1 4 4 0 2 3 3 1 3 5 0 0 2 4
output:
9
result:
ok 1 number(s): "9"
Test #2:
score: 0
Accepted
time: 1ms
memory: 4792kb
input:
5 4 0 0 0 2 1 3 3 3 1
output:
5
result:
ok 1 number(s): "5"
Test #3:
score: 0
Accepted
time: 1ms
memory: 4432kb
input:
3 0 0 3 0 0 3
output:
1
result:
ok 1 number(s): "1"
Test #4:
score: 0
Accepted
time: 1ms
memory: 4700kb
input:
6 0 0 3 0 3 2 0 2 1 1 2 1
output:
7
result:
ok 1 number(s): "7"
Test #5:
score: 0
Accepted
time: 0ms
memory: 4484kb
input:
4 0 0 0 3 3 0 3 3
output:
1
result:
ok 1 number(s): "1"
Test #6:
score: -100
Time Limit Exceeded
input:
2000 86166 617851 383354 -277127 844986 386868 -577988 453392 -341125 -386775 -543914 -210860 -429613 606701 -343534 893727 841399 339305 446761 -327040 -218558 -907983 787284 361823 950395 287044 -351577 -843823 -198755 138512 -306560 -483261 -487474 -857400 885637 -240518 -297576 603522 -748283 33...