Background
还有一个礼拜就省选了，连板子都不会打的Zars19觉得应该来一次模板补全计划。
（尽管好多该学的东西还没学）
Update:省选已经完了…但是还没补全
树
1.0 树链剖分（BZOJ1036 [ZJOI2008]树的统计Count）
#include<iostream> #include<cstdio> #include<cstdlib> #include<cstring> #define INF 0x3f3f3f3f #define MAXN 30005 using namespace std; int n,q,sz=0,head[MAXN],w[MAXN],ans; int dep[MAXN],top[MAXN],pos[MAXN],num[MAXN],father[MAXN],siz[MAXN],cnt=0; struct Node1 { int next,to; }Edges[MAXN*2]; void addedge(int u,int v) { Edges[++cnt].next=head[u]; head[u]=cnt; Edges[cnt].to=v; } int read() { int x=0,f=1;char c=getchar(); while(c<'0'||c>'9'){ if(c=='-')f=-1;c=getchar(); } while(c>='0'&&c<='9'){ x=x*10+c-'0';c=getchar(); } return x*f; } void dfs1(int u) { siz[u]=1; for(int i=head[u];~i;i=Edges[i].next) { int v=Edges[i].to; if(v==father[u])continue; father[v]=u,dep[v]=dep[u]+1; dfs1(v); siz[u]+=siz[v]; } } void dfs2(int u,int t) { sz++,pos[u]=sz,num[sz]=u; int maxv=0,k=0; top[u]=t; for(int i=head[u];~i;i=Edges[i].next) { int v=Edges[i].to; if(v==father[u])continue; if(siz[v]>maxv)maxv=siz[v],k=v; } if(k)dfs2(k,t); for(int i=head[u];~i;i=Edges[i].next) { int v=Edges[i].to; if(v==father[u]||v==k)continue; dfs2(v,v); } } struct Node2 { int l,r,sum,maxn; }t[MAXN*4]; void build(int idx,int l,int r) { t[idx].l=l,t[idx].r=r; if(l==r) { t[idx].sum=t[idx].maxn=w[num[l]]; return; } int mid=(l+r)>>1; build(idx<<1,l,mid); build(idx<<1|1,mid+1,r); t[idx].maxn=max(t[idx<<1].maxn,t[idx<<1|1].maxn); t[idx].sum=t[idx<<1].sum+t[idx<<1|1].sum; } int query1(int idx,int a,int b) { if(a<=t[idx].l&&b>=t[idx].r) return t[idx].maxn; int mid=(t[idx].l+t[idx].r)>>1; if(b<=mid)return query1(idx<<1,a,b); if(a>mid)return query1(idx<<1|1,a,b); return max(query1(idx<<1,a,b),query1(idx<<1|1,a,b)); } int query2(int idx,int a,int b) { if(a<=t[idx].l&&b>=t[idx].r) return t[idx].sum; int mid=(t[idx].l+t[idx].r)>>1; if(b<=mid)return query2(idx<<1,a,b); if(a>mid)return query2(idx<<1|1,a,b); return query2(idx<<1,a,b)+query2(idx<<1|1,a,b); } void change(int idx,int a,int b) { if(t[idx].l==t[idx].r){t[idx].maxn=t[idx].sum=b;return;} int mid=(t[idx].l+t[idx].r)>>1; if(a<=mid)change(idx<<1,a,b); else change(idx<<1|1,a,b); t[idx].maxn=max(t[idx<<1].maxn,t[idx<<1|1].maxn); t[idx].sum=t[idx<<1].sum+t[idx<<1|1].sum; } void QMAX(int a,int b) { ans=-INF; while(top[a]!=top[b]) { if(dep[top[a]]<dep[top[b]])swap(a,b); ans=max(ans,query1(1,pos[top[a]],pos[a])); a=father[top[a]]; } if(pos[a]>pos[b])swap(a,b); ans=max(ans,query1(1,pos[a],pos[b])); printf("%d ",ans); } void QSUM(int a,int b) { ans=0; while(top[a]!=top[b]) { if(dep[top[a]]<dep[top[b]])swap(a,b); ans+=query2(1,pos[top[a]],pos[a]); a=father[top[a]]; } if(pos[a]>pos[b])swap(a,b); ans+=query2(1,pos[a],pos[b]); printf("%d ",ans); } int main() { memset(head,-1,sizeof(head)); n=read(); for(int i=1;i<n;i++) { int a=read(),b=read(); addedge(a,b); addedge(b,a); } for(int i=1;i<=n;i++) w[i]=read(); dfs1(1);dfs2(1,1); build(1,1,sz); q=read(); char opt[10];int a,b; for(int i=1;i<=q;i++) { scanf("%s",opt); a=read(),b=read(); if(!strcmp(opt,"CHANGE")) change(1,pos[a],b); else if(!strcmp(opt,"QMAX")) QMAX(a,b); else QSUM(a,b); } return 0; }
2.0 Tarjan离线LCA
2.1 倍增LCA
3.0 点分治（BZOJ2152 聪聪可可）
#include<iostream> #include<cstdio> #include<cstdlib> #include<cstring> #define MAXN 20005 #define INF 0x3f3f3f3f using namespace std; int n,head[MAXN],siz[MAXN],maxv[MAXN],root=0,tot=0,num=0,cnt=0,t[3],p,q; bool vis[MAXN]; int read() { int x=0,f=1;char c=getchar(); while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();} while(c>='0'&&c<='9'){x=x*10+c-'0';c=getchar();} return x*f; } struct Node { int next,to,w; }Edges[MAXN*2]; int gcd(int a,int b){return b?gcd(b,a%b):a;} void addedge(int u,int v,int w) { Edges[cnt].next=head[u]; head[u]=cnt; Edges[cnt].to=v; Edges[cnt++].w=w; } void getroot(int u,int f) { siz[u]=1,maxv[u]=0; for(int i=head[u];~i;i=Edges[i].next) { int v=Edges[i].to; if(v==f||vis[v])continue; getroot(v,u); siz[u]+=siz[v],maxv[u]=max(maxv[u],siz[v]); } maxv[u]=max(maxv[u],tot-siz[u]); if(maxv[u]<maxv[root])root=u; } void getdeep(int u,int f,int d) { t[d]++; for(int i=head[u];~i;i=Edges[i].next) { int v=Edges[i].to; if(v==f||vis[v])continue; getdeep(v,u,(d+Edges[i].w)%3); } } int calc(int u,int d) { memset(t,0,sizeof(t)); getdeep(u,0,d); return t[0]*t[0]+t[1]*t[2]*2; } void work(int u) { vis[u]=1;p+=calc(u,0); for(int i=head[u];~i;i=Edges[i].next) { int v=Edges[i].to; if(vis[v])continue; p-=calc(v,Edges[i].w%3); tot=siz[v],root=0; getroot(v,u),work(root); } } int main() { memset(head,-1,sizeof(head)); n=read(); for(int i=1;i<n;i++) { int u=read(),v=read(),w=read(); addedge(u,v,w),addedge(v,u,w); } maxv[0]=INF,tot=n; p=0,q=n*n; getroot(1,0),work(1); int t=gcd(p,q); printf("%d/%d ",p/t,q/t); return 0; }
数据结构
1.0 splay（BZOJ3223 Tyvj 1729 文艺平衡树）
#include<cstdio> #include<cstdlib> #include<cstring> #include<iostream> using namespace std; int n,m,a[100005],root,siz=0; struct Node{ int ch[2],father,val,rev,siz; }t[100005]; inline int read() { int x=0,f=1;char c=getchar(); while(c<'0'||c>'9'){ if(c=='-')f=-1;c=getchar(); } while(c>='0'&&c<='9'){ x=x*10+c-'0';c=getchar(); } return x*f; } void Update(int x) { t[x].siz=t[t[x].ch[0]].siz+t[t[x].ch[1]].siz+1; } void Pushdown(int x) { if(t[x].rev) { t[x].rev=0; if(t[x].ch[0])t[t[x].ch[0]].rev^=1; if(t[x].ch[1])t[t[x].ch[1]].rev^=1; swap(t[x].ch[0],t[x].ch[1]); } } void Rotate(int x,int &k) { Pushdown(x); int y=t[x].father,z=t[y].father; int p=(t[y].ch[0]==x)?0:1; if(y!=k) { if(t[z].ch[0]==y)t[z].ch[0]=x; else t[z].ch[1]=x; } else k=x; t[x].father=z; t[y].ch[p]=t[x].ch[p^1]; t[t[x].ch[p^1]].father=y; t[x].ch[p^1]=y; t[y].father=x; Update(y),Update(x); } void Splay(int x,int &k) { while(x!=k) { int y=t[x].father,z=t[y].father; if(y!=k) { if((t[y].ch[0]==x)^(t[z].ch[0]==y)) Rotate(x,k); else Rotate(y,k); } Rotate(x,k); } } int Build(int l,int r,int f) { if(l>r)return 0; int mid=(l+r)>>1,now=++siz; t[now].father=f; t[now].rev=0; t[now].val=mid; t[now].ch[0]=Build(l,mid-1,now); t[now].ch[1]=Build(mid+1,r,now); Update(now); return now; } int Find(int x,int k) { if(!k)return 0; Pushdown(x); if(t[t[x].ch[0]].siz>=k)return Find(t[x].ch[0],k); else if(t[t[x].ch[0]].siz+1<k)return Find(t[x].ch[1],k-t[t[x].ch[0]].siz-1); return x; } void Print(int k) { if(!k)return; Pushdown(k); Print(t[k].ch[0]); if(t[k].val!=0&&t[k].val!=n+1) printf("%d ",t[k].val); Print(t[k].ch[1]); } int main() { n=read(),m=read(); root=Build(0,n+1,0); for(int i=1;i<=m;i++) { int l,r; l=read(),r=read(); int x=Find(root,l),y=Find(root,r+2); Splay(x,root);Splay(y,t[root].ch[1]); t[t[y].ch[0]].rev^=1; }Print(root); return 0; }
1.1 treap（BZOJ3224 TYVJ 1728 普通平衡树）
#include<iostream> #include<cstdio> #include<cstring> #include<cstdlib> #include<ctime> using namespace std; int n,siz=0,root=0,ans; struct Node { int lch,rch,val,siz,w,rank; }t[100005]; inline int read() { int x=0,f=1;char c=getchar(); while(c<'0'||c>'9'){ if(c=='-')f=-1;c=getchar(); } while(c>='0'&&c<='9'){ x=x*10+c-'0';c=getchar(); } return x*f; } void update(int k) { t[k].siz=t[t[k].lch].siz+t[t[k].rch].siz+t[k].w; } void leftRotate(int &k) { int p=t[k].rch; t[k].rch=t[p].lch; t[p].lch=k; t[p].siz=t[k].siz; update(k);k=p; } void rightRotate(int &k) { int p=t[k].lch; t[k].lch=t[p].rch; t[p].rch=k; t[p].siz=t[k].siz; update(k);k=p; } void Insert(int &k,int x) { if(!k){ siz++;k=siz; t[k].siz=t[k].w=1; t[k].val=x; t[k].rank=rand(); return; } t[k].siz++; if(t[k].val==x) {t[k].w++;return;} if(x<t[k].val){ Insert(t[k].lch,x); if(t[t[k].lch].rank<t[k].rank)rightRotate(k); return; } else{ Insert(t[k].rch,x); if(t[t[k].rch].rank<t[k].rank)leftRotate(k); return; } } void Delete(int &k,int x) { if(!k)return; if(t[k].val==x) { if(t[k].w>1) {t[k].siz--;t[k].w--;return;} if(!t[k].lch||!t[k].rch) {k=t[k].lch+t[k].rch;return;} if(t[t[k].lch].rank>t[t[k].rch].rank){ leftRotate(k);Delete(k,x); return; } else{ rightRotate(k);Delete(k,x); return; } } t[k].siz--; if(x<t[k].val){ Delete(t[k].lch,x); return; } else{ Delete(t[k].rch,x); return; } } int queryRank(int k,int x) { if(!k)return 0; if(x==t[k].val)return t[t[k].lch].siz+1; else if(x<t[k].val)return queryRank(t[k].lch,x); else return t[t[k].lch].siz+t[k].w+queryRank(t[k].rch,x); } int queryNum(int k,int x) { if(!k)return 0; if(x<=t[t[k].lch].siz)return queryNum(t[k].lch,x); else if(x>t[t[k].lch].siz+t[k].w)return queryNum(t[k].rch,x-t[t[k].lch].siz-t[k].w); else return t[k].val; } void queryPre(int k,int x) { if(!k)return; if(x<=t[k].val)queryPre(t[k].lch,x); else {ans=t[k].val,queryPre(t[k].rch,x);} } void querySuc(int k,int x) { if(!k)return; if(x>=t[k].val)querySuc(t[k].rch,x); else {ans=t[k].val,querySuc(t[k].lch,x);} } int main() { srand(time(0)); n=read(); for(int i=1;i<=n;i++) { int opt,x; opt=read(),x=read(); switch(opt) { case 1:Insert(root,x);break; case 2:Delete(root,x);break; case 3:printf("%d ",queryRank(root,x));break; case 4:printf("%d ",queryNum(root,x));break; case 5:ans=0;queryPre(root,x);printf("%d ",ans);break; case 6:ans=0;querySuc(root,x);printf("%d ",ans);break; } } return 0; }
图论
1.0 强连通分量
void tarjan(int u) { dfn[u]=low[u]=++dfn_clock; vis[u]=ins[u]=1;s.push(u); for(int i=head[u];~i;i=Edges[i].next) { int v=Edges[i].to; if(!vis[v]) { tarjan(v); low[u]=min(low[u],low[v]); } else if(ins[v]) {low[u]=min(low[u],dfn[v]);} } if(dfn[u]==low[u]) { tot++;int t=-1; while(t!=u) { t=s.top(); sccno[t]=tot; ins[t]=0; s.pop(); } } }
1.1 割点
1.2 割边
2.0 Dinic （草地排水）
#include<cstdio> #include<cstdlib> #include<cstring> #include<iostream> #include<queue> #define INF 0x3f3f3f3f #define MAXN 250 using namespace std; int m,n,s,t,level[MAXN],head[MAXN],cnt=0; struct Node{ int next,to,cap; }Edges[MAXN*2]; void addedge(int u,int v,int c) { Edges[cnt].next=head[u]; head[u]=cnt; Edges[cnt].to=v; Edges[cnt++].cap=c; } void insert(int u,int v,int c){ addedge(u,v,c); addedge(v,u,0); } bool bfs() { memset(level,-1,sizeof(level)); level[s]=0; queue<int>q; q.push(s); while(!q.empty()) { int u=q.front();q.pop(); for(int i=head[u];~i;i=Edges[i].next) { int v=Edges[i].to; if(level[v]==-1&&Edges[i].cap) level[v]=level[u]+1,q.push(v); } } if(level[t]==-1)return false; return true; } int dfs(int u,int flow) { int f=0,d=0; if(u==t)return flow; for(int i=head[u];~i&&flow>f;i=Edges[i].next) { int v=Edges[i].to; if(level[v]==level[u]+1&&Edges[i].cap) { d=dfs(v,min(flow-f,Edges[i].cap)); f+=d; Edges[i].cap-=d; Edges[i^1].cap+=d; } } if(!f)level[u]=-1; return f; } int main() { memset(head,-1,sizeof(head)); scanf("%d%d",&m,&n); s=1,t=n; for(int i=1;i<=m;i++) { int u,v,c; scanf("%d%d%d",&u,&v,&c); insert(u,v,c); } int ans=0,d; while(bfs()) { while(d=dfs(s,INF)) ans+=d; } printf("%d",ans); return 0; }
2.1 费用流
#include<cstdio> #include<cstdlib> #include<cstring> #include<iostream> #include<queue> #define INF 0x3f3f3f3f using namespace std; int m,n,s,t,a[450],pre[450],dis[450],head[450],cnt=0,MF,MC; bool inq[450]; struct Node{ int next,from,to,cap,w; }Edges[30005]; void addedge(int u,int v,int c,int w) { Edges[cnt].next=head[u]; head[u]=cnt; Edges[cnt].from=u; Edges[cnt].to=v; Edges[cnt].cap=c; Edges[cnt++].w=w; } void insert(int u,int v,int c,int w){ addedge(u,v,c,w); addedge(v,u,0,-w); } void MCMF() { MF,MC=0; while(1) { memset(dis,0x3f,sizeof(dis)); memset(a,0,sizeof(a)); int f=0; queue<int>q; q.push(s); inq[s]=1,a[s]=INF,dis[s]=0; while(!q.empty()) { int u=q.front();q.pop();inq[u]=0; for(int i=head[u];~i;i=Edges[i].next) { int v=Edges[i].to; if(dis[u]+Edges[i].w<dis[v]&&Edges[i].cap>0) { dis[v]=dis[u]+Edges[i].w; a[v]=min(a[u],Edges[i].cap); pre[v]=i; if(!inq[v]){q.push(v);inq[v]=1;} } } } if(a[t]==0)break; int p=t; MC+=a[t]*dis[t]; while(p!=s){ Edges[pre[p]].cap-=a[t]; Edges[pre[p]^1].cap+=a[t]; p=Edges[pre[p]].from; } MF+=a[t]; } } int main() { memset(head,-1,sizeof(head)); scanf("%d%d",&n,&m); s=1,t=n; for(int i=1;i<=m;i++) { int u,v,c,w; scanf("%d%d%d%d",&u,&v,&c,&w); insert(u,v,c,w); } MCMF(); printf("%d %d ",MF,MC); return 0; }
3.0 匈牙利算法（UOJ#78. 二分图最大匹配）
#include<iostream> #include<cstdio> #include<cstring> #include<cstdlib> using namespace std; int n1,n2,m,head[505],cnt=0,ans=0,link[505]; bool vis[505]; struct Node { int next,to; }Edges[250005]; void addedge(int u,int v) { Edges[++cnt].next=head[u]; head[u]=cnt; Edges[cnt].to=v; } int read() { int x=0,f=1;char c=getchar(); while(c<'0'||c>'9'){ if(c=='-')f=-1;c=getchar(); } while(c>='0'&&c<='9'){ x=x*10+c-'0';c=getchar(); } return x*f; } bool dfs(int u) { for(int i=head[u];~i;i=Edges[i].next) { int v=Edges[i].to; if(!vis[v]) { vis[v]=1; if(!link[v]||dfs(link[v])) {link[v]=u;return true;} } } return false; } int main() { memset(head,-1,sizeof(head)); n1=read(),n2=read(),m=read(); for(int i=1;i<=m;i++) { int v=read(),u=read(); addedge(u,v); } for(int i=1;i<=n2;i++) { memset(vis,0,sizeof(vis)); if(dfs(i))ans++; } printf("%d ",ans); for(int i=1;i<=n1;i++) printf("%d ",link[i]); return 0; }
字符串
1.0 KMP
#include<iostream> #include<cstdio> #include<cstring> #include<cstdlib> #define MAXN 1000005 using namespace std; int n,m,next[MAXN],cnt=0; char a[MAXN],b[MAXN]; int main() { scanf("%s%s",a+1,b+1); n=strlen(a+1),m=strlen(b+1); int j=0;next[1]=0; for(int i=2;i<=m;i++) { while(j!=0&&b[i]!=b[j+1])j=next[j]; if(b[i]==b[j+1])j++; next[i]=j; } j=0; for(int i=1;i<=n;i++) { while(j!=0&&a[i]!=b[j+1])j=next[j]; if(a[i]==b[j+1])j++; if(j==m){j=next[j],++cnt;} } printf("%d ",cnt); return 0; }
2.0 AC自动机（BZOJ3172 TJOI2013 单词）
#include<iostream> #include<cstdio> #include<cstdlib> #include<cstring> using namespace std; int n,siz,root,q[1000010],head,tail,pos[202]; char word[1000010]; struct Node{ int next[26],cnt,fail; bool vis; }trie[1000010]; int newnode() { siz++; trie[siz].cnt=trie[siz].fail=trie[siz].vis=0; memset(trie[siz].next,0,sizeof(trie[siz].next)); return siz; } void insert(int x,char* word) { int i=0,p=root; while(word[i]) { int idx=word[i]-'a'; if(!trie[p].next[idx])trie[p].next[idx]=newnode(); p=trie[p].next[idx]; trie[p].cnt++; i++; } pos[x]=p; } void build() { head=0,tail=0; q[++tail]=root; while(head<tail) { int p=q[++head]; for(int i=0;i<26;i++) { int t=trie[p].fail; while(t&&!trie[t].next[i])t=trie[t].fail; if(trie[p].next[i]) { trie[trie[p].next[i]].fail=t?trie[t].next[i]:root; q[++tail]=trie[p].next[i]; } else trie[p].next[i]=t?trie[t].next[i]:root; } } } void work() { int res=0; for(int p=tail;p>0;p--) { int t=trie[q[p]].fail; trie[t].cnt+=trie[q[p]].cnt; } for(int i=1;i<=n;i++) printf("%d ",trie[pos[i]].cnt); } int main() { scanf("%d",&n); siz=0,root=newnode(); for(int i=1;i<=n;i++) { scanf("%s",word); insert(i,word); } build();work(); return 0; }
3.0 Manachar
4.0 SAM
5.0 SA
计算几何
1.0 点和直线
int dcmp(double x){ //实数比较 if(fabs(x)<EPS)return 0; return x>0?1:-1; } struct Point{ //点向量的定义 double x,y; Point(double x=0,double y=0):x(x),y(y){} Point operator + (Point A){return Point(x+A.x,y+A.y);} Point operator - (Point A){return Point(x-A.x,y-A.y);} Point operator * (double p){return Point(x*p,y*p);} Point operator / (double p){return Point(x/p,x/p);} bool operator == (Point A){return dcmp(x-A.x)==0&&dcmp(y-A.y)==0;} }; typedef Point Vector; double dot(Vector A,Vector B){ //点积 return A.x*B.x+A.y*B.y; } double cross(Vector A,Vector B){ //叉积 return A.x*B.y-B.x*A.y; } double length(Vector A){ //向量的长度 return sqrt(dot(A,A)); } double angle(Vector A,Vector B){ //两向量的转角 return acos(dot(A,B)/length(A)/length(B)); } Vector rotate(Vector A,double rad){ //向量的旋转 return Vector(cos(rad)*A.x-sin(rad)*A.y,sin(rad)*A.x+cos(rad)*A.y); } Vector normal(Vector A){ //法向量 double l=length(A); return Vector(-A.y/l,A.x/l); } struct Line{ //线 Point p;Vector v; Line(Point p=Point(0,0),Vector v=Vector(0,0)):p(p),v(v){} }; Point get_intersection(Line A,Line B){ //两直线求交 Point u=A.p-B.p; double t=cross(B.v,u)/cross(A.v,B.v); return A.p+A.v*t; } double dis_line(Point P,Point A,Point B){ //点到直线的距离 Vector v1=B-A,v2=P-A; return fabs(cross(v1,v2)/length(v1)); } double dis_segment(Point P,Point A,Point B){ //点到线段的距离 Vector v1=B-A,v2=P-A,v3=P-B; if(dcmp(dot(v1,v2)<0))return length(v2); if(dcmp(dot(v1,v3)>0))return length(v3); return fabs(cross(v1,v2)/length(v1)); } Point get_projection(Point P,Point A,Point B){ //点在直线上的投影 Vector v=B-A; return A+v*(dot(P-A,v)/dot(v,v)); } bool segment_properintersection(Point a1,Point a2,Point b1,Point b2) //线段相交判定 { double c1=cross(b2-b1,a1-b1),c2=cross(b2-b1,a2-b1), c3=cross(a2-a1,b1-a1),c4=cross(a2-a1,b2-a1); return dcmp(c1)*dcmp(c2)<=0&&dcmp(c3)*dcmp(c4)<=0; }
2.0 圆
struct Circle{ Point c;double r; Point getpoint(double ang){ //获取圆上弧度角为ang的点 return Point(c.x+r*cos(ang),c.y+r*sin(ang)); } }; int getLineCircle_intersection(Line L,Circle C,double& t1,double& t2,vector<Point>& sol){ double a=L.v.x,b=L.p.x-C.c.x,c=L.v.y,d=L.p.y-C.c.y; //直线与圆的交点 double e=a*a+c*c,f=2*a*b+2*c*d,g=b*b+d*d-C.r*C.r; double delta=(f*f)-4*e*g; if(dcmp(delta)<0)return 0; if(!dcmp(delta)){ t1=-f/(2*e);sol.push_back(L.p+L.v*t1); return 1; } t1=-f+sqrt(delta)/(2*e);t2=-f-sqrt(delta)/(2*e); sol.push_back(L.p+L.v*t1);sol.push_back(L.p+L.v*t2); return 2; } double angle(Vector A){ //极角 return atan2(A.y,A.x); } int getCircleCircle_intersection(Circle C1,Circle C2,vector<Point>& sol){ double d=length(C1.c-C2.c); //两圆交点 if(dcmp(C1.r+C2.r-d)<0)return 0; if(dcmp(fabs(C1.r-C2.r)-d)>0)return 0; double a=angle(C2.c-C1.c); double da=acos((d*d+C1.r*C1.r-C2.r*C2.r)/(2*d*C1.r)); Point p1=C1.getpoint(a+da),p2=C1.getpoint(a-da); if(p1==p2){ sol.push_back(p1);return 1; }; sol.push_back(p1),sol.push_back(p2); return 2; } int get_tangents(Point p,Circle C,vector<Point>& sol){ Vector u=C.c-p; //切线 double dis=length(u); if(dcmp(dis-C.r)<0)return 0; if(!dcmp(dis-C.r)){ sol.push_back(rotate(u,pi/2));return 1; } double ang=asin(C.r/dis); sol.push_back(rotate(u,ang));sol.push_back(rotate(u,-ang)); return 2; }
3.0 凸包
4.0 半平面交
5.0 自适应Simpson积分
double simpson(double a,double b){ double c=a+(b-a)/2; return (F(a)+4*F(c)+F(b))*(b-a)/6.0; } double asr(double a,double b,double eps,double A){ double c=a+(b-a)/2; double L=simpson(a,c),R=simpson(c,b); if(fabs(L+R-A)<eps*15)return (L+R)+(L+R-A)/15; return asr(a,c,eps/2,L)+asr(c,b,eps/2,R); }
6.0 旋转卡壳
数学
1.0 欧几里得算法
LL gcd(LL a,LL b){ return (b==0)?a:gcd(b,a%b); }
1.1 扩展欧几里得算法
void exgcd(LL a,LL b,LL& d,LL& x,LL& y){ if(!b){d=a,x=1,y=0;} else {exgcd(b,a%b,d,y,x);y-=x*(a/b);} }
2.0 乘法逆元
LL inv(LL a,LL p){ LL d,x,y; exgcd(a,p,d,x,y); return (d==1)?(x+p)%p:-1; }
3.0 FFT（UOJ#34. 多项式乘法）
#include<iostream> #include<cstdio> #include<cstring> #include<cstdlib> #include<cmath> #define MAXN 400005 #define pi acos(-1) using namespace std; int n,m; struct cp { double r,i; cp(double r=0,double i=0):r(r),i(i){} cp operator + (const cp& A) {return cp(r+A.r,i+A.i);} cp operator - (const cp& A) {return cp(r-A.r,i-A.i);} cp operator * (const cp& A) {return cp(r*A.r-i*A.i,r*A.i+i*A.r);} }a[MAXN],b[MAXN]; void brc(cp* x,int l) { int k=l/2; for(int i=1;i<l-1;i++) { if(i<k)swap(x[i],x[k]); int j=l/2; while(j<=k) { k-=j; j>>=1; } if(k<j)k+=j; } } void fft(cp* x,int l,int on) { brc(x,l); for(int h=2;h<=l;h<<=1) { cp wn(cos(2*on*pi/h),sin(2*on*pi/h)); for(int i=0;i<l;i+=h) { cp w(1,0); for(int j=i;j<i+h/2;j++) { cp u=x[j]; cp t=w*x[j+h/2]; x[j]=u+t; x[j+h/2]=u-t; w=w*wn; } } } if(on==-1)for(int i=0;i<l;i++)x[i].r/=l; } int main() { scanf("%d%d",&n,&m); n++,m++; int l=1; while(l<n*2||l<m*2)l<<=1; for(int i=0;i<n;i++) { int x; scanf("%d",&x); a[i]=cp(x,0); } for(int i=n;i<l;i++)a[i]=cp(0,0); for(int i=0;i<m;i++) { int x; scanf("%d",&x); b[i]=cp(x,0); } for(int i=m;i<l;i++)b[i]=cp(0,0); fft(a,l,1);fft(b,l,1); for(int i=0;i<l;i++)a[i]=a[i]*b[i]; fft(a,l,-1); for(int i=0;i<=n+m-2;i++) { int x=(int)(a[i].r+0.5); printf("%d ",x); } return 0; }
4.0 NTT
5.0 欧拉函数
void phi_table() { phi[1]=1; for(int i=1;i<=n;i++) { if(!phi[i]) for(int j=i;j<=n;j+=i) { if(!phi[j])phi[j]=j; phi[j]=phi[j]*(i-1)/i; } } }
6.0 中国剩余定理（CodeVS 3990 中国余数定理 2）
#include<iostream> #include<cstdio> #include<cstring> #include<cstdlib> using namespace std; typedef long long LL; LL n,a,b,c[15],m[15],M=1,res=0; LL read() { LL x=0,f=1;char c=getchar(); while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();} while(c>='0'&&c<='9'){x=x*10+c-'0';c=getchar();} return x*f; } void exgcd(LL a,LL b,LL &x,LL &y) { if(!b)x=1,y=0; else exgcd(b,a%b,y,x),y-=x*(a/b); } int main() { n=read(),a=read(),b=read(); for(int i=1;i<=n;i++) m[i]=read(),c[i]=read(),M*=m[i]; for(int i=1;i<=n;i++) { LL t=M/m[i],x,y; exgcd(t,m[i],x,y); x=(x+m[i])%m[i]; res=(res+((x*t)%M*c[i])%M)%M; } if(a>res) { if((a-res)%M==0)res+=(a-res)/M*M; else res+=((a-res)/M+1)*M; } if(res>b||res<a){printf("0 0 ");return 0;} printf("%lld %lld ",(b-res)/M+1,res); return 0; }
6.1 扩展中国剩余定理（POJ 2891 Strange Way to Express Integers）
#include<iostream> #include<cstdio> #include<cstdlib> #include<cstring> #define MAXN 50005 using namespace std; typedef long long LL; LL k,c[MAXN],m[MAXN]; LL read() { LL x=0,f=1;char c=getchar(); while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();} while(c>='0'&&c<='9'){x=x*10+c-'0';c=getchar();} return x*f; } LL gcd(LL a,LL b){return b?gcd(b,a%b):a;} void exgcd(LL a,LL b,LL &d,LL &x,LL& y) { if(!b)d=a,x=1,y=0; else exgcd(b,a%b,d,y,x),y-=x*(a/b); } LL inv(LL a,LL p) { LL d,x,y;exgcd(a,p,d,x,y); return (x+p)%p==0?p:(x+p)%p; } int main() { LL m1,m2,c1,c2; while(~scanf("%lld",&k)) { for(int i=1;i<=k;i++) m[i]=read(),c[i]=read(); for(int i=2;i<=k;i++) { m1=m[i-1],m2=m[i],c1=c[i-1],c2=c[i]; LL t=gcd(m1,m2); if((c2-c1)%t!=0){c[k]=-1;break;} m[i]=m1*m2/t; c[i]=inv(m1/t,m2/t)*((c2-c1)/t)%(m2/t)*m1+c1; c[i]=(c[i]%m[i]+m[i])%m[i]; } printf("%lld ",c[k]); } return 0; }
7.0 Lucas
7.1 扩展Lucas
其他
1.0 高精度