模板合集
神奇的模板...总之各种各样的模板整理...已经准备用我现在的码风重新打一遍了...
高精度
- 已重载运算符.没写FFT什么的...
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 | #include<cstdio> #include<cmath> #include<vector> #include<algorithm> #include<iostream> using namespace std; typedef long long LL; const int B = 10; const int W = 1; struct Big{ vector< int > s; void clear(){ s.clear(); } Big(LL num=0){ * this =num; } Big operator = (LL x){ clear(); do { s.push_back(x%B),x/=B; } while (x); return * this ; } Big operator = ( const string &str){ clear(); int x,len=(str.length()-1)/W+1,l=str.length(); for ( int i=0;i<len;i++){ int tt=l-i*W,st=max(0,tt-W); sscanf (str.substr(st,tt-st).c_str(), "%d" ,&x); s.push_back(x); } return * this ; } }; istream& operator >> (istream & in,Big &a){ string s; if (!(in>>s)) return in; a=s; return in; } ostream& operator << (ostream &out, const Big &a){ cout<<a.s.back(); for ( int i=a.s.size()-2;~i;i--){ cout.width(W),cout.fill( '0' ),cout<<a.s[i]; } return out; } bool operator < ( const Big &a, const Big &b){ int la=a.s.size(),lb=b.s.size(); if (la<lb) return 1; if (la>lb) return 0; for ( int i=la-1;~i;i--){ if (a.s[i]<b.s[i]) return 1; if (a.s[i]>b.s[i]) return 0; } return 0; } bool operator <= ( const Big &a, const Big &b){ return !(b<a); } bool operator > ( const Big &a, const Big &b){ return b<a; } bool operator >= ( const Big &a, const Big &b){ return !(a<b); } bool operator == ( const Big &a, const Big &b){ return !(a>b) && !(a<b); } bool operator != ( const Big &a, const Big &b){ return a>b || a<b ; } Big operator + ( const Big &a, const Big &b){ Big c;c.clear(); int lim=max(a.s.size(),b.s.size()),la=a.s.size(),lb=b.s.size(),i,g,x; for (i=0,g=0;;i++){ if (g==0 && i>=lim) break ; x=g; if (i<la) x+=a.s[i]; if (i<lb) x+=b.s[i]; c.s.push_back(x%B),g=x/B; }i=c.s.size()-1; while (c.s[i]==0 && i) c.s.pop_back(),i--; return c; } Big operator - ( const Big &a, const Big &b){ Big c;c.clear(); int i,g,x,la=a.s.size(),lb=b.s.size(); for (i=0,g=0;i<la;i++){ x=a.s[i]-g; if (i<lb) x-=b.s[i]; if (x>=0) g=0; else g=1,x+=B; c.s.push_back(x); }i=c.s.size()-1; while (c.s[i]==0 && i) c.s.pop_back(),i--; return c; } Big operator * ( const Big &a, const Big &b){ Big c; int i,j,la=a.s.size(),lb=b.s.size(),lc=la+lb; c.s.resize(lc,0); for (i=0;i<la;i++) for (j=0;j<lb;j++) c.s[i+j]+=a.s[i]*b.s[j]; for (i=0;i<lc;i++) c.s[i+1]+=c.s[i]/B,c.s[i]%=B; i=lc-1; while (c.s[i]==0 && i) c.s.pop_back(),i--; return c; } Big operator / ( const Big &a, const Big &b){ Big c,f=0; int la=a.s.size(),i; c.s.resize(la,0); for (i=la-1;~i;i--){ f=f*B,f.s[0]=a.s[i]; int l=0,r=B,mid; while (l<=r){ mid=(l+r)>>1; if (mid*b > f) r=mid-1; else l=mid+1; } f=f-r*b,c.s[i]=r; // while(f>=b) f=f-b,c.s[i]++; }i=la-1; while (c.s[i]==0 && i) c.s.pop_back(),i--; return c; } Big operator % ( const Big &a, const Big &b){ Big c=a-(a/b)*b; return c; } Big operator ^ (Big &a,Big &b){ Big c=1; for (;b!=0;b=b/2,a=a*a){ if (b.s[0] & 1) c=c*a; } return c; } Big operator += (Big &a, const Big &b){ return a=a+b; } Big operator -= (Big &a, const Big &b){ return a=a-b; } Big operator *= (Big &a, const Big &b){ return a=a*b; } Big operator /= (Big &a, const Big &b){ return a=a/b; } Big operator %= (Big &a, const Big &b){ return a=a%b; } int main(){ Big A,B; cin>>A>>B; cout<<A/B; return 0; } |
- FFT O(nlogn)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 | #include <bits/stdc++.h> using namespace std; #define mpr make_pair #define rr first #define ii second const int N = 5e5+50; const int M = 25; const double Pi = M_PI; typedef pair< double , double > Complex; Complex operator + ( const Complex &a, const Complex &b) { return mpr(a.rr+b.rr,a.ii+b.ii); } Complex operator - ( const Complex &a, const Complex &b) { return mpr(a.rr-b.rr,a.ii-b.ii); } Complex operator * ( const Complex &a, const Complex &b) { return mpr(a.rr*b.rr-a.ii*b.ii,a.rr*b.ii+a.ii*b.rr); } int n,m; Complex a[N],b[N],c[N]; int ans[N],pow2[M]; void init( int x) { pow2[0]=1; for ( int i=1;i<M;i++) pow2[i]=pow2[i-1]<<1; for (m=0,n=1;n<x;n<<=1,m++); n<<=1,m++; } void Rev(Complex a[]) { for ( int i=0,j=0;i<n;i++) { if (i>j) swap(a[i],a[j]); for ( int k=n>>1;(j^=k)<k;k>>=1); } } void DFT(Complex y[], int r) { Rev(y); for ( int i=2;i<=n;i<<=1) { Complex wi=mpr( cos (2.0*Pi/i),r* sin (2.0*Pi/i)); for ( int k=0;k<n;k+=i) { Complex w=mpr(1.0,0.0); for ( int j=k;j<k+i/2;j++) { Complex t1=y[j],t2=w*y[j+i/2]; y[j]=t1+t2,y[j+i/2]=t1-t2; w=w*wi; } } } if (r==-1) for ( int i=0;i<n;i++) y[i].rr/=n; } void FFT(Complex a[],Complex b[],Complex c[]) { DFT(a,1),DFT(b,1); for ( int i=0;i<n;i++) c[i]=a[i]*b[i]; DFT(c,-1); } int main() { string s1,s2; cin>>s1>>s2; reverse(s1.begin(),s1.end()); reverse(s2.begin(),s2.end()); init(( int )max(s1.length(),s2.length())); for ( int i=0;i<( int )s1.length();i++) a[i]=mpr(s1[i]- '0' ,0); for ( int i=0;i<( int )s2.length();i++) b[i]=mpr(s2[i]- '0' ,0); FFT(a,b,c); for ( int i=0;i<n;i++) ans[i]=c[i].rr+0.5; for ( int i=0;i<n;i++) ans[i+1]+=ans[i]/10,ans[i]%=10; for (;!ans[n] && n;n--); for ( int i=n;~i;i--) putchar (ans[i]+ '0' ); return 0; } |
- FNT O(nlogn)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 | #include <bits/stdc++.h> using namespace std; typedef long long LL; const int N = 5e5+50; const int p = (479 << 21) + 1; const int g = 3; int n; LL a[N],b[N],c[N]; LL Pow(LL a,LL b,LL r=1) { for (;b;b>>=1,a=a*a%p) if (b&1) r=r*a%p; return r; } void init( int x) { for (n=1;n<x;n<<=1);n<<=1; } void Rev(LL a[]) { for ( int i=0,j=0;i<n;i++) { if (i>j) swap(a[i],a[j]); for ( int k=n>>1;(j^=k)<k;k>>=1); } } void FNT(LL y[], int r) { Rev(y); for ( int i=2;i<=n;i<<=1) { LL wi=Pow(g,(p-1)/i); if (r==-1) wi=Pow(wi,p-2); for ( int k=0;k<n;k+=i) { LL w=1; for ( int j=k;j<k+i/2;j++) { LL t1=y[j],t2=(w*y[j+i/2])%p; y[j]=(t1+t2)%p,y[j+i/2]=(t1-t2+p)%p; w=w*wi%p; } } } if (r==-1) { LL inv=Pow(n,p-2); for ( int i=0;i<n;i++) y[i]=y[i]*inv%p; } } void FFT(LL a[],LL b[],LL c[]) { FNT(a,1),FNT(b,1); for ( int i=0;i<n;i++) c[i]=a[i]*b[i]%p; FNT(c,-1); } int main() { string s1,s2; cin>>s1>>s2; reverse(s1.begin(),s1.end());reverse(s2.begin(),s2.end()); for ( int i=0;i<s1.length();i++) a[i]=s1[i]- '0' ; for ( int i=0;i<s2.length();i++) b[i]=s2[i]- '0' ; init(max(s1.length(),s2.length())); FFT(a,b,c); for ( int i=0;i<n;i++) c[i+1]=(c[i+1]+c[i]/10),c[i]=c[i]%10; int p=n; for (;!c[p] && p>0;p--); for (;~p;p--) printf ( "%d" ,c[p]); return 0; } |
优化
- 读入优化
1 2 3 4 5 | char *ps=( char *) malloc (20000000); inline LL in(LL x=0){ for (;*ps> '9' ||*ps< '0' ;ps++); for (;*ps>= '0' &&*ps<= '9' ;ps++) x=(x<<3)+(x<<1)+*ps- '0' ; return x; } fread (ps,1,20000000,stdin); |
- 输出优化
1 2 3 4 5 6 7 | inline void Out(LL x){ int l=0; char ch[65]; if (!x){ putchar ( '0' ); return ; } if (x<0) putchar ( '-' ),x=-x; while (x) ch[++l]=x%10+ '0' ,x/=10; for ( int i=l;i;i--) putchar (ch[i]); } |
计算几何
- qwq
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 | #include <bits/stdc++.h> using namespace std; namespace CG { typedef long double LD; const LD Pi = M_PI; const LD PI = 2 * acos (0.0); const LD eps = 1e-18; const LD oo = 1e15; #define sqr(x) ((x)*(x)) int dcmp(LD x) { return fabs (x)<=eps?0:(x<0?-1:1); } struct Point { LD x,y; Point(LD _x=0,LD _y=0) :x(_x),y(_y) {} void out() { cout<< "(" <<x<< "," <<y<< ")" ; } }; typedef Point Vector; int cmpx( const Point &a, const Point &b) { return dcmp(a.x-b.x)==0?a.y<b.y:a.x<b.x; } Vector operator + ( const Vector &a, const Vector &b) { return Vector(a.x+b.x,a.y+b.y); } Vector operator - ( const Vector &a, const Vector &b) { return Vector(a.x-b.x,a.y-b.y); } Vector operator * ( const Vector &a,LD b) { return Vector(a.x*b,a.y*b); } Vector operator / ( const Vector &a,LD b) { return Vector(a.x/b,a.y/b); } bool operator == ( const Point &a, const Point &b) { return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0; } LD Dot(Vector a,Vector b) { return a.x*b.x+a.y*b.y; } LD Cross(Vector a,Vector b) { return a.x*b.y-b.x*a.y; } Vector Rot(Vector a,LD rd) { return Vector(a.x* cos (rd)-a.y* sin (rd),a.x* sin (rd)+a.y* cos (rd)); } LD get_l(Vector a) { return sqrt (Dot(a,a)); } LD get_d(Point a,Point b) { return sqrt (Dot(a-b,a-b)); } LD get_a(Vector a) { return atan2 (a.y,a.x); } LD get_a(Vector a,Vector b) { return acos (Dot(a,b)/get_l(a)/get_l(b)); } LD get_s(Point a,Point b,Point c) { return Cross(b-a,c-a)/2.0; } struct Line { Point p; Vector v; LD ang; Line(Point _p=Point(),Vector _v=Vector()):p(_p),v(_v) { ang=get_a(v); } LD get_l() { return sqrt (Dot(v,v)); } Point get_p(LD t) { return p+v*t; } Point get_s() { return p; } Point get_t() { return p+v; } int chkleft(Point P) { return dcmp(Cross(v,P-p))>0; } }; int cmpa( const Line &a, const Line &b) { return dcmp(a.ang-b.ang)==-1; } Point get_l_l(Line a,Line b) { Vector u=a.p-b.p; LD t=Cross(b.v,u)/Cross(a.v,b.v); return a.get_p(t); } typedef Line Hp; int get_h_h(vector<Hp> &hs,vector<Point> &pt) { sort(hs.begin(),hs.end(),cmpa); vector<Point> p(hs.size()); vector<Hp> q(hs.size()); int h,t; q[h=t=0]=hs[0]; for ( int i=1;i<( int )hs.size();i++) { while (h<t && !hs[i].chkleft(p[t-1])) t--; while (h<t && !hs[i].chkleft(p[h])) h++; q[++t]=hs[i]; if ( fabs (Cross(q[t].v,q[t-1].v))<eps) { t--; if (q[t].chkleft(hs[i].p)) q[t]=hs[i]; } if (h<t) p[t-1]=get_l_l(q[t-1],q[t]); } while (h<t && !q[h].chkleft(p[t-1])) t--; p[t]=get_l_l(q[h],q[t]); for ( int i=h;i<=t;i++) pt.push_back(p[i]); return t-h+1; } struct Circle { Point c; LD r; Point get_p(LD t) { return c+Point( cos (t)*r, sin (t)*r); } LD get_rd(Point a,Point b) { return get_a(a-c,b-c); } LD get_l(LD rd) { return r*rd; } }; int get_c_l(Line L,Circle C,vector<Point> &res) { LD a=L.v.x,b=L.p.x-C.c.x,c=L.v.y,d=L.p.y-C.c.y; LD e=sqr(a)+sqr(c),f=2.0*(a*b+c*d),g=sqr(b)+sqr(d)-sqr(C.r); LD dt=f*f-4*e*g; if (dcmp(dt)<0) return 0; if (dcmp(dt)==0) return res.push_back(L.get_p(-f/(2.0*e))),1; LD x1=(-f- sqrt (dt))/(2.0*e),x2=(-f+ sqrt (dt))/(2.0*e); if (x1>x2) swap(x1,x2); res.push_back(L.get_p(x1)),res.push_back(L.get_p(x2)); return 2; } int get_c_c(Circle A,Circle B,vector<Point> &res) { LD d=get_l(A.c-B.c); if (dcmp(d)==0) return dcmp(A.r-B.r)==0?-1:0; if (dcmp(A.r+B.r-d)<0) return 0; if (dcmp( fabs (A.r-B.r)-d)>0) return 0; LD a=get_a(B.c-A.c); LD rd= acos ((sqr(A.r)+sqr(d)-sqr(B.r))/(2.0*A.r*d)); Point p1,p2; p1=A.get_p(a+rd),p2=A.get_p(a-rd); res.push_back(p1); if (p1==p2) return 1; res.push_back(p2); return 2; } /*---io---*/ ostream & operator << (ostream &os, const Point &p) { os<<p.x<< " " <<p.y; return os; } istream & operator >> (istream &is,Point &p) { is>>p.x>>p.y; return is; } ostream & operator << (ostream &os, const Circle &C) { os<<C.c<< " " <<C.r; return os; } istream & operator >> (istream &is,Circle &C) { is>>C.c>>C.r; return is; } }; int main() { } |
图论
- Tarjan-割点 O(m)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 | #include<cstdio> #include<vector> #include<iostream> using namespace std; const int N = 100005; #define debug(a) cout<<#a<<"="<<a<<" " int n,m,cnt,ans; vector< int > g[N]; int b[N],out[N],du[N]; int dfsn[N],low[N]; inline int in( int x=0, char ch= getchar ()){ while (ch> '9' ||ch< '0' ) ch= getchar (); while (ch>= '0' &&ch<= '9' ) x=(x<<3)+(x<<1)+ch- '0' ,ch= getchar (); return x; } void Tarjan( int u, int fa){ dfsn[u]=low[u]=++cnt; int c=0; for ( int i=0,v;i<du[u];i++) if ((v=g[u][i])!=fa){ if (!dfsn[v]){ Tarjan(v,u),low[u]=min(low[u],low[v]),c++; if (fa>0&&dfsn[u]<=low[v]) b[u]=1; } else low[u]=min(low[u],dfsn[v]); } if (fa==0&&c>1) b[u]=1; } int main(){ n=in(),m=in(); for ( int i=1,u,v;i<=m;i++) u=in(),v=in(),du[u]++,du[v]++,g[u].push_back(v),g[v].push_back(u); for ( int i=1;i<=n;i++) if (!dfsn[i]) Tarjan(i,0); for ( int i=1;i<=n;i++) if (b[i]) out[++ans]=i; printf ( "%d\n" ,ans); for ( int i=1;i<=ans;i++) printf ( "%d " ,out[i]); putchar ( '\n' ); return 0; } |
- Tarjan-割边(桥) O(m)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 | #include<cstdio> #include<vector> #include<iostream> using namespace std; const int N = 100005; #define mpr(a,b) make_pair(a,b) int n,m,cnt,ans; int iscut[N],e[N]; int dfsn[N],low[N]; struct Edge{ int fr,to,id; }edge[N]; vector<Edge> g[N]; inline int in( int x=0, char ch= getchar ()){ while (ch> '9' ||ch< '0' ) ch= getchar (); while (ch>= '0' &&ch<= '9' ) x=(x<<3)+(x<<1)+ch- '0' ,ch= getchar (); return x; } inline void Add_Edge( int u, int v, int id){ edge[id]=(Edge){ u,v,id }; g[u].push_back((Edge){ u,v,id }); g[v].push_back((Edge){ v,u,id }); } void Tarjan( int u, int fa){ dfsn[u]=low[u]=++cnt; for ( int i=0,lim=g[u].size(),v;i<lim;i++) if ((v=g[u][i].to)!=fa){ if (!dfsn[v]){ Tarjan(v,u); if (low[v]>dfsn[u]) iscut[g[u][i].id]=1; low[u]=min(low[u],low[v]); } else low[u]=min(low[u],dfsn[v]); } } int main(){ n=in(),m=in(); for ( int i=1,u,v;i<=m;i++) u=in(),v=in(),Add_Edge(u,v,i); for ( int i=1;i<=n;i++) if (!dfsn[i]) Tarjan(i,0); for ( int i=1;i<=m;i++) if (iscut[i]) e[++ans]=i; printf ( "%d\n" ,ans); for ( int i=1;i<=ans;i++) printf ( "%d\n" ,e[i]); return 0; } |
- Tarjan-强连通分量+缩点. O(m)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 | #include<cstdio> #include<stack> #include<vector> #include<iostream> using namespace std; const int N = 10005; #define debug(a) cout<<#a<<"="<<a<<" " #define ct cout<<endl #define _ct cout<<"----------"<<endl int n,m,cnt,bcnt; int dfsn[N],low[N],ins[N],b[N],sz[N]; vector< int > g[N]; vector< int > h[N]; stack< int > stk; struct Edge{ int fr,to; }edge[N*5]; inline int in( int x=0, char ch= getchar ()){ while (ch> '9' ||ch< '0' ) ch= getchar (); while (ch>= '0' &&ch<= '9' ) x=(x<<3)+(x<<1)+ch- '0' ,ch= getchar (); return x; } void Tarjan( int u){ dfsn[u]=low[u]=++cnt,ins[u]=1,stk.push(u); for ( int i=0,lim=g[u].size(),v;i<lim;i++){ v=g[u][i]; if (!dfsn[v]){ Tarjan(v),low[u]=min(low[u],low[v]); } else if (ins[v]) low[u]=min(low[u],dfsn[v]); } if (dfsn[u]==low[u]){ ++bcnt; int v; for (;;){ v=stk.top(),stk.pop(),ins[v]=0,b[v]=bcnt,sz[bcnt]++; if (u==v) break ; } } } int main(){ // freopen("in.in","r",stdin); n=in(),m=in(); for ( int i=1,u,v;i<=m;i++) u=in(),v=in(),g[u].push_back(v),edge[i]=(Edge){ u,v }; for ( int i=1;i<=n;i++) if (!dfsn[i]) Tarjan(i); // _ct;debug(bcnt),ct; for ( int i=1,u,v;i<=m;i++){ u=edge[i].fr,v=edge[i].to; // debug(u),debug(v),ct; // debug(b[u]),debug(b[v]),ct; if (b[u]!=b[v]) h[b[u]].push_back(b[v]); } return 0; } |
- LCA-倍增 O(nlogn+mlogn)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 | #include<cstdio> #include<utility> #include<vector> #include<iostream> using namespace std; #define mpr make_pair #define debug(a) cout<<#a<<"="<<a<<" " typedef pair< int , int > pr; const int N = 50005; const int M = 31; int n,m,k; vector<pr> h[N]; int pow2[M],d[N]; int f[N][M],g[N][M]; inline int in( int x=0, char ch= getchar ()){ while (ch> '9' || ch< '0' ) ch= getchar (); while (ch>= '0' && ch<= '9' ) x=(x<<3)+(x<<1)+ch- '0' ,ch= getchar (); return x; } void DFS( int u, int fa, int dep){ d[u]=dep; for ( int i=0,v;i<h[u].size();i++) if ((v=h[u][i].first)!=fa){ DFS(v,u,dep+1),f[v][0]=u,g[v][0]=h[u][i].second; } } void work(){ pow2[0]=1; for ( int i=1;i<M;i++) pow2[i]=pow2[i-1]<<1; for ( int j=1;j<M;j++) for ( int i=0;i<n;i++) f[i][j]=f[f[i][j-1]][j-1],g[i][j]=g[i][j-1]+g[f[i][j-1]][j-1]; } int Dis( int u, int v){ if (d[u]<d[v]) swap(u,v); int l=d[u]-d[v],res=0; if (l) for ( int i=0;i<M;i++) if (l&pow2[i]) res+=g[u][i],u=f[u][i]; if (u==v) return res; for ( int i=M-1;~i;--i){ if (f[u][i]!=f[v][i]) res+=g[u][i]+g[v][i],u=f[u][i],v=f[v][i]; } return g[u][0]+g[v][0]+res; } int main(){ n=in(); for ( int i=1,u,v,w;i<n;i++) u=in(),v=in(),w=in(),h[u].push_back(mpr(v,w)),h[v].push_back(mpr(u,w)); DFS(0,0,1); work(); for (k=in();k--;){ int u=in(),v=in(); printf ( "%d\n" ,Dis(u,v)); } return 0; } |
- LCA-ST表 O(nlogn+m)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | #include<cstdio> #include<cmath> #include<cstring> #include<utility> #include<vector> #include<iostream> using namespace std; #define debug(a) cout<<#a<<"="<<a<<" " #define mpr make_pair typedef pair< int , int > pr; const int N = 200005; const int M = 25; int n,m,cnt; vector< pr > g[N]; int pow2[M],dfs[N],d[N],val[N],pos[N],lg2[N]; int f[N][M]; inline int in( int x=0, char ch= getchar ()){ while (ch> '9' || ch< '0' ) ch= getchar (); while (ch>= '0' && ch<= '9' ) x=(x<<3)+(x<<1)+ch- '0' ,ch= getchar (); return x; } void DFS( int u, int fa, int dep, int value){ dfs[++m]=u,d[u]=dep,val[u]=value,pos[u]=m,f[m][0]=u; for ( int i=0,v;i<g[u].size();i++) if ((v=g[u][i].first)!=fa) DFS(v,u,dep+1,value+g[u][i].second),dfs[++m]=u,f[m][0]=u; } void init(){ pow2[0]=1; for ( int i=1;i<M;i++) pow2[i]=pow2[i-1]<<1; lg2[0]=-1; for ( int i=1;i<=m;i++) lg2[i]=lg2[i>>1]+1; for ( int j=1;j<M;j++) for ( int i=1;i<=m;i++) if (i+pow2[j]-1<=m){ int u=f[i][j-1],v=f[i+pow2[j-1]][j-1]; if (d[u]<d[v]) f[i][j]=u; else f[i][j]=v; } } int Dis( int u, int v, int lca=0){ if (pos[u]<pos[v]) swap(u,v); int lg=lg2[pos[u]-pos[v]+1]; if (d[f[pos[v]][lg]]<d[f[pos[u]-pow2[lg]+1][lg]]) lca=f[pos[v]][lg]; else lca=f[pos[u]-pow2[lg]+1][lg]; return val[u]+val[v]-2*val[lca]; } int main(){ memset (d,0x3f, sizeof (d)); n=in(); for ( int i=1,u,v,w;i<n;i++) u=in(),v=in(),w=in(),g[u].push_back(mpr(v,w)),g[v].push_back(mpr(u,w)); DFS(0,0,1,0),init(); for ( int k=in(),u,v;k--;){ u=in(),v=in(); printf ( "%d\n" ,Dis(u,v)); } return 0; } |
- 网络流-ISAP O(V2E)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 | #include<cstdio> #include<cstring> #include<vector> #include<queue> #include<iostream> using namespace std; const int INF = 0x7fffffff; const int N = 505; const int M = 805; inline int in( int x=0, char ch= getchar ()){ while (ch> '9' ||ch< '0' ) ch= getchar (); while (ch>= '0' &&ch<= '9' ) x=(x<<3)+(x<<1)+ch- '0' ,ch= getchar (); return x; } struct NetWork{ int n,m,s,t; struct Edge{ int fr,to,flow; }edge[M<<1]; int cnte; vector< int > g[N]; int flow; int num[N],cur[N],d[N],p[N]; bool v[N]; void Add_Edge( int fr, int to, int fl){ edge[cnte++]=(Edge){ fr,to,fl },edge[cnte++]=(Edge){ to,fr,0 }; g[fr].push_back(cnte-2),g[to].push_back(cnte-1); } int Add_Flow(){ int a=INF; for ( int x=t;x!=s;x=edge[p[x]].fr) a=min(a,edge[p[x]].flow); for ( int x=t;x!=s;x=edge[p[x]].fr) edge[p[x]].flow-=a,edge[p[x]^1].flow+=a; return a; } void BFS(){ for ( int i=1;i<=n;i++) d[i]=n; memset (v,0, sizeof (v)); queue< int > q;q.push(t),v[t]=1,d[t]=0; for ( int x;!q.empty();){ x=q.front(),q.pop(); for ( int i=0,lim=g[x].size();i<lim;i++){ Edge &e=edge[g[x][i]]; Edge &u=edge[g[x][i]^1]; if (!v[e.to]&&u.flow) d[e.to]=d[x]+1,v[e.to]=1,q.push(e.to); } } } int ISAP(){ BFS(); int flow=0; memset (num,0, sizeof (num)), memset (cur,0, sizeof (cur)); for ( int i=1;i<=n;i++) num[d[i]]++; for ( int x=s,ok;d[s]<n;){ if (x==t) flow+=Add_Flow(),x=s;ok=0; for ( int &i=cur[x],lim=g[x].size();i<lim;i++){ Edge &e=edge[g[x][i]]; if (e.flow&&d[x]==d[e.to]+1){ ok=1,p[e.to]=g[x][i],x=e.to; break ; } } if (!ok){ int tmp=n-1; for ( int i=0,lim=g[x].size();i<lim;i++) tmp=min(tmp,d[edge[g[x][i]].to]); if (!(--num[d[x]])) break ;num[d[x]=m+1]++,cur[x]=0; if (x!=s) x=edge[p[x]].fr; } } return flow; } }isap; int main(){ return 0; } |
- 网络流-Dinic O(VE2)/二分图O(√VE)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 | #include<cstdio> #include<queue> #include<cstring> #include<vector> #include<iostream> using namespace std; const int N = 505; const int INF = 0x7fffffff; int T,n,m,cnt,ans; struct NetWork{ int n,m,s,t,flow; struct Edge{ int fr,to,flow; }; vector<Edge> edge;vector< int > g[N]; int cur[N],d[N],p[N]; void Add_Edge( int fr, int to, int flow){ edge.push_back((Edge){ fr,to,flow }); edge.push_back((Edge){ to,fr,0 }); m=edge.size(); g[fr].push_back(m-2),g[to].push_back(m-1); } int BFS(){ memset (d,-1, sizeof (d)); queue< int > q;q.push(s),d[s]=0; for ( int x;!q.empty();){ x=q.front(),q.pop(); for ( int i=0,lim=g[x].size();i<lim;i++){ Edge &e=edge[g[x][i]]; if (e.flow&&d[e.to]==-1) d[e.to]=d[x]+1,q.push(e.to); } } return d[t]!=-1; } int Dinic(){ flow=0; for ( int x,k;BFS();){ memset (cur,0, sizeof (cur));x=s,k=0; for ( int ok;;){ if (x==t){ int mine=-1,minf=0x7fffffff; for ( int i=0;i<k;i++) if (edge[p[i]].flow<minf) minf=edge[p[i]].flow,mine=i; for ( int i=0;i<k;i++) edge[p[i]].flow-=minf,edge[p[i]^1].flow+=minf; x=edge[p[mine]].fr,k=mine,flow+=minf; }ok=0; for ( int &i=cur[x],lim=g[x].size();i<lim;i++){ Edge &e=edge[g[x][i]]; if (e.flow>0&&d[x]+1==d[e.to]){ p[k++]=g[x][i],x=e.to,ok=1; break ; } } if (!ok){ if (!k) break ;d[x]=-1,x=edge[p[--k]].fr; } } } return flow; } }dinic; int main(){ return 0; } |
- 最小生成树计数Matrix-Tree定理 O(n3)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 | #include<cstdio> #include<cstring> #include<iostream> using namespace std; const double eps = 1e-8; const int N = 105; #define _0(x) ((x>0?x:-x)+eps>0) int n,m; int g[N][N],d[N]; double a[N][N]; double det( int n){ double res=1; int swpt=0; for ( int i=0,j,k;i<n;i++){ if (!_0(a[i][i])){ for (j=i+1;j<n;j++) if (_0(a[j][i])) break ; if (j>=n) return 0; for (k=i;k<n;k++) swap(a[i][k],a[j][k]); swpt++; }res*=a[i][i]; // for(j=i+1;j<n;j++) a[i][j]/=a[i][i]; for (j=i+1;j<n;j++) for (k=i+1;k<n;k++) a[j][k]-=a[j][i]*a[i][k]/a[i][i]; if (swpt&1) return -res; return res; } inline int in( int x=0, char ch= getchar ()){ while (ch> '9' ||ch< '0' ) ch= getchar (); while (ch>= '0' &&ch<= '9' ) x=(x<<3)+(x<<1)+ch- '0' ,ch= getchar (); return x; } int main(){ for ( int T=in();T--;){ n=in(),m=in(); memset (a,0, sizeof (a)), memset (g,0, sizeof (g)), memset (d,0, sizeof (d)); for ( int i=1,u,v;i<=m;i++) u=in()-1,v=in()-1,g[u][v]=g[v][u]=1,d[u]++,d[v]++; for ( int i=0;i<n;i++) a[i][i]=d[i]; for ( int i=0;i<n;i++) for ( int j=0;j<n;j++) if (g[i][j]) a[i][j]-=1; // for(int i=0;i<n;i++) for(int j=0;j<n;j++) printf("%.0lf%c",a[i][j]," \n"[j==n-1]); printf ( "%.0lf\n" ,det(n-1)); // for(int i=0;i<n;i++) for(int j=0;j<n;j++) printf("%.0lf%c",a[i][j]," \n"[j==n-1]); } return 0; } |
- 曼哈顿最小生成树 O(nlogn)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 | #include<cstdio> #include<cstring> #include<vector> #include<utility> #include<queue> #include<algorithm> #include<iostream> using namespace std; #define mpr(a,b) make_pair(a,b) const int N = 50005; int n,ans; struct seat{ int x,y,id; }a[N],b[N]; bool operator < ( const seat &a, const seat &b){ return a.x==b.x?a.y>b.y:a.x>b.x; } int d[N<<1],id[N<<1],cnt,ys[N]; struct Edge{ int u,v,w; }; bool operator < ( const Edge &a, const Edge &b){ return a.w>b.w; } priority_queue<Edge> q; int f[N]; inline int in( int x=0, char ch= getchar (), int v=1){ while (ch!= '-' &&(ch> '9' ||ch< '0' )) ch= getchar (); if (ch== '-' ) v=-1,ch= getchar (); while (ch>= '0' &&ch<= '9' ) x=(x<<3)+(x<<1)+ch- '0' ,ch= getchar (); return x*v; } //int cmpx(const seat &a,const seat &b){ return a.x==b.x?a.x<b.x:a.y<b.y; } //int cmpxy(const seat &a,const seat &b){ return a.y-a.x<b.y-b.x; } inline int abs ( int x){ return x<0?-x:x; } int find( int x){ return f[x]==x?x:f[x]=find(f[x]); } void Add_Edge( int u, int v){ int dis= abs (a[u].x-a[v].x)+ abs (a[u].y-a[v].y); q.push((Edge){ u,v,dis }); } void Add( int x, int v, int pos){ for (;x;x-=x&-x) if (d[x]>v) d[x]=v,id[x]=pos; } int Query( int x){ int minv=0x7f7f7f7f,pos=-1; for (;x<=cnt;x+=x&-x) if (d[x]<minv) minv=d[x],pos=id[x]; return pos; } void out(seat a){ cout<<a.x<< " " <<a.y<< " " <<a.id<<endl<< "***************\n" ; } void Build(){ /* Part1 x1>x0&&y1-x1>y0-x0 dis=(x1+y1)-(x0+y0) */ memset (d,0x7f, sizeof (d)), memset (id,-1, sizeof (id)), memset (ys,0, sizeof (ys));cnt=0; for ( int i=1;i<=n;i++) b[i]=a[i]; // for(int i=1;i<=n;i++) out(a[i]); sort(b+1,b+n+1); // for(int i=1;i<=n;i++) out(b[i]); for ( int i=1;i<=n;i++) ys[i]=b[i].y-b[i].x; sort(ys+1,ys+n+1); cnt=unique(ys+1,ys+n+1)-ys-1; // cout<<cnt<<endl; // for(int i=1;i<=cnt;i++) cout<<ys[i]<<" ";cout<<endl; for ( int i=1;i<=n;i++){ int x=lower_bound(ys+1,ys+cnt+1,b[i].y-b[i].x)-ys; int pos=Query(x); if (~pos) Add_Edge(b[i].id,pos); // cout<<b[i].id<<"-->"<<pos<<endl; Add(x,b[i].x+b[i].y,b[i].id); } /* Part2 swap(x,y) */ memset (d,0x7f, sizeof (d)), memset (id,-1, sizeof (id)), memset (ys,0, sizeof (ys));cnt=0; for ( int i=1;i<=n;i++) b[i].y=a[i].x,b[i].x=a[i].y,b[i].id=a[i].id; sort(b+1,b+n+1); // for(int i=1;i<=n;i++) out(b[i]); for ( int i=1;i<=n;i++) ys[i]=b[i].y-b[i].x; sort(ys+1,ys+n+1); cnt=unique(ys+1,ys+n+1)-ys-1; // cout<<cnt<<endl; // for(int i=1;i<=cnt;i++) cout<<ys[i]<<" ";cout<<endl; for ( int i=1;i<=n;i++){ int x=lower_bound(ys+1,ys+cnt+1,b[i].y-b[i].x)-ys; int pos=Query(x); if (~pos) Add_Edge(b[i].id,pos); // cout<<b[i].id<<"-->"<<pos<<endl; Add(x,b[i].x+b[i].y,b[i].id); } /* Part3 y=-y */ memset (d,0x7f, sizeof (d)), memset (id,-1, sizeof (id)), memset (ys,0, sizeof (ys));cnt=0; for ( int i=1;i<=n;i++) b[i]=a[i],b[i].y=-b[i].y; sort(b+1,b+n+1); // for(int i=1;i<=n;i++) out(b[i]); for ( int i=1;i<=n;i++) ys[i]=b[i].y-b[i].x; sort(ys+1,ys+n+1); cnt=unique(ys+1,ys+n+1)-ys-1; // cout<<cnt<<endl; // for(int i=1;i<=cnt;i++) cout<<ys[i]<<" ";cout<<endl; for ( int i=1;i<=n;i++){ int x=lower_bound(ys+1,ys+cnt+1,b[i].y-b[i].x)-ys; int pos=Query(x); if (~pos) Add_Edge(b[i].id,pos); // cout<<b[i].id<<"-->"<<pos<<endl; Add(x,b[i].x+b[i].y,b[i].id); } /* Part4 swap(x,y) y=-y */ memset (d,0x7f, sizeof (d)), memset (id,-1, sizeof (id)), memset (ys,0, sizeof (ys));cnt=0; for ( int i=1;i<=n;i++) b[i].x=-a[i].y,b[i].y=a[i].x,b[i].id=a[i].id; sort(b+1,b+n+1); // for(int i=1;i<=n;i++) out(b[i]); for ( int i=1;i<=n;i++) ys[i]=b[i].y-b[i].x; sort(ys+1,ys+n+1); cnt=unique(ys+1,ys+n+1)-ys-1; // cout<<cnt<<endl; // for(int i=1;i<=cnt;i++) cout<<ys[i]<<" ";cout<<endl; for ( int i=1;i<=n;i++){ int x=lower_bound(ys+1,ys+cnt+1,b[i].y-b[i].x)-ys; int pos=Query(x); if (~pos) Add_Edge(b[i].id,pos); // cout<<b[i].id<<"-->"<<pos<<endl; Add(x,b[i].x+b[i].y,b[i].id); } /* MST */ for ( int i=1;i<=n;i++) f[i]=i; for ( int k=1;!q.empty();){ Edge e=q.top();q.pop(); int u=e.u,v=e.v; int f1=find(u),f2=find(v); if (f1!=f2) k++,f[f2]=f1,ans+=e.w; if (k>=n) break ; }cout<<ans<<endl; } int main(){ // freopen("in.in","r",stdin); // freopen("out.out","w",stdout); n=in(); for ( int i=1;i<=n;i++) a[i].x=in(),a[i].y=in(),a[i].id=i; Build(); return 0; } |
- 朱刘算法/最小树形图 O(nm)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 | #include <bits/stdc++.h> using namespace std; inline int in( int x=0, char ch= getchar ()) { while (ch> '9' || ch< '0' ) ch= getchar (); while (ch>= '0' && ch<= '9' ) x=x*10+ch- '0' ,ch= getchar (); return x; } const int N = 55; const int M = N*N+50; struct Edge { int fr,to; double v; }; Edge edge[M]; int n,m,rt; int b[N]; double mic[N]; double miv[N]; int pre[N],vis[N],id[N]; void AddEdge( int fr, int to, double v) { edge[++m]=(Edge){ fr,to,v }; } double Solve( int n) { double res=0; for ( int cnt,tmp;;) { for ( int i=1;i<=n;i++) miv[i]=1e9,pre[i]=0; for ( int i=1;i<=m;i++) { Edge &e=edge[i]; if (e.v<miv[e.to]) miv[e.to]=e.v,pre[e.to]=e.fr; } for ( int i=1;i<=n;i++) if (pre[i]) res+=miv[i]; memset (vis,0, sizeof (vis)); memset (id,0, sizeof (id)); vis[0]=tmp=1,cnt=0; for ( int i=1;i<=n;i++) if (!vis[i]) { ++tmp; int u=i; for (;!vis[u];u=pre[u]) vis[u]=tmp; if (vis[u]==tmp) { ++cnt; for (;!id[u];u=pre[u]) id[u]=cnt; } } if (!cnt) break ; for ( int i=1;i<=n;i++) if (!id[i]) id[i]=++cnt; int mm=m;m=0; for ( int i=1;i<=mm;i++) { Edge &e=edge[i]; if (id[e.fr]!=id[e.to]) AddEdge(id[e.fr],id[e.to],e.v-miv[e.to]); } n=cnt; } return res; } int main() { n=in(),rt=n+1; for ( int i=1;i<=n;i++) { double x; scanf ( "%lf" ,&x); mic[i]=x; b[i]=in(); if (b[i]) AddEdge(rt,i,x); } for ( int k=in();k--;) { int x=in(),y=in(); double z; scanf ( "%lf" ,&z); if (b[x] && b[y]) { AddEdge(x,y,z); mic[y]=min(mic[y],z); } } double ans=Solve(n+1); // cout<<ans<<endl; // for(int i=1;i<=n;i++) cout<<mic[i]<<" ";cout<<endl; for ( int i=1;i<=n;i++) if (b[i]) ans+=(b[i]-1)*mic[i]; printf ( "%.2lf\n" ,ans); return 0; } |
数学
- 快速幂 O(logn) 快速乘 O(1)
1 2 3 4 5 6 | inline LL Mul(LL a,LL b,LL p){ if (p<=1000000000) return a*b%p; return (a*b-(LL)(a/( long double )p*b+1e-3)*p+p)%p; // for(;b;b>>=1,a=(a+a)%p) if(b&1) res=(res+a)%p;return res; } inline LL Pow(LL a,LL b,LL p,LL res=1){ for (;b;b>>=1,a=Mul(a,a,p)) if (b&1) res=Mul(res,a,p); return res; } |
-
φ(n) O(√n)
1 2 3 4 5 6 7 8 | inline LL GetPhi(LL p){ LL res=p,m= sqrt (p)+0.5; for ( int i=2;i<=m;i++) if (p%i==0){ res=res/i*(i-1); while (p%i==0) p/=i; } if (p>1) res=res/p*(p-1); return res; } |
- 线性筛 μ O(n)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | #include<cstdio> #include<cmath> #include<iostream> using namespace std; const int N = 1000005; int mu[N],pr[N],cnt; bool b[N]; void Pre(){ mu[1]=1; for ( int i=2;i<=N;i++){ if (!b[i]) mu[i]=-1,pr[++cnt]=i; for ( int j=1;j<=cnt&&pr[j]*i<=N;j++){ b[i*pr[j]]=1; if (i%pr[j]) mu[i*pr[j]]=-mu[i]; else break ; } } // for(int i=1;i<=10;i++) cout<<mu[i]<<" ";cout<<endl; } int main(){ Pre(); return 0; } |
- 矩阵乘法和矩阵快速幂 O(n3)O(n3logn)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | #include<cstdio> #include<vector> #include<iostream> using namespace std; typedef long long LL; typedef vector<LL> Vec; typedef vector<Vec> Mat; const LL p = 10000000007LL; Mat operator * ( const Mat &A, const Mat &B){ Mat C(A.size(),Vec(B[0].size())); for ( int i=0;i<A.size();i++) for ( int j=0;j<B[0].size();j++) for ( int k=0;k<A[0].size();k++) C[i][j]=(C[i][j]+A[i][k]*B[k][j])%p; return C; } Mat operator ^ (Mat A,LL b){ Mat res(A.size(),Vec(A[0].size())); for ( int i=0;i<A.size();i++) for ( int j=0;j<A[0].size();j++) res[i][j]=(i==j)?1:0; for (;b;b>>=1,A=A*A) if (b&1) res=res*A; return res; } int main(){ return 0; } |
- 扩展欧几里得 O(logn)
1 2 3 4 5 | LL Exgcd(LL a,LL b,LL &x,LL &y){ if (!b){ x=1,y=0; return a; } LL r=Exgcd(b,a%b,x,y);LL t=x; x=y,y=t-(a/b)*y; return r; } |
- 中国剩余定理 O(nlogn)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 | #include<cstdio> #include<iostream> using namespace std; typedef long long LL; const int N = 1005; int n; LL m[N],a[N]; LL Exgcd(LL a,LL b,LL &x,LL &y){ if (!b){ x=1,y=0; return a; } LL r=Exgcd(b,a%b,x,y);LL t=x; x=y,y=t-(a/b)*y; return r; } LL Solve(){ LL M=m[1],MM,res=0,x,y; for ( int i=2;i<=n;i++) M*=m[i]; for ( int i=1;i<=n;i++){ MM=M/m[i]; Exgcd(MM,m[i],x,y); res=(res+MM*x*a[i])%M; } return res; } int main(){ cin>>n; for ( int i=1;i<=n;i++) cin>>m[i]>>a[i]; Solve(); return 0; } |
- 求解模线性方程组 O(nlogn)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 | #include<cstdio> #include<utility> #include<algorithm> #include<iostream> using namespace std; typedef long long LL; #define mpr make_pair const int N = 1005; LL n,a1,a2,b1,b2; pair< LL,LL > m[N]; inline LL in(LL x=0, char ch= getchar ()){ while (ch> '9' || ch< '0' ) ch= getchar (); while (ch>= '0' && ch<= '9' ) x=(x<<3)+(x<<1)+ch- '0' ,ch= getchar (); return x; } LL Exgcd(LL a,LL b,LL &x,LL &y){ if (!b){ x=1,y=0; return a; } LL r=Exgcd(b,a%b,x,y);LL t=x; x=y,y=t-(a/b)*y; return r; } int Solve(){ LL x,y,d=Exgcd(a1,a2,x,y); if ((b2-b1)%d) return 0; Exgcd(a1/d,a2/d,x,y),x*=(b2-b1)/d,x=(x%(a2/d)+a2/d)%(a2/d); b1=a1*x+b1,a1=a1/d*a2,b1=(b1%a1+a1)%a1; return 1; } int main(){ n=in(); for (LL i=1,u,v;i<=n;i++) u=in(),v=in(),m[i]=mpr(u,v); a1=m[1].first,b1=m[1].second; for ( int i=2;i<=n;i++){ a2=m[i].first,b2=m[i].second; if (!Solve()) return puts ( "-1" ),0; } return printf ( "%lld\n" ,b1),0; } |
字符串
- 后缀数组 O(nlogn)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 | #include <bits/stdc++.h> using namespace std; const int N = 200050; int n,m=26; char s[N]; int a[N]; namespace SuffixArray { int s1[N],s2[N],sa[N],rk[N],ht[N],c[N]; void get_sa( int a[], int n=::n, int m=::m) { int *x=s1,*y=s2; for ( int i=1;i<=n;i++) c[x[i]=a[i]]++; for ( int i=1;i<=m;i++) c[i]+=c[i-1]; for ( int i=n;i;--i) sa[c[a[i]]--]=i; for ( int k=1,p=0;k<n;k<<=1,p=0) { for ( int i=n-k+1;i<=n;i++) y[++p]=i; for ( int i=1;i<=n;i++) if (sa[i]>k) y[++p]=sa[i]-k; for ( int i=0;i<=m;i++) c[i]=0; for ( int i=1;i<=n;i++) c[x[i]]++; for ( int i=1;i<=m;i++) c[i]+=c[i-1]; for ( int i=n;i;--i) sa[c[x[y[i]]]--]=y[i]; swap(x,y);x[sa[1]]=p=1; for ( int i=2;i<=n;i++) x[sa[i]]=(y[sa[i]]==y[sa[i-1]] && y[sa[i]+k]==y[sa[i-1]+k])?p:++p; if (p>=n) break ; m=p; } } void get_ht( int a[], int n=::n) { for ( int i=1;i<=n;i++) rk[sa[i]]=i; for ( int i=1,k=0,j;i<=n;ht[rk[i++]]=k) for (j=sa[rk[i]-1],k=k?k-1:k;a[i+k]==a[j+k];k++); } } int main() { scanf ( "%s" ,s+1),n= strlen (s+1); for ( int i=1;i<=n;i++) a[i]=s[i]- 'a' +1; using namespace SuffixArray; get_sa(a);get_ht(a); for ( int i=1;i<=n;i++) printf ( "%d%c" ,sa[i], " \n" [i==n]); // for(int i=1;i<=n;i++) cout<<rk[i]<<" ";cout<<endl; for ( int i=2;i<=n;i++) printf ( "%d%c" ,ht[i], " \n" [i==n]); return 0; } |
- Manacher O(n) 寻找最长回文串
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 | #include<cstdio> #include<cstring> #include<iostream> using namespace std; const int N = 1000005; int p[N]; char s[N]; char ch[N]; int Manacher( char s[]){ int l= strlen (s+1),mx=0,res=0,id=0; // cout<<l<<endl; memset (p,0, sizeof (p)); for ( int i=1;i<=l;i++){ if (mx>i) p[i]=min(p[id*2-i],mx-i); else p[i]=1; while (s[i+p[i]]==s[i-p[i]]) p[i]++; if (mx<i+p[i]) mx=i+p[i],id=i; } for ( int i=1;i<=l;i++) res=max(p[i],res); // for(int i=1;i<=l;i++) cout<<p[i]<<" ";cout<<endl; return res-1; } int main(){ cin>>(s+1);ch[0]= '$' ;ch[1]= '#' ; for ( int i=1;i<= strlen (s+1);i++) ch[i*2]=s[i],ch[i*2+1]= '#' ; // cout<<(ch+1)<<endl; cout<<Manacher(ch)<<endl; return 0; } |
- 后缀自动机(SAM) O(n)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 | #include<cstdio> #include<cstring> #include<iostream> using namespace std; const int N = 250005; struct State{ State *par,*go[26]; int val; State( int _val):par(0),val(_val){ memset (go,0, sizeof (go)); } }*rt,*lst; void extend( int w){ State *p=lst,*np= new State(p->val+1); while (p && p->go[w]==0) p->go[w]=np,p=p->par; if (!p) np->par=rt; else { State *q=p->go[w]; if (q->val == p->val+1) np->par=q; else { State *nq= new State(p->val+1); memcpy (nq->go,q->go, sizeof (q->go)); nq->par=q->par; np->par=q->par=nq; while (p && p->go[w]==q) p->go[w]=nq,p=p->par; } }lst=np; } int main(){ rt= new State(0),lst=rt; } |
数据结构
- Treap O(nlogn)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 | #include <bits/stdc++.h> using namespace std; #define debug(a) cout<<(#a)<<"="<<a<<" " #define lc(o) ch[o][0] #define rc(o) ch[o][1] #define uor(i,j,k) for(int i=j;i<=(int)k;i++) #define uep(i,j,k) for(int i=j;i<(int)k;i++) #define dor(i,j,k) for(int i=j;i>=(int)k;i--) typedef long long ll; typedef pair< int , int > pr; typedef vector< int > vi; typedef vector<ll> vl; typedef vector<string> vs; const int N = 100050; const int M = 25; const int oo = 0x3fffffff; const ll OO = 1e18; const ll p = 1000000007; ll Pow(ll a,ll b,ll r=1) { for (;b;b>>=1,a=a*a%p) if (b&1) r=r*a%p; return r; } ll Pow(ll a,ll b,ll p,ll r=1) { for (;b;b>>=1,a=a*a%p) if (b&1) r=r*a%p; return r; } ll inv(ll x) { return Pow(x,p-2); } void Add(ll &x,ll y) { x=(x+y%p)%p; } void Sub(ll &x,ll y) { x=(x-y%p+p)%p; } void Mul(ll &x,ll y) { x=x*(y%p)%p; } int chkmax(ll &x,ll y) { return x<y?x=y,1:0; } int chkmin(ll &x,ll y) { return x>y?x=y,1:0; } inline ll in(ll x=0, char ch= getchar (), int v=1) { while (ch> '9' || ch< '0' ) v=ch== '-' ?-1:v,ch= getchar (); while (ch>= '0' && ch<= '9' ) x=x*10+ch- '0' ,ch= getchar (); return x*v; } /*end*/ namespace Treap { int cp,rt; int sz[N],ss[N],ch[N][2],f[N],rv[N]; int val[N]; int Newnode( int v) { ++cp,ss[cp]=sz[cp]=1,f[cp]=lc(cp)=rc(cp)=0,val[cp]=v,rv[cp]= rand (); return cp; } void init() { rt=0,rv[0]=-oo; } void Update( int o) { sz[o]=sz[lc(o)]+sz[rc(o)]+ss[o]; } void Rot( int &o, int d) { int t=ch[o][d];ch[o][d]=ch[t][d^1],ch[t][d^1]=o,Update(o),Update(t),o=t; } void insert( int &o, int v) { if (!o) { o=Newnode(v); return ; } if (val[o]==v) { ss[o]++,Update(o); return ; } int d=v>val[o]; insert(ch[o][d],v); if (rv[ch[o][d]]>rv[o]) Rot(o,d); else Update(o); } void earse( int &o, int v) { if (val[o]==v) { if (ss[o]>1) { ss[o]--,Update(o); return ; } int d=rv[lc(o)]<rv[rc(o)]; if (!ch[o][d]) { o=0; return ; } Rot(o,d),earse(ch[o][d^1],v); } else earse(ch[o][v>val[o]],v); Update(o); } int rk( int o, int v) { if (val[o]<v) return sz[lc(o)]+ss[o]+rk(rc(o),v); else if (val[o]>v) return rk(lc(o),v); else return sz[lc(o)]; } int kth( int o, int k) { if (sz[lc(o)]>=k) return kth(lc(o),k); else if (sz[lc(o)]+ss[o]<k) return kth(rc(o),k-sz[lc(o)]-ss[o]); else return val[o]; } int pre( int o, int v) { if (!o) return -oo; if (val[o]>=v) return pre(lc(o),v); else return max(val[o],pre(rc(o),v)); } int nxt( int o, int v) { if (!o) return oo; if (val[o]<=v) return nxt(rc(o),v); else return min(val[o],nxt(lc(o),v)); } void insert( int v) { insert(rt,v); } void earse( int v) { earse(rt,v); } int rk( int v) { return rk(rt,v); } int kth( int k) { return kth(rt,k); } int pre( int v) { return pre(rt,v); } int nxt( int v) { return nxt(rt,v); } }; int main() { Treap::init(); for ( int T=in();T--;) { int opt=in(),x=in(); switch (opt) { case 1:Treap::insert(x); break ; case 2:Treap::earse(x); break ; case 3: printf ( "%d\n" ,Treap::rk(x)+1); break ; case 4: printf ( "%d\n" ,Treap::kth(x)); break ; case 5: printf ( "%d\n" ,Treap::pre(x)); break ; case 6: printf ( "%d\n" ,Treap::nxt(x)); break ; } } return 0; } |
- Splay O(nlogn)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 | #include <bits/stdc++.h> using namespace std; typedef long long LL; const int N = 200050; inline LL in(LL x=0, char ch= getchar (), int v=1) { while (ch> '9' || ch< '0' ) v=ch== '-' ?-1:v,ch= getchar (); while (ch>= '0' && ch<= '9' ) x=x*10+ch- '0' ,ch= getchar (); return x*v; } int n,q,nw; LL a[N]; struct SplayTree { #define lc(o) ch[o][0] #define rc(o) ch[o][1] #define mid ((l+r)>>1) int cp,rt; LL sum[N],v[N],d[N],rev[N],sz[N],f[N],ch[N][2]; int NewNode() { ++cp; sum[cp]=v[cp]=d[cp]=rev[cp]=lc(cp)=rc(cp)=0; sz[cp]=1; return cp; } void Update( int o) { if (!o) return ; sz[o]=sz[lc(o)]+sz[rc(o)]+1; sum[o]=sum[lc(o)]+sum[rc(o)]+v[o]+d[o]*sz[o]; } void Push( int o) { if (!o) return ; Push(f[o]); if (rev[o]) { swap(lc(o),rc(o)); if (lc(o)) rev[lc(o)]^=1; if (rc(o)) rev[rc(o)]^=1; rev[o]=0; } if (d[o]) { if (lc(o)) d[lc(o)]+=d[o]; if (rc(o)) d[rc(o)]+=d[o]; v[o]+=d[o],d[o]=0; }Update(lc(o)),Update(rc(o)),Update(o); } void Pushdown( int o) { if (!o) return ; if (rev[o]) { swap(lc(o),rc(o)); if (lc(o)) rev[lc(o)]^=1; if (rc(o)) rev[rc(o)]^=1; rev[o]=0; } if (d[o]) { if (lc(o)) d[lc(o)]+=d[o]; if (rc(o)) d[rc(o)]+=d[o]; v[o]+=d[o],d[o]=0; }Update(lc(o)),Update(rc(o)),Update(o); } int Build( int l, int r) { if (l>r){ return 0; } int o=NewNode(); lc(o)=Build(l,mid-1); v[o]=a[nw++]; rc(o)=Build(mid+1,r); if (lc(o)) f[lc(o)]=o; if (rc(o)) f[rc(o)]=o; Update(o); return o; } void Build( int n) { rt=Build(1,n+2); } void Rot( int o) { int p=f[o],k=f[p],r=rc(p)==o; // Pushdown(k),Pushdown(p),Pushdown(o); if (k) ch[k][rc(k)==p]=o; f[p]=o,f[ch[o][r^1]]=p,f[o]=k; ch[p][r]=ch[o][r^1],ch[o][r^1]=p; Update(p),Update(o),Update(k); } void Splay( int o, int ff) { Push(o); for (;f[o]!=ff;) { int p=f[o],k=f[p]; if (k!=ff) Rot((rc(k)==p)==(rc(p)==o)?p:o); Rot(o); } Update(o); if (!ff) rt=o; } int Kth( int o, int k) { Pushdown(o); if (sz[lc(o)]>=k) return Kth(lc(o),k); else if (sz[lc(o)]+1==k) return o; else return Kth(rc(o),k-sz[lc(o)]-1); } LL Kthw( int o, int k) { Pushdown(o); if (sz[lc(o)]>=k) return Kthw(lc(o),k)+d[o]; else if (sz[lc(o)]+1==k) return v[o]+d[o]; else return Kthw(rc(o),k-sz[lc(o)]-1)+d[o]; } LL Kthw( int k) { return Kthw(rt,k+1); } void Add( int l, int r,LL w) { l++,r++; int L=Kth(rt,l-1),R=Kth(rt,r+1); Splay(L,0),Splay(R,L); d[lc(R)]+=w; Update(lc(R)),Update(R),Update(L); } void Insert( int x,LL w) { x++; int L=Kth(rt,x),R=Kth(rt,x+1); Splay(L,0),Splay(R,L); int np=NewNode();lc(R)=np,v[np]=w,f[np]=R; Update(np),Update(R),Update(L); } void Del( int l, int r) { l++,r++; int L=Kth(rt,l-1),R=Kth(rt,r+1); Splay(L,0),Splay(R,L); lc(R)=0,Update(R),Update(L); } LL Qur( int l, int r) { l++,r++; int L=Kth(rt,l-1),R=Kth(rt,r+1); Splay(L,0),Splay(R,L); return sum[lc(R)]; } void Rev( int l, int r) { l++,r++; int L=Kth(rt,l-1),R=Kth(rt,r+1); Splay(L,0),Splay(R,L); rev[lc(R)]^=1; } }py; int main() { n=in(); for ( int i=1;i<=n;i++) a[i]=in(); py.Build(n); char opt[20]; int l,r,k,x,v; for (q=in();q--;) { scanf ( "%s" ,opt); if (opt[0]== 'A' ) l=in(),r=in(),v=in(),py.Add(l,r,v); if (opt[0]== 'I' ) x=in(),v=in(),py.Insert(x,v); if (opt[0]== 'D' ) l=in(),r=in(),py.Del(l,r); if (opt[0]== 'Q' ) l=in(),r=in(), printf ( "%lld\n" ,py.Qur(l,r)); if (opt[0]== 'K' ) k=in(), printf ( "%lld\n" ,py.Kthw(k)); if (opt[0]== 'R' ) l=in(),r=in(),py.Rev(l,r); } return 0; } |
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