Premier Bob的算法模板库（II）

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Geometry_Calculate_Basic .hpp （计算几何基础运算）

#include<cmath>
#include<iostream>
#include<cstdlib>
#include<cstdio>
using namespace std;namespace Geometry_Calculate_Basic
{const double PI=acos(-1.0);struct Point{double x,y;Point(double X=0,double Y=0){x=X;y=Y;}};typedef Point Vector;Vector operator+(Vector A,Vector B){return Vector(A.x+B.x,A.y+B.y);}Vector operator-(Point A,Point B){return Point(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);}bool operator<(const Point& a, const Point& b){return a.x<b.x || (a.x==b.x && a.y<b.y);}const double eps=1e-10;int dcmp(double x){if(fabs(x)<eps)return 0;else return x<0 ? -1 : 1;}bool operator==(const Point& a,const Point& b){return dcmp(a.x-b.x)==0 && dcmp(a.y-b.y)==0;}double Dot(Vector A,Vector B){return A.x*B.x+A.y*B.y;}double Length(Vector A){return sqrt(Dot(A,A));}double Angle(Vector A,Vector B){return acos(Dot(A,B)/Length(A)/Length(B));}double Cross(Vector A,Vector B){return A.x*B.y-A.y*B.x;}double Area2(Point A,Point B,Point C){return Cross(B-A,C-A);}typedef double ArcAngle;Vector Rotate(Vector A,ArcAngle rad){return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));}Vector Normal(Vector A){double L=Length(A);return Vector(-A.y/L,A.x/L);}Point GetLineIntersection(Point P,Vector v,Point Q,Vector w){Vector u=P-Q;double t=Cross(w,u)/Cross(v,w);return P+v*t;}double DistanceToLine(Point P,Point A,Point B){Vector v1=B-A,v2=P-A;return fabs(Cross(v1,v2))/Length(v1);}double DistanceToSegment(Point P,Point A,Point B){if(A==B)return Length(P-A);Vector v1=B-A,v2=P-A,v3=P-B;if(dcmp(Dot(v1,v2))<0)return Length(v2);else if(dcmp(Dot(v1,v3))>0)return Length(v3);else return fabs(Cross(v1,v2))/Length(v1);}Point GetLineProjection(Point P,Point A,Point B){Vector v=B-A;return A+v*(Dot(v,P-A)/Dot(v,v));}bool SegmentProperIntersection(Point a1,Point a2,Point b1,Point b2){double c1=Cross(a2-a1,b1-a1),c2=Cross(a2-a1,b2-a1),c3=Cross(b2-b1,a1-b1),c4=Cross(b2-b1,a2-b1);return dcmp(c1)*dcmp(c2)<0 && dcmp(c3)*dcmp(c4)<0;}double PolygonArea(Point* p,int n){double area=0;for(int i=1;i<n-1;i++)area+=Cross(p[i]-p[0],p[i+1]-p[0]);return area/2;}
}

但愿这个不是使用样例：

#include"Geometry_Calculate_Basic.hpp"
int main()
{int T;cin>>T;for(int i=1;i<=T;i++){Geometry_Calculate_Basic::Point A,B,C;cin>>A.x>>A.y>>B.x>>B.y>>C.x>>C.y;Geometry_Calculate_Basic::ArcAngle c_a=Geometry_Calculate_Basic::Angle(A-B,C-B);Geometry_Calculate_Basic::ArcAngle a_b=Geometry_Calculate_Basic::Angle(B-C,A-C);Geometry_Calculate_Basic::ArcAngle b_c=Geometry_Calculate_Basic::Angle(C-A,A-B);Geometry_Calculate_Basic::Vector a1,a2,b1,b2,c1,c2;a1=Geometry_Calculate_Basic::Rotate(C-A,b_c/3*2);a2=Geometry_Calculate_Basic::Rotate(C-A,b_c/3);b1=Geometry_Calculate_Basic::Rotate(A-B,c_a/3*2);b2=Geometry_Calculate_Basic::Rotate(A-B,c_a/3);c1=Geometry_Calculate_Basic::Rotate(B-C,a_b/3*2);c2=Geometry_Calculate_Basic::Rotate(B-C,a_b/3);Geometry_Calculate_Basic::Point D,E,F;D=Geometry_Calculate_Basic::GetLineIntersection(B,b1,C,c2);E=Geometry_Calculate_Basic::GetLineIntersection(A,a1,B,b2);F=Geometry_Calculate_Basic::GetLineIntersection(C,c1,A,a2);cout<<D.x<<" "<<D.y<<" "<<E.x<<" "<<E.y<<" "<<F.x<<" "<<F.y<<endl;}return 0;
}

所以说应该写成这样：

#include"Geometry_Calculate_Basic.hpp"
using namespace Geometry_Calculate_Basic;
//using namespace!
int main()
{int T;cin>>T;for(int i=1;i<=T;i++){Point A,B,C;cin>>A.x>>A.y>>B.x>>B.y>>C.x>>C.y;ArcAngle c_a=Angle(A-B,C-B);ArcAngle a_b=Angle(B-C,A-C);ArcAngle b_c=Angle(C-A,A-B);Vector a1,a2,b1,b2,c1,c2;a1=Rotate(C-A,b_c/3*2);a2=Rotate(C-A,b_c/3);b1=Rotate(A-B,c_a/3*2);b2=Rotate(A-B,c_a/3);c1=Rotate(B-C,a_b/3*2);c2=Rotate(B-C,a_b/3);Point D,E,F;D=GetLineIntersection(B,b1,C,c2);E=GetLineIntersection(A,a1,B,b2);F=GetLineIntersection(C,c1,A,a2);cout<<D.x<<" "<<D.y<<" "<<E.x<<" "<<E.y<<" "<<F.x<<" "<<F.y<<endl;}return 0;
}

NlogN_LIS .hpp （nlogn时间复杂度求解LIS长度）

#include<algorithm>
using namespace std;namespace NlogN_LIS
{const int INF=2147483647;const int maxn=1048576;int g[maxn],d[maxn];int LIS(int* Array,int n){for(int i=1;i<=n;i++)g[i]=INF;int ans=0;for(int i=1;i<=n;i++){int k=lower_bound(g+1,g+n+1,Array[i])-g;d[i]=k;g[k]=Array[i];ans=max(ans,d[i]);}return ans;}
}

UnionFindSet .hpp （并查集模板）

//made by GGN -from NECY
#pragma once#include<cstdio>
#include<cstdlib>namespace UnionFindSet
{const int UFS_Size=1048576;//you can use this to change the size of UFSclass UFS{int Father[UFS_Size];bool NeedInit;int UseSize;public:UFS(){NeedInit=1;}void Init(int NodeCount){NeedInit=0;for(int i=1;i<=NodeCount;i++)Father[i]=i;UseSize=NodeCount;}int Find(int NodeNum){if(NeedInit){printf("Error \"UnionFindSet\":Find  you have to init before use!\n");system("pause>nul");return -1;}if(NodeNum<=0 || NodeNum>UseSize){printf("Error \"UnionFindSet\":Find NodeNum=%d (<=0 or >UseSize=%d) is not allowed!\n",NodeNum,UseSize);system("pause>nul");return -1;}if(NodeNum!=Father[NodeNum])Father[NodeNum]=Find(Father[NodeNum]);return Father[NodeNum];}int Union(int NodeX,int NodeY){if(NeedInit){printf("Error \"UnionFindSet\":Union  you have to init before use!\n");system("pause>nul");return -1;}if(NodeX<=0 || NodeX>UseSize){printf("Error \"UnionFindSet\":Union NodeX=%d (<=0 or >UseSize=%d) is not allowed!\n",NodeX,UseSize);system("pause>nul");return -1;}if(NodeY<=0 || NodeY>UseSize){printf("Error \"UnionFindSet\":Union NodeY=%d (<=0 or >UseSize=%d) is not allowed!\n",NodeY,UseSize);system("pause>nul");return -1;}Father[Find(NodeY)]=Find(NodeX);}int Judge(int NodeX,int NodeY){if(NeedInit){printf("Error \"UnionFindSet\":Judge  you have to init before use!\n");system("pause>nul");return -1;}if(NodeX<=0 || NodeX>UseSize){printf("Error \"UnionFindSet\":Judge NodeX=%d (<=0 or >UseSize=%d) is not allowed!\n",NodeX,UseSize);system("pause>nul");return -1;}if(NodeY<=0 || NodeY>UseSize){printf("Error \"UnionFindSet\":Judge NodeY=%d (<=0 or >UseSize=%d) is not allowed!\n",NodeY,UseSize);system("pause>nul");return -1;}return Find(NodeX)==Find(NodeY);}int Ancestor(int Node){if(NeedInit){printf("Error \"UnionFindSet\":Ancestor  you have to init before use!\n");system("pause>nul");return -1;}if(Node<=0 || Node>UseSize){printf("Error \"UnionFindSet\":Ancestor Node=%d (<=0 or >UseSize=%d) is not allowed!\n",Node,UseSize);system("pause>nul");return -1;}return Father[Node];}};
}

TernarySearch .hpp （三分法求单峰函数最小值）

//made by GGN -from NEYC
#pragma once#include<cstdio>
#include<cstdlib>
#include<cmath>
namespace TernarySearch
{double TSmin(double L,double R,double (*function)(double x),double eps=1e-7){//make a ternary search for min value and return xif(R==L)return L;if(R<L){printf("Error \"Ternary Search\":TSmin R=%d (<L=%d) is not allowed!\n",R,L);system("pause>nul");return L;}if(function==NULL){printf("Error \"Ternary Search\":TSmin f=[NULL] is not allowed!\n");system("pause>nul");return L;}while(fabs(L-R)>eps){double m1=L+(R-L)/3;double m2=R-(R-L)/3;if(function(m1)<function(m2))R=m2;elseL=m1;}return L;}double TSmax(double L,double R,double (*function)(double x),double eps=1e-7){//make a ternary search for max value and return xif(R==L)return L;if(R<L){printf("Error \"Ternary Search\":TSmin R=%d (<L=%d) is not allowed!\n",R,L);system("pause>nul");return L;}if(function==NULL){printf("Error \"Ternary Search\":TSmin f=[NULL] is not allowed!\n");system("pause>nul");return L;}while(fabs(L-R)>eps){double m1=L+(R-L)/3;double m2=R-(R-L)/3;if(function(m1)>function(m2))R=m2;elseL=m1;}return L;}
}

Treap的基本板子

详见 Treap树堆的基本模板（无讲解）

后记

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Premier Bob的算法模板库（II）

Geometry_Calculate_Basic .hpp （计算几何基础运算）

NlogN_LIS .hpp （nlogn时间复杂度求解LIS长度）

UnionFindSet .hpp （并查集模板）

TernarySearch .hpp （三分法求单峰函数最小值）

Treap的基本板子

后记

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