蒟蒻_WA自动机的模板库

更新日志

2019.2.16

  • 修复珂朵莉树代码中的错误
  • FFT板子更新为预处理单位复根的版本(多项式基本操作请移步多项式算法总结qwq)

2019.2.17

  • 新增NTT板子

2019.2.25

  • 新增替罪羊树板子

2019.3.6

  • 新增K-D Tree(2-D Tree) -> [简单题AC代码]
  • 更新高消板子
  • 更新LCT板子

2019.3.31

  • 新增Miller-Rabin素数判断
  • 新增Pollard-Rho大数分解

2019.4.4

  • 新增SAM板子

2019.4.22

  • 新增二维凸包
  • 新增笛卡尔树
  • 新增Manacher

2019.4.26

  • 新增毒瘤圆方树

2019.4.27

  • 新增广义圆方树

2019.7.18

  • 咕咕咕新增Johnson费用流
  • 预告:将有(?)封装的多项式全家桶

数学

线性筛

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inline void sieve(int n)
{
for (int i=2;i<=n;++i)
{
if (!v[i]) {v[i]=i;prime[++cnt]=i;}
for (int j=1;j<=cnt;++j)
{
if (prime[j]>v[i] || i*prime[j]>n) break;
v[i*prime[j]]=prime[j];
}
}
for (int i=1;i<=cnt;++i)
isprime[prime[i]]=true;
}

高斯消元

模板题【SDOI2006】异或方程组

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#include <cstdio>
#include <cmath>
#include <algorithm>

using std::fabs;
using std::swap;

const int maxn=1e3+10;
const double eps=1e-6;

inline int Gauss_Elimination(double (*A)[maxn],double* f,int n)
{
for (int i=1,c=1,j;i<=n;++i)
{
for (j=c;j<=n && fabs(A[j][i])<eps;++j);
if (j==n+1) continue;
for (int k=1;k<=n+1;++k) swap(A[c][k],A[j][k]);
for (int j=c+1;j<=n;++j)
if (fabs(A[j][i])>eps)
{
double t=A[j][i]/A[c][i];
for (int k=i;k<=n+1;++k)
A[j][k]-=t*A[c][k];
}
++c;
}
bool NoAnswer=false,InfAnswer=false;
for (int i=n;i;--i)
{
bool NoVariables=true;
for (int j=i;j<=n;++j)
if (fabs(A[i][j])>eps) NoVariables=false;
if (NoVariables)
if (fabs(A[i][n+1])>eps) NoAnswer=true; // 0=C,C!=0,无解
else InfAnswer=true; // 0=0,无穷多组解
else
{
for (int j=i+1;j<=n;++j) A[i][n+1]-=A[i][j]*f[j];
f[i]=A[i][n+1]/A[i][i];
}
}
if (NoAnswer) return -1; // 无解返回-1..
return !InfAnswer; //无穷多解返回0,有唯一解返回1.
}

int main()
{
static double A[maxn][maxn],f[maxn];
int n;
scanf("%d",&n);
for (int i=1;i<=n;++i)
for (int j=1;j<=n+1;++j)
scanf("%lf",&A[i][j]);
int result=Gauss_Elimination(A,f,n);
if (result^1) return printf("%d\n",result)&0;
for (int i=1;i<=n;++i) printf("x%d=%.2lf\n",i,f[i]);
}

三分

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inline double F(double x)
{
double f=0;
for (int i=n;~i;--i)
f=f*x+a[i];
return f;
}

int main()
{
double l,r;
scanf("%d%lf%lf",&n,&l,&r);
for (int i=n;~i;--i)
scanf("%lf",a+i);
while (l+eps<r)
{
double m1=l+(r-l)/3;
double m2=r-(r-l)/3;
if (F(m1)>F(m2)) r=m2;
else l=m1;
}
printf("%.5lf",l);
}

矩阵快速幂

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Matrix operator^ (ll k)
{
Matrix ans(n,m);
for (int i=1;i<=n;++i)
ans.a[i][i]=1;
Matrix t=*this;
for (;k;k>>=1)
{
if (k&1) ans=ans*t;
t=t*t;
}
return ans;
}

乘法逆元

线性递推

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inv[1]=1;
inv[i]=(p-p/i)*inv[p%i]%p;

阶乘逆元

$\text{inv}(i)=\text{inv}(i+1) \times(i+1)$

有理数取模

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inline ll pow(int a,int b,int mod)
{
ll ans=1ll;
for (;b;b>>=1)
{
if (b&1) ans=ans*a%mod;
a=(ll)a*a%mod;
}
return ans;
}

inline ll read()
{
char ch;
while (!isdigit(ch=getchar()));
ll x=ch-48;
while (isdigit(ch=getchar()))
x=(x*10+ch-48)%mod;
return x;
}

int main()
{
ll a,b;
a=read();b=read();
if (!b) return puts("Angry!"),0;
printf("%lld",(ll)a*pow(b,mod-2,mod)%mod);
}

Miller-Rabin

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int pr[]={2,3,5,7,11,13,17,19,23,29,31,37};

inline ll qpow(ll a,ll b,ll p)
{
ll ans=1%p;
for (;b;b>>=1)
{
if (b&1) ans=ans*a%p;
a=a*a%p;
}
return ans;
}

inline bool miller_rabin(int n)
{
if (n==1) return false;
for (int i=0;i<12;++i) if (n==pr[i]) return true;
int m=(n-1),k=0;
while (!(m&1)) m>>=1,++k;
for (int i=0;i<12 && pr[i]<n;++i)
{
ll x=qpow(pr[i],m,n),y=x;
for (int t=0;t<k;++t)
{
x=x*x%n;
if (x==1 && y!=1 && y!=n-1) return false;
y=x;
}
if (x!=1) return false;
}
return true;
}

Pollard-Rho

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#include <cstdio>
#include <ctime>
#include <cmath>
#include <random>
#include <chrono>

using std::abs;

std::mt19937_64 Rnd(std::chrono::steady_clock::now().time_since_epoch().count());

typedef long long ll;
typedef unsigned long long ull;

int pr[]={2,3,5,7,11,13,17,19,23,29,31,37};

inline ll gcd(ll a,ll b){return b==0?a:gcd(b,a%b);}

inline ll rnd(ll x){return (ll)(Rnd()%x+1);}

inline ll quick_pow(ll a,ll b,ll p)
{
ll ans=1%p;
for (;b;b>>=1)
{
if (b&1) ans=ans*a%p;
a=a*a%p;
}
return ans;
}

inline ll slow_mul(ull a,ll b,ll p)
{
ull ans=0;
for (;b;b>>=1)
{
if (b&1) ans=(ull)(ans+a);
if (ans>=p) ans-=p;
a=(ull)(a+a)%p;
if (a>=p) a-=p;
}
return ans;
}

inline bool miller_rabin(ll n)
{
if (n==1) return false;
for (int i=0;i<12;++i) if (n==pr[i]) return true;
if (n%2==0 || n%3==0 || n%5==0) return false;
ll m=(n-1),k=0;
while (!(m&1)) m>>=1,++k;
for (int i=0;i<12 && pr[i]<n;++i)
{
ll x=quick_pow(pr[i],m,n),y=x;
for (int t=0;t<k;++t)
{
x=slow_mul(x,x,n);
if (x==1 && y!=1 && y!=n-1) return false;
y=x;
}
if (x!=1) return false;
}
return true;
}

#define f(x) ((slow_mul(x,x,n)+c)%n)
inline ll rho(ll n)
{
if (!(n&1)) return 2;
if (n%3==0) return 3;
ll x=0,y=0,t=1,c=rnd(n-1),q=1;
for (int k=2;;k<<=1,y=x,q=1)
{
for (int i=1;i<k;++i)
{
x=f(x);
q=slow_mul(q,abs(x-y),n);
if (!(i&0x7f))
if ((t=gcd(q,n))>1) break;
}
if (t>1 || (t=gcd(q,n))>1) break;
}
return t;
}

ll max_p;

ll solve(ll n)
{
if (n==1) return 1;
if (miller_rabin(n)) return max_p=n>max_p?n:max_p;
ll t=n;
while (t==n) t=rho(n);
solve(n/t);solve(t);
return max_p;
}

int main()
{
freopen("pol.in","r",stdin);
freopen("pol.out","w",stdout);
int T;
scanf("%d",&T);
while (T--)
{
ll x;
scanf("%lld",&x);max_p=0;
ll ret=solve(x);
if (ret==x) puts("Prime");
else printf("%lld\n",ret);
}
fprintf(stderr,"%d",clock());
}

FFT

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#include <cstdio>
#include <cmath>

const double Pi=acos(-1.0);
const int maxn=2e6+100;

double q[maxn];
int limit=1,rev[maxn];

struct Complex
{
double real,imag;
Complex(double real,double imag):real(real),imag(imag){}
Complex(){}
Complex conj();
}w[maxn],winv[maxn],A[maxn];

inline Complex Complex::conj(){return Complex(real,-imag);}
inline Complex operator+(const Complex& a,const Complex& b){return Complex(a.real+b.real,a.imag+b.imag);}
inline Complex operator-(const Complex& a,const Complex& b){return Complex(a.real-b.real,a.imag-b.imag);}
inline Complex operator*(const Complex& a,const Complex& b){return Complex(a.real*b.real-a.imag*b.imag,a.real*b.imag+a.imag*b.real);}

template<typename T>
inline void swap(T& a,T& b){T t=a;a=b;b=t;}

inline void DFT(Complex* A,Complex* w,int limit)
{
for (int i=0;i<limit;++i)
if (i<rev[i]) swap(A[i],A[rev[i]]);
for (int mid=1;mid<limit;mid<<=1)
for (int R=mid<<1,j=0;j<limit;j+=R)
for (int k=0;k<mid;++k)
{
Complex x=A[j+k],y=w[limit/mid/2*k]*A[j+mid+k];
A[j+k]=x+y;
A[j+mid+k]=x-y;
}
}

inline void prework(int n)
{
int l=0;
while (limit<=(n<<1)+1) limit<<=1,++l;
for (int i=0;i<limit;++i)
rev[i]=(rev[i>>1]>>1)|((i&1)<<(l-1));
for (int i=0;i<limit;++i)
w[i]=Complex(cos(Pi*2/limit*i),sin(Pi*2/limit*i)),winv[i]=w[i].conj();
}

int main()
{
int n,m;
scanf("%d%d",&n,&m);
for (int i=0;i<=n;++i)
scanf("%lf",&A[i].real);
for (int i=0;i<=m;++i)
scanf("%lf",&A[i].imag);
prework(n>=m?n:m);
DFT(A,w,limit);
for (int i=0;i<limit;++i)
A[i]=A[i]*A[i];
DFT(A,winv,limit);
for (int i=0;i<=n+m;++i)
printf("%d ",(int)(A[i].imag/2/limit+0.1));
}

NTT

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inline int qpow(int a,int b,int p)
{
int ans=1%p;
for (;b;b>>=1,a=(ll)a*a%p)
if (b&1) ans=(ll)ans*a%p;
return ans;
}

inline void prework(int n,int m)
{
int l=0;
while (limit<=(n+m+1)) limit<<=1,++l;
w[0]=1;w[1]=qpow(g,(P-1)/limit,P),winv[0]=1,winv[1]=qpow(w[1],P-2,P);
for (int i=2;i<limit;++i)
w[i]=(ll)w[i-1]*w[1]%P,winv[i]=1ll*winv[i-1]*winv[1]%P;
for (int i=1;i<limit;++i)
rev[i]=(rev[i>>1]>>1)|((i&1)<<(l-1));
}

inline void NTT(int *A,int *w,int limit)
{
for (int i=0;i<limit;++i)
if (i<rev[i]) swap(A[i],A[rev[i]]);
for (int mid=1;mid<limit;mid<<=1)
for (int R=mid<<1,j=0;j<limit;j+=R)
for (int k=0;k<mid;++k)
{
int x=A[j+k],y=(ll)A[j+k+mid]*w[limit/2/mid*k]%P;
A[j+k]=(x+y)%P;A[j+mid+k]=(x-y+P)%P;
}
}

inline void DFT(int *A){ NTT(A,w,limit); }

inline void IDFT(int *A)
{
NTT(A,winv,limit);
int inv=qpow(limit,P-2,P);
for (int i=0;i<=limit;++i)
A[i]=((ll)A[i]*inv)%P;
}

计算几何

二维凸包

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#include <cstdio>
#include <cmath>
#include <algorithm>

using std::sort;
using std::sqrt;

const int maxn=1e5+100;

struct Point
{
double x,y;
Point(double x,double y):x(x),y(y){}
Point(){}
bool operator< (const Point& p) const{return x==p.x?y<p.y:x<p.x;}
Point operator- (const Point& p){return Point(x-p.x,y-p.y);}
double operator* (const Point& p){return x*p.x+y*p.y;}
}p[maxn];

typedef Point Vector;

inline double dis(const Point& a,const Point& b){return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));}

inline double cross(const Vector& a,const Vector& b){return a.x*b.y-b.x*a.y;}

int main()
{
int n;
scanf("%d",&n);
for (int i=1;i<=n;++i)
scanf("%lf%lf",&p[i].x,&p[i].y);
sort(p+1,p+n+1);
static int stack[maxn];
int top=0;
stack[++top]=1;
bool used[maxn];
for (int i=2;i<=n;++i)
{
while (top>1 && cross(p[stack[top]]-p[stack[top-1]],p[i]-p[stack[top]])<=0) used[stack[top--]]=false;
stack[++top]=i;
used[i]=true;
}
int prec=top;
for (int i=n;i;--i)
if (!used[i])
{
while (top>prec && cross(p[stack[top]]-p[stack[top-1]],p[i]-p[stack[top]])<=0) used[stack[top--]]=false;
stack[++top]=i;
used[i]=true;
}
double ans=0;
for (int i=2;i<=top;++i)
ans+=dis(p[stack[i]],p[stack[i-1]]);
printf("%.2lf",ans);
}

字符串

Manacher

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#include <cstdio>
#include <cstring>

const int maxn=3e7+10;

char buf[maxn],s[maxn];
int f[maxn];

template<class T>inline T min(T a,T b){return a<b?a:b;}
template<class T>inline T max(T a,T b){return a<b?b:a;}

inline void manacher(int n)
{
int maxright=0,mid=0;
for (int i=1;i<n;++i)
{
if (i<maxright) f[i]=min(f[(mid<<1)-i],f[mid]+mid-i);
else f[i]=1;
while (s[i+f[i]]==s[i-f[i]]) ++f[i];
if (i+f[i]>maxright) maxright=i+f[i],mid=i;
}
}

int main()
{
int n;
scanf("%s",buf);
n=strlen(buf);
s[0]=s[1]='@';
for (int i=0;i<n;++i)
s[(i<<1)+2]=buf[i],s[(i<<1)+3]='@';
n=n*2+2;s[n]=0;
manacher(n);
int ans=0;
for (int i=0;i<n;++i)
ans=max(ans,f[i]);
printf("%d",ans-1);
}

制胡窜哈希

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inline void hs1(char* s)
{
pw1[0]=1;hsh1[0]=s[0];
for (int i=1;i<n;++i)
{
pw1[i]=(ll)pw1[i-1]*seed%mod1;
hsh1[i]=((ll)hsh1[i-1]*seed+s[i])%mod1;
}
}

inline void hs2(char* s)
{
pw2[0]=1;hsh2[0]=s[0];
for (int i=1;i<n;++i)
{
pw2[i]=(ll)pw2[i-1]*seed%mod2;
hsh2[i]=((ll)hsh2[i-1]*seed+s[i])%mod2;
}
}

inline pair<int,int> gethash(int l,int r)
{
int t1=((hsh1[r]-(ll)hsh1[l-1]*pw1[r-l+1]%mod1)+mod1)%mod1;
int t2=((hsh2[r]-(ll)hsh2[l-1]*pw2[r-l+1]%mod2)+mod2)%mod2;
return make_pair(t1,t2);
}

KMP

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inline void getfail(int n)
{
for (int i=1,j;i<n;++i)
{
j=f[i];
while (j && P[j]!=P[i]) j=f[j];
f[i+1]=P[i]==P[j]?j+1:0;
}
}

inline void kmp(int n,int m)
{
for (int i=0,j=0;i<n;++i)
{
while (j && T[i]!=P[j]) j=f[j];
if (T[i]==P[j]) ++j;
if (j==m) printf("%d\n",i-m+2);
}
}

AC自动机

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void add(const char* s)
{
int n=strlen(s),u=0;
for (int i=0;i<n;++i)
{
int c=idx(s[i]);
if (!ch[u][c]) ch[u][c]=++cnt;
u=ch[u][c];
}
++tag[u];
}

void getfail()
{
queue<int> q;
for (int i=0;i<26;++i)
if (ch[0][i]) q.push(ch[0][i]);
while (!q.empty())
{
int u=q.front();q.pop();
for (int i=0;i<26;++i)
{
int c=ch[u][i];
if (!c) {ch[u][i]=ch[f[u]][i];continue;}
q.push(c);
int v=f[u];
while (v && !ch[v][i]) v=f[v];
f[c]=ch[v][i];
last[c]=tag[f[c]]?f[c]:last[f[c]];
}
}
}

int get(const char *s)
{
int n=strlen(s);
int x=0,ret=0;
for(int i=0;i<n;++i)
{
x=ch[x][idx(s[i])];
for(int j=x;j;j=last[j])
if(!vis[j])vis[j]=1,ret+=tag[j];
}
return ret;
}

SA

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inline void build_sa(int n,int m)
{
int *x=t1,*y=t2;
for (int i=0;i<m;++i) c[i]=0;
for (int i=0;i<n;++i) c[x[i]=s[i]]++;
for (int i=1;i<m;++i) c[i]+=c[i-1];
for (int i=n-1;~i;--i) sa[--c[x[i]]]=i;
for (int k=1,p=1;k<=n && p<n;k<<=1,m=p)
{
p=0;
for (int i=n-k;i<n;++i) y[p++]=i;
for (int i=0;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=0;i<n;++i) c[t3[i]=x[y[i]]]++;
for (int i=1;i<m;++i) c[i]+=c[i-1];
for (int i=n-1;~i;--i) sa[--c[t3[i]]]=y[i];
p=1;swap(x,y);x[sa[0]]=0;
for (register int i=1;i<n;++i)
x[sa[i]]=(y[sa[i]+k]==y[sa[i-1]+k] && y[sa[i]]==y[sa[i-1]])?p-1:p++;
}
}

inline void get_height(int n)
{
int k=0,j=0;
for (int i=0;i<=n;++i) rank[sa[i]]=i;
for (int i=0;i<n;height[rank[i++]]=k)
for (k?--k:0,j=sa[rank[i]-1];s[j+k]==s[i+k];++k);
}

SAM

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#include <cstdio>
#include <cstring>

const int maxn=2e6+1000;

int tr[maxn][26],parent[maxn],mx[maxn],right[maxn],cnt=1,last=1;

inline void radixsort(int n)
{
static int c[maxn],id[maxn];
for (int i=1;i<=cnt;++i) ++c[mx[i]];
for (int i=1;i<=n;++i) c[i]+=c[i-1];
for (int i=cnt;i;--i) id[--c[mx[i]]]=i;
for (int i=cnt-1;~i;--i) right[parent[id[i]]]+=right[id[i]];
}

inline void insert(int x)
{
int p=last,np=last=++cnt;
right[np]=1;mx[np]=mx[p]+1;
while (p && !tr[p][x]) tr[p][x]=np,p=parent[p];
if (!p) parent[np]=1;
else
{
int q=tr[p][x];
if (mx[q]==mx[p]+1) parent[np]=q;
else
{
int nq=++cnt;
mx[nq]=mx[p]+1;
memcpy(tr[nq],tr[q],sizeof(tr[q]));
while (p && tr[p][x]==q) tr[p][x]=nq,p=parent[p];
parent[nq]=parent[q];parent[q]=parent[np]=nq;
}
}
}

int main()
{
int n;
static char s[maxn];
scanf("%s",s);
n=strlen(s);
for (int i=0;i<n;++i) insert(s[i]-'a');
radixsort(n);
int ans=0;
for (int i=1;i<=cnt;++i) if (right[i]>1 && right[i]*mx[i]>ans) ans=right[i]*mx[i];
printf("%d\n",ans);
}

图论

广义圆方树(APIO2018 铁人两项)

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#include <cstdio>
#include <vector>
#include <algorithm>

using std::vector;

const int maxn=2e6+100;

vector<int> G[maxn],T[maxn];
int dfn[maxn],low[maxn],dfc,tot,cnt,val[maxn],siz[maxn];

template<class T>inline T max(T a,T b){return a<b?b:a;}
template<class T>inline T min(T a,T b){return a<b?a:b;}
template<class T>inline void swap(T& a,T& b){a^=b^=a^=b;}

inline void tarjan(int u,int ff)
{
static int stack[maxn],top=0;
dfn[u]=low[u]=++dfc;
stack[++top]=u;
++cnt;val[u]=-1;
for (auto v:G[u])
{
if (v==ff) continue;
if (!dfn[v])
{
tarjan(v,u);
low[u]=min(low[u],low[v]);
if (low[v]>=dfn[u])
{
++tot;
int x;
do
{
x=stack[top--];
++val[tot];
T[x].push_back(tot);
T[tot].push_back(x);
} while (x!=v);
T[u].push_back(tot);
T[tot].push_back(u);
++val[tot];
}
}
else low[u]=min(low[u],dfn[v]);
}
}

inline int64_t calc(int u,int ff,int n,int N)
{
int64_t ans=0;
siz[u]=(u<=N);
for (auto v:T[u])
{
if (v==ff) continue;
ans+=calc(v,u,n,N);
ans+=(int64_t)siz[u]*siz[v]*val[u];
siz[u]+=siz[v];
}
ans+=(int64_t)siz[u]*(n-siz[u])*val[u];
return ans;
}

int main()
{
int n,m;
scanf("%d%d",&n,&m);
tot=n;
for (int i=1,u,v;i<=m;++i)
scanf("%d%d",&u,&v),G[u].push_back(v),G[v].push_back(u);
int64_t ans=0;
for (int i=1;i<=n;++i)
if (!dfn[i])
{
cnt=0;
tarjan(i,0);
ans+=calc(i,0,cnt,n);
}
printf("%lld\n",ans*2);
}

静态仙人掌(圆方树)

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#include <cstdio>
#include <algorithm>

const int maxn=3e4+1200;

struct Graph
{
struct Edge
{
int to,next,w;
}edge[maxn<<1];
int head[maxn],cnt;

inline void _add(int u,int v,int w)
{
edge[++cnt].next=head[u];
edge[cnt].to=v;
edge[cnt].w=w;
head[u]=cnt;
}
inline void add(int u,int v,int w){_add(u,v,w);_add(v,u,w);}
}G,T;

int dfn[maxn],low[maxn],tot,dfc;
int fa[maxn],val[maxn],sum[maxn];

template<class T>inline T min(T a,T b){return a<b?a:b;}
template<class T>inline T max(T a,T b){return a<b?b:a;}
template<class T>inline void swap(T &a,T &b){a^=b^=a^=b;}

inline void build(int u,int v,int w)
{
++tot;
int s=w;
for (int x=v;x!=fa[u];x=fa[x])
sum[x]=s,s+=val[x];
sum[tot]=sum[u];
sum[u]=0;
for (int x=v;x!=fa[u];x=fa[x])
{
int sp=min(sum[x],sum[tot]-sum[x]);
T.add(x,tot,sp);
}
}

inline void tarjan(int u,int ff)
{
dfn[u]=low[u]=++dfc;
for (int i=G.head[u];i;i=G.edge[i].next)
{
int v=G.edge[i].to;
if (v==ff) continue;
if (!dfn[v])
{
fa[v]=u;
val[v]=G.edge[i].w;
tarjan(v,u);
low[u]=min(low[u],low[v]);
}
else low[u]=min(low[u],dfn[v]);
if (low[v]<=dfn[u]) continue;
T.add(u,v,G.edge[i].w);
}
for (int i=G.head[u];i;i=G.edge[i].next)
{
int v=G.edge[i].to;
if (fa[v]!=u && dfn[v]>dfn[u])
build(u,v,G.edge[i].w);
}
}

int depth[maxn],siz[maxn],top[maxn],son[maxn],dis[maxn];

inline void dfs(int u,int ff,int dep,int di)
{
depth[u]=dep;
dis[u]=di;
fa[u]=ff;
int maxs=-1;
siz[u]=1;
for (int i=T.head[u];i;i=T.edge[i].next)
{
int v=T.edge[i].to;
if (v!=ff)
{
dfs(v,u,dep+1,di+T.edge[i].w);
siz[u]+=siz[v];
if (siz[v]>maxs) maxs=siz[v],son[u]=v;
}
}
}

inline void dfs(int u,int topf)
{
top[u]=topf;
if (!son[u]) return;
dfs(son[u],topf);
for (int i=T.head[u];i;i=T.edge[i].next)
{
int v=T.edge[i].to;
if (v!=fa[u] && v!=son[u])
dfs(v,v);
}
}

inline int LCA(int u,int v)
{
while (top[u]!=top[v])
{
if (depth[top[u]]<depth[top[v]]) swap(u,v);
u=fa[top[u]];
}
return depth[u]>depth[v]?v:u;
}

inline int find(int u,int lca)
{
int res=son[lca];
while (top[u]!=top[lca])
res=top[u],u=fa[top[u]];
return u==lca?res:son[lca];
}

inline int query(int u,int v,int n)
{
int lca=LCA(u,v);
if (lca<=n) return dis[u]+dis[v]-2*dis[lca];
int x=find(u,lca),y=find(v,lca);
int ans=dis[u]+dis[v]-dis[x]-dis[y];
if (sum[x]<sum[y]) swap(x,y);
ans+=min(sum[x]-sum[y],sum[lca]-sum[x]+sum[y]);
return ans;
}

int main()
{
int n,m,q;
scanf("%d%d%d",&n,&m,&q);
for (int i=1,u,v,w;i<=m;++i)
scanf("%d%d%d",&u,&v,&w),G.add(u,v,w);
tot=n;
tarjan(1,0);
dfs(1,0,1,0);
dfs(1,1);
for (int i=1,u,v;i<=q;++i)
{
scanf("%d%d",&u,&v);
printf("%d\n",query(u,v,n));
}
}

Kruskal

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struct Edge
{
int u,v,w;
bool operator< (const Edge& e) const {return w<e.w;}
}edge[maxn];
int fa[maxn],cnt;

inline int find(int x){return x==fa[x]?x:fa[x]=find(fa[x]);}

inline int kruskal(int m)
{
int ans=0;
std::sort(edge+1,edge+m+1);
for (int i=1;i<=m;++i)
{
int u=edge[i].u,v=edge[i].v,w=edge[i].w;
if (find(u)!=find(v))
++cnt,fa[find(u)]=find(v),ans+=w;
}
return ans;
}

LCA

树剖

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void dfs(int u,int f,int dep)
{
depth[u]=dep;
fa[u]=f;
siz[u]=1;
int maxs=-1;
for (int i=head[u];i;i=edge[i].next)
{
int v=edge[i].to;
if (v!=f)
{
dfs(v,u,dep+1);
siz[u]+=siz[v];
if (siz[v]>=maxs) maxs=siz[v],son[u]=v;
}
}
}

void dfs(int u,int topf)
{
top[u]=topf;
if (!son[u]) return;
dfs(son[u],topf);
for (int i=head[u];i;i=edge[i].next)
{
int v=edge[i].to;
if (v!=fa[u] && v!=son[u]) dfs(v,v);
}
}

int lca(int u,int v)
{
while (top[u]!=top[v])
{
if (depth[top[u]]<depth[top[v]]) swap(u,v);
u=fa[top[u]];
}
if (depth[u]>depth[v]) swap(u,v);
return u;
}

倍增

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inline void dfs(int u,int fa,int dep)
{
f[u][0]=fa;
depth[u]=dep;
for (int i=1;(1<<i)<=n;++i)
f[u][i]=f[f[u][i-1]][i-1];
for (int i=head[u];i;i=edge[i].next)
{
int v=edge[i].to;
if (v!=fa) dfs(v,u,dep+1);
}
}

inline int lca(int u,int v)
{
if (depth[u]<depth[v]) swap(u,v);
int l=depth[u]-depth[v];
for (int i=0;(1<<i)<=l;++i)
if (l&(1<<i)) u=f[u][i];
if (u==v) return u;
for (int i=22;i>=0;--i)
if (f[u][i]!=f[v][i])
u=f[u][i],v=f[v][i];
return f[u][0];
}

DFS序转RMQ

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inline int Min(int x,int y){return depth[x]<depth[y]?x:y;}

void dfs(int u,int f,int dep)
{
fa[u]=f;
dfn[++tot]=u;
pre[u]=tot;
depth[tot]=dep;
for (int i=head[u];i;i=edge[i].next)
{
int v=edge[i].to;
if (v!=f)
{
dfs(v,u,dep+1);
dfn[++tot]=u;
depth[tot]=dep;
}
}
}

inline void rmq_init()
{
for (int i=1;i<=tot;++i) st[i][0]=i;
for (int j=1;(1<<j)<=tot;++j)
for (int i=1;i+(1<<j)-1<=tot;++i)
st[i][j]=Min(st[i][j-1],st[i+(1<<(j-1))][j-1]);
}

inline int rmq(int L,int R)
{
int k=0;
while ((1<<(k+1))<=R-L+1) ++k;
return Min(st[L][k],st[R-(1<<k)+1][k]);
}

inline int lca(int x,int y)
{
x=pre[x];y=pre[y];
if (x>y) swap(x,y);
return dfn[rmq(x,y)];
}

Tarjan

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inline int find(int x){ return x==fa[x]?x:fa[x]=find(fa[x]);}

void dfs(int u,int f)
{
fa[u]=u;
for (int i=head[u];i;i=edge[i].next)
{
int v=edge[i].to;
if (v!=f) dfs(v,u),fa[v]=u;
}
for (int i=query_head[u];~i;i=query[i].next)
{
int v=query[i].v;
if (vis[v]) query[i].ans=query[i^1].ans=find(v);
}
vis[u]=true;
}

单源最短路径

Dijkstra

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void Dijkstra(int s)
{
memset(d,0x3f,sizeof(d));
std::priority_queue<Node> q;
d[s]=0;
q.push(Node(s,0));
while (!q.empty())
{
int u=q.top().u,di=q.top().dis;q.pop();
if (di!=d[u]) continue;
for (int i=head[u];i;i=edge[i].next)
{
int v=edge[i].to;
if (d[v]>d[u]+edge[i].w)
{
d[v]=d[u]+edge[i].w;
q.push(Node(v,d[v]));
}
}
}
}

SPFA

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void spfa()
{
d[s]=0;
vis[s]=1;
queue<int> q;
q.push(s);
while (!q.empty())
{
int u=q.front(); q.pop();vis[u]=false;
for (int i=head[u];i;i=edges[i].next)
{
Edge& e=edges[i];
if (d[e.to]>d[u]+e.w)
{
d[e.to]=d[u]+e.w;
if (!vis[e.to]) q.push(e.to),vis[e.to]=true;
}
}
}
}

网络流

Dinic最大流

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bool bfs()
{
queue<int> q;
q.push(s);
memset(depth,0,sizeof(depth));
depth[s]=1;
while (!q.empty())
{
int u=q.front();q.pop();
for (int i=head[u];~i;i=edge[i].next)
{
int v=edge[i].to;
if (!depth[v] && edge[i].w>0)
depth[v]=depth[u]+1,q.push(v);
}
}
return depth[t]>0;
}

int dfs(int u,int flow)
{
if (u==t) return flow;
for (int &i=cur[u];~i;i=edge[i].next)
{
int v=edge[i].to;
if (depth[v]==depth[u]+1 && edge[i].w>0)
{
int d=dfs(v,min(flow,edge[i].w));
if (d>0)
{
edge[i].w-=d;
edge[i^1].w+=d;
return d;
}
}
}
return 0;
}

int dinic(int n)
{
int ans=0;
while (bfs())
{
memcpy(cur,head,sizeof(cur));
while (int d=dfs(s,INF)) ans+=d;
}
return ans;
}

Johnson费用流(Dijkstra)

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#include <cstdio>
#include <cstring>
#include <queue>

using std::priority_queue;

const int maxn=5e4+1000;
const int INF=0x3f3f3f3f;

struct Edge
{
int to,next,flow,cost;
}edge[maxn];

struct Node
{
int u,dis;
Node(int u,int dis):u(u),dis(dis){}
bool operator< (const Node& nd){return dis>nd.dis;}
};

int head[maxn],cnt=-1;

inline void _add(int u,int v,int w,int c)
{
edge[++cnt].next=head[u];
edge[cnt].to=v;
edge[cnt].flow=w;
edge[cnt].cost=c;
head[u]=cnt;
}

inline void add(int u,int v,int w,int c){_add(u,v,w,c);_add(v,u,0,-c);}

template<class T>inline T min(T a,T b){return a<b?a:b;}
template<class T>inline T max(T a,T b){return a<b?b:a;}

int dis[maxn],minflow[maxn],pre[maxn],h[maxn];

inline bool Dijkstra(int S,int T,int &mc,int &mf,int n)
{
memset(dis,0x3f,sizeof(dis));
dis[S]=0;pre[S]=-1;minflow[S]=INF;
priority_queue<Node> q;
q.push(Node(S,0));
while (!q.empty())
{
int u=q.top().u,d=q.top().dis;q.pop();
if (dis[u]<d) continue;
for (int i=head[u];~i;i=edge[i].next)
{
if (edge[i].flow==0) continue;
int v=edge[i].to,w=edge[i].cost+h[u]-h[v];
if (dis[v]>d+w)
{
dis[v]=d+w,q.push(Node(v,dis[v]));
pre[v]=i;minflow[v]=min(minflow[u],edge[i].flow);
}
}
}
if (dis[T]==INF) return 0;
for (int i=1;i<=n;++i)
if (dis[i]<INF) h[i]+=dis[i];
int c=minflow[T];
mf+=c;mc+=c*h[T];
for (int u=T;~pre[u];u=edge[pre[u]^1].to)
edge[pre[u]].flow-=c,edge[pre[u]^1].flow+=c;
// printf("%d %d\n",mc,mf);
return 1;
}

inline void mcmf(int S,int T,int n)
{
int mc=0,mf=0;
while (Dijkstra(S,T,mc,mf,n));
printf("%d %d\n",mf,mc);
}

int main()
{
int n,m,S,T;
scanf("%d%d%d%d",&n,&m,&S,&T);
memset(head,-1,sizeof(int)*(n+1));
for (int i=1,u,v,w,f;i<=m;++i)
scanf("%d%d%d%d",&u,&v,&w,&f),add(u,v,w,f);
mcmf(S,T,n);
}

Edmonds-Karp费用流

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inline bool spfa()
{
static int vis[maxn];
queue<int> q;
q.push(s);
memset(vis,0,sizeof(vis));
memset(d,0x3f,sizeof(d));
d[s]=0;vis[s]=true;
while (!q.empty())
{
int u=q.front();q.pop();
vis[u]=false;
for (int i=head[u];~i;i=edge[i].next)
{
int v=edge[i].to;
if (edge[i].flow>0 && d[v]>d[u]+edge[i].cost)
{
d[v]=d[u]+edge[i].cost;
incf[v]=edge[i].flow;
inedge[v]=i;
pre[v]=u;
if (!vis[v]) vis[v]=true,q.push(v);
}
}
}
return d[t]<inf;
}

inline void mcmf()
{
int flow=0,cost=0;
while (spfa())
{
int u=t,mn=inf;
for (int i=t;i!=s;i=pre[i])
mn=min(mn,incf[i]);
for (int i=t;i!=s;i=pre[i])
{
edge[inedge[i]].flow-=mn;
edge[inedge[i]^1].flow+=mn;
}
cost+=d[t]*mn;
flow+=mn;
}
printf("%d %d",flow,cost);
}

割点

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inline void tarjan(int u,int rt)
{
int chd=0;
dfn[u]=low[u]=++idx;
for (int i=head[u];i;i=edge[i].next)
{
int v=edge[i].to;
if (!dfn[v])
{
tarjan(v,rt);
low[u]=min(low[u],low[v]);
if (low[v]>=dfn[u])
{
++chd;
if (chd>1 || u!=rt)
iscut[u]=true;
}
}
else low[u]=min(low[u],dfn[v]);
}
}

Tarjan缩点

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struct Graph
{
int head[maxn],cnt;
Edge edge[maxm];
inline void add(int u,int v)
{
edge[++cnt].next=head[u];
edge[cnt].to=v;
head[u]=cnt;
}
}old,dag;

void tarjan(int u)
{
dfn[u]=low[u]=++idx;
stk[++top]=u;
instack[u]=true;
for (int i=old.head[u];i;i=old.edge[i].next)
{
int v=old.edge[i].to;
if (!dfn[v])
{
tarjan(v);
low[u]=min(low[u],low[v]);
}
else if (instack[v]) low[u]=min(low[u],dfn[v]);
}
if (dfn[u]==low[u])
{
int v;
++scc_cnt;
do
{
v=stk[top--];
belong[v]=scc_cnt;
w[scc_cnt]+=val[v];
instack[v]=false;
}while (v!=u);
}
}

inline void rebuild(int n)
{
for (int u=1;u<=n;++u)
for (int i=old.head[u];i;i=old.edge[i].next)
if (belong[u]!=belong[old.edge[i].to])
dag.add(belong[u],belong[old.edge[i].to]);
}

inline void work(int n)
{
for (int i=1;i<=n;++i)
if (!dfn[i]) tarjan(i);
}

2-SAT

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inline void tarjan(int u)
{
dfn[u]=low[u]=++idx;
instack[u]=true;
stk[++top]=u;
for (int i=head[u];i;i=edge[i].next)
{
int v=edge[i].to;
if (instack[v]) low[u]=min(low[u],dfn[v]);
else if (!dfn[v])
tarjan(v),low[u]=min(low[u],low[v]);
}
if (dfn[u]==low[u])
{
int v;++scc_cnt;
do
{
v=stk[top--];
belong[v]=scc_cnt;
instack[v]=false;
}while (v!=u);
}
}

inline bool twosat(int n)
{
for (int i=1;i<=n<<1;++i)
if (!dfn[i]) tarjan(i);
for (int i=1;i<=n;++i)
if (belong[i]==belong[i+n]) return false;
return true;
}

数据结构

ST表

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inline void prework(int n)
{
for (rint j=1;(1<<j)<=n;++j)
for (rint i=1;(i+(1<<j)-1)<=n;++i)
d[i][j]=max(d[i][j-1],d[i+(1<<(j-1))][j-1]);
}

inline int query(int i,int j)
{
int k=0,len=j-i+1;
while (1<<(k+1)<=len)++k;
return max(d[i][k],d[j-(1<<k)+1][k]);
}

线段树2

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void build(int l,int r,int o)
{
mul[o]=1;
if (l==r)
{
scanf("%lld",sumv+o);
return;
}
int m=(l+r)>>1;
build(ls);build(rs);
pushup(o);
}

inline void pushdown(int o,int len)
{
sumv[o<<1]=(sumv[o<<1]*mul[o]+addv[o]*(len-(len>>1)))%p;
sumv[o<<1|1]=(sumv[o<<1|1]*mul[o]+addv[o]*(len>>1))%p;
mul[o<<1]=mul[o<<1]*mul[o]%p;
mul[o<<1|1]=mul[o<<1|1]*mul[o]%p;
addv[o<<1]=(addv[o<<1]*mul[o]+addv[o])%p;
addv[o<<1|1]=(addv[o<<1|1]*mul[o]+addv[o])%p;
addv[o]=0;mul[o]=1;
}

void multiplicate(int L,int R,int c,int l,int r,int o)
{
if (L<=l && R>=r)
{
mul[o]=mul[o]*c%p;
addv[o]=addv[o]*c%p;
sumv[o]=sumv[o]*c%p;
return;
}
pushdown(o,r-l+1);
int m=(l+r)>>1;
if (L<=m) multiplicate(L,R,c,ls);
if (R>m) multiplicate(L,R,c,rs);
pushup(o);
}

void add(int L,int R,int c,int l,int r,int o)
{
if (L<=l && R>=r)
{
addv[o]=(addv[o]+c)%p;
sumv[o]=(sumv[o]+c*(r-l+1))%p;
return;
}
pushdown(o,r-l+1);
int m=(l+r)>>1;
if (L<=m) add(L,R,c,ls);
if (R>m) add(L,R,c,rs);
pushup(o);
}

long long Querysum(int L,int R,int l,int r,int o)
{
if (L<=l && R>=r) return sumv[o]%p;
pushdown(o,r-l+1);
int m=(l+r)>>1;
long long tot=0;
if (L<=m) tot=(tot+Querysum(L,R,ls))%p;
if (R>m) tot=(tot+Querysum(L,R,rs))%p;
pushup(o);
return tot;
}

左偏树

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inline int merge(int x,int y)
{
if (!x || !y) return x+y;
if (val[x]>val[y] || (val[x]==val[y] && x>y))
swap(x,y);
rs(x)=merge(rs(x),y);
fa[rs(x)]=x;
if (dis[rs(x)]>dis[ls(x)]) swap(ls(x),rs(x));
dis[x]=dis[rs(x)]+1;
return x;
}

inline int findroot(int x)
{
while (fa[x]) x=fa[x];
return x;
}

inline int pop(int x)
{
int ret=val[x];
fa[ls(x)]=fa[rs(x)]=0;
val[x]=-1;
merge(ls(x),rs(x));
ls(x)=rs(x)=0;
return ret;
}

主席树

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inline void insert(int x,int &rt,int oldrt,int l,int r)
{
rt=++num;
tree[rt]=tree[oldrt];
++tree[rt].sumv;
if (l==r) return;
int m=(l+r)>>1;
if (x<=m) insert(x,tree[rt].ls,tree[oldrt].ls,l,m);
else insert(x,tree[rt].rs,tree[oldrt].rs,m+1,r);
}

inline int query(int x,int lrt,int rrt,int l,int r)
{
if (l==r) return l;
int m=(l+r)>>1;
int k=tree[tree[rrt].ls].sumv-tree[tree[lrt].ls].sumv;
if (x<=k) return query(x,tree[lrt].ls,tree[rrt].ls,l,m);
else return query(x-k,tree[lrt].rs,tree[rrt].rs,m+1,r);
}

CDQ分治(三维偏序)

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#include <cstdio>
#include <algorithm>
#include <cstring>

using std::sort;

const int maxn=1e5+1000;

struct Tuple
{
int a,b,c,cnt,ans;
bool operator< (const Tuple& Tp) const
{
if (a!=Tp.a) return a<Tp.a;
if (b!=Tp.b) return b<Tp.b;
return c<Tp.c;
}
bool operator!= (const Tuple& Tp)
{
return a!=Tp.a || b!=Tp.b || c!=Tp.c;
}
}tmp[maxn],a[maxn];

struct cmp
{
bool operator() (const Tuple& a,const Tuple& b)
{
if (a.b!=b.b) return a.b<b.b;
return a.c<b.c;
}
};

int c[maxn*2],n,k;

inline void update(int x,int y)
{
for (int i=x;i<=k;i+=i&-i) c[i]+=y;
}

inline int query(int x)
{
int ans=0;
for (int i=x;i;i-=i&-i) ans+=c[i];
return ans;
}

void solve(int l,int r)
{
if (l==r) return;
int mid=(l+r)>>1;
solve(l,mid);solve(mid+1,r);
sort(a+l,a+mid+1,cmp());sort(a+mid+1,a+r+1,cmp());
for (int t1=l,t2=mid+1;t2<=r;++t2)
{
while (a[t1].b<=a[t2].b && t1<=mid) update(a[t1].c,a[t1].cnt),++t1;
a[t2].ans+=query(a[t2].c);
}
for (int i=l;i<=mid;++i)
if (a[i].b<=a[r].b) update(a[i].c,-a[i].cnt);
else break;
// memset(c,0,sizeof(c));
}

int main()
{
scanf("%d%d",&n,&k);
for (int i=1;i<=n;++i)
scanf("%d%d%d",&tmp[i].a,&tmp[i].b,&tmp[i].c);
std::sort(tmp+1,tmp+n+1);
int tot;a[tot=1]=tmp[1];a[1].cnt=1;
for (int i=2;i<=n;++i)
if (tmp[i]!=tmp[i-1]) a[++tot]=tmp[i],a[tot].cnt=1;
else ++a[tot].cnt;
solve(1,tot);
// for (int i=1;i<=tot;++i) printf("%d ",a[i].ans);
static int ans[maxn];
for (int i=1;i<=tot;++i) ans[a[i].ans+a[i].cnt-1]+=a[i].cnt;
for (int i=0;i<n;++i) printf("%d\n",ans[i]);
}

点分治

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void getroot(int u,int fa)
{
mxsiz[u]=0;siz[u]=1;
for (int i=head[u];i;i=edge[i].next)
{
int v=edge[i].to;
if (vis[v] || v==fa) continue;
getroot(v,u);
siz[u]+=siz[v];
mxsiz[u]=max(mxsiz[u],siz[v]);
}
mxsiz[u]=max(mxsiz[u],S-siz[u]);
if (mxsiz[u]<mxsiz[root]) root=u;
}

void getdis(int u,int fa,int d)
{
tmp[++cnt]=d;
for (int i=head[u];i;i=edge[i].next)
{
int v=edge[i].to;
if (vis[v] || v==fa) continue;
getdis(v,u,d+edge[i].w);
}
}

void getans(int opt)
{
sort(tmp+1,tmp+cnt+1);
for (int u=1;u<=cnt;++u)
{
for (int t=1;t<=m;++t)
{
pair<int*,int*> p=equal_range(tmp+1,tmp+cnt+1,query[t]-tmp[u]);
if (p.second!=p.first) count[t]+=opt*(p.second-p.first);
// assert(p.second==p.first);
}
}
}

void solve(int u)
{
vis[u]=1;
getdis(u,cnt=0,0);
getans(1);
for (int i=head[u];i;i=edge[i].next)
{
int v=edge[i].to;
if (vis[v]) continue;
getdis(v,cnt=0,edge[i].w);
getans(-1);
mxsiz[root=0]=0x3f3f3f3f;
S=siz[v];
getroot(v,0);
solve(v);
}
}

笛卡尔树(Luogu P3793)

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#include <cstdio>

typedef long long unsigned int uint64_t;

namespace GenHelper
{
unsigned z1,z2,z3,z4,b;
unsigned rand_()
{
b=((z1<<6)^z1)>>13;
z1=((z1&4294967294U)<<18)^b;
b=((z2<<2)^z2)>>27;
z2=((z2&4294967288U)<<2)^b;
b=((z3<<13)^z3)>>21;
z3=((z3&4294967280U)<<7)^b;
b=((z4<<3)^z4)>>12;
z4=((z4&4294967168U)<<13)^b;
return (z1^z2^z3^z4);
}
}

void srand(unsigned x)
{
using namespace GenHelper;
z1=x;
z2=(~x)^0x233333333U;
z3=x^0x1234598766U;
z4=(~x)+51;
}

int read()
{
using namespace GenHelper;
int a=rand_()&32767;
int b=rand_()&32767;
return a*32768+b;
}

const int maxn=2e7+1000;
const int INF=0x7fffffff;

int a[maxn],ls[maxn],rs[maxn],root;

inline void init(int n)
{
static int stack[maxn];
int top=0;
a[0]=-INF;
for (int i=1;i<=n;++i)
{
while (top && a[stack[top]]<=a[i]) ls[i]=stack[top--];
rs[stack[top]]=i;
stack[++top]=i;
}
root=stack[1];
}

inline uint64_t query(int l,int r)
{
for (int x=root;;x=x<l?rs[x]:ls[x])
if (x>=l && x<=r) return a[x];
}

int main()
{
int n,m,s;
scanf("%d%d%d",&n,&m,&s);
srand(s);
for (int i=1;i<=n;++i) a[i]=read();
uint64_t ans=0;int l,r;
init(n);
for (int i=1;i<=m;++i)
{
l=read()%n+1;
r=read()%n+1;
ans+=l>r?query(r,l):query(l,r);
}
printf("%llu",ans);
}

树链剖分(LOJ模板题,带换根)

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#include <cstdio>
#include <cstring>
#include <algorithm>
#define ls l,m,o<<1
#define rs m+1,r,o<<1|1

typedef long long ll;

const int maxn=1e5+1000;

int val[maxn],top[maxn],fa[maxn],siz[maxn],son[maxn];
int f[maxn][30],depth[maxn],head[maxn],cnt,root,id[maxn],w[maxn];
ll sumv[maxn<<2],addv[maxn<<2],tot,n;

struct Edge
{
int to,next;
}edge[maxn<<1];

inline void _add(int u,int v)
{
edge[++cnt].next=head[u];
edge[cnt].to=v;
head[u]=cnt;
}

inline void add(int u,int v)
{
_add(u,v);_add(v,u);
}

void dfs(int u,int fa,int dep)
{
depth[u]=dep;
::fa[u]=fa;
siz[u]=1;int maxs=-1;
for (int i=head[u];i;i=edge[i].next)
{
int v=edge[i].to;
if (v!=fa)
{
dfs(v,u,dep+1);
siz[u]+=siz[v];
if (siz[v]>maxs) son[u]=v,maxs=siz[v];
}
}
}

void dfs(int u,int topf)
{
id[u]=++tot;
w[tot]=val[u];
top[u]=topf;
if (!son[u]) return;
dfs(son[u],topf);
for (int i=head[u];i;i=edge[i].next)
{
int v=edge[i].to;
if (v!=fa[u] && v!=son[u]) dfs(v,v);
}
}

inline void pushup(int o){sumv[o]=sumv[o<<1]+sumv[o<<1|1];}

inline void pushdown(int o,int len)
{
addv[o<<1]+=addv[o];
addv[o<<1|1]+=addv[o];
sumv[o<<1]+=addv[o]*(len-(len>>1));
sumv[o<<1|1]+=addv[o]*(len>>1);
addv[o]=0;
}

void build(int l,int r,int o)
{
if (l==r) {sumv[o]=w[l];return;}
int m=(l+r)>>1;
build(ls);build(rs);
pushup(o);
}

void update(int L,int R,int c,int l,int r,int o)
{
if (L<=l && R>=r)
{
addv[o]+=c;
sumv[o]+=c*(r-l+1);
return;
}
pushdown(o,r-l+1);
int m=(l+r)>>1;
if (L<=m) update(L,R,c,ls);
if (R> m) update(L,R,c,rs);
pushup(o);
}

ll query(int L,int R,int l,int r,int o)
{
if (L<=l && R>=r) return sumv[o];
int m=(l+r)>>1;
pushdown(o,r-l+1);
ll tot=0;
if (L<=m) tot+=query(L,R,ls);
if (R> m) tot+=query(L,R,rs);
return tot;
}

inline void AddRoute(int u,int v,int k)
{
while (top[u]!=top[v])
{
if (depth[top[u]]<depth[top[v]]) u^=v^=u^=v;
update(id[top[u]],id[u],k,1,n,1);
u=fa[top[u]];
}
if (depth[u]>depth[v]) u^=v^=u^=v;
update(id[u],id[v],k,1,n,1);
}

inline ll QueryRoute(int u,int v)
{
ll ans=0;
while (top[u]!=top[v])
{
if (depth[top[u]]<depth[top[v]]) u^=v^=u^=v;
ans+=query(id[top[u]],id[u],1,n,1);
u=fa[top[u]];
}
if (depth[u]>depth[v]) u^=v^=u^=v;
ans+=query(id[u],id[v],1,n,1);
return ans;
}

inline int lca(int u,int v)
{
while (top[u]!=top[v])
{
if (depth[top[u]]<depth[top[v]]) u^=v^=u^=v;
u=fa[top[u]];
}
return depth[u]>depth[v]?v:u;
}

inline int get_son(int u,int prec)
{
for (int i=20;~i;--i)
if (depth[f[u][i]]>depth[prec]) u=f[u][i];
return u;
}

inline void AddSubTree(int u,int k)
{
if (u==root) update(1,n,k,1,n,1);
else if (lca(u,root)!=u)
update(id[u],id[u]+siz[u]-1,k,1,n,1);
else
{
update(1,n,k,1,n,1);
int v=get_son(root,u);
update(id[v],id[v]+siz[v]-1,-k,1,n,1);
}
}

inline ll QuerySubTree(int u)
{
if (u==root) return query(1,n,1,n,1);
else if (lca(u,root)!=u)
return query(id[u],id[u]+siz[u]-1,1,n,1);
else
{
int v=get_son(root,u);
return query(1,n,1,n,1)-query(id[v],id[v]+siz[v]-1,1,n,1);
}
// return query(1,n,1,n,1)-query(id[u]+1,id[u]+siz[u]-1,1,n,1);
// // else return query(1,n,1,n,1);
}

inline void get_anc()
{
for (int i=1;i<=n;++i) f[i][0]=fa[i];
for (int i=1;i<=20;++i)
for (int u=1;u<=n;++u)
f[u][i]=f[f[u][i-1]][i-1];
}

int main()
{
// freopen("tree2.in","r",stdin);
// freopen("tree20.out","w",stdout);
int m;
scanf("%d",&n);root=1;
for (int i=1;i<=n;++i) scanf("%d",val+i);
for (int i=1,tmp;i<n;++i) scanf("%d",&tmp),add(tmp,i+1);
dfs(1,0,1);dfs(1,1);build(1,n,1);get_anc();
scanf("%d",&m);
for (int i=1,opt,u,v,k;i<=m;++i)
{
scanf("%d",&opt);
switch (opt)
{
case 1:scanf("%d",&root);break;
case 2:scanf("%d%d%d",&u,&v,&k);AddRoute(u,v,k);break;
case 3:scanf("%d%d",&u,&k);AddSubTree(u,k);break;
case 4:scanf("%d%d",&u,&v);printf("%lld\n",QueryRoute(u,v));break;
case 5:scanf("%d",&u);printf("%lld\n",QuerySubTree(u));break;
}
}
}

LCT

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#include <cstdio>
#define ls(x) (ch[x][0])
#define rs(x) (ch[x][1])

const int maxn=3e5+1000;

int val[maxn],ch[maxn][2],fa[maxn],rev[maxn],s[maxn];

inline void swap(int &a,int &b){a^=b^=a^=b;}
inline bool nroot(int x){return ls(fa[x])==x || rs(fa[x])==x;}
inline void pushup(int x){s[x]=s[ls(x)]^s[rs(x)]^val[x];}

inline void pushr(int x)
{
swap(ls(x),rs(x));rev[x]^=1;
}

inline void pushdown(int x)
{
if (rev[x]) pushr(ls(x)),pushr(rs(x)),rev[x]=0;
}

inline void rotate(int x)
{
int y=fa[x],z=fa[y],k=ch[y][1]==x;
if (nroot(y)) ch[z][ch[z][1]==y]=x;
fa[x]=z;
ch[y][k]=ch[x][k^1];
if (ch[x][k^1]) fa[ch[x][k^1]]=y;
ch[x][k^1]=y;
fa[y]=x;
pushup(y);pushup(x);
}

inline void splay(int x)
{
static int stack[maxn];
int y=x,z=0;
while (nroot(y)) stack[++z]=y,y=fa[y];
stack[++z]=y;
while (z) pushdown(stack[z--]);
while (nroot(x))
{
y=fa[x],z=fa[y];
if (nroot(y)) rotate(((ls(z)==y)^(ls(y)==x))?x:y);
rotate(x);
}
}

inline void access(int x)
{
for (int y=0;x;y=x,x=fa[x])
splay(x),ch[x][1]=y,pushup(x);
}

inline void makeroot(int x)
{
access(x);splay(x);pushr(x);
}

inline int findroot(int x)
{
access(x);
splay(x);
while (ls(x)) pushdown(x),x=ls(x);// 这里一定记得pushdown!
splay(x);
return x;
}

inline void link(int x,int y)
{
makeroot(x);
if (findroot(y)!=x) fa[x]=y;
}

inline void cut(int x,int y)
{
makeroot(x);
if (findroot(y)==x && fa[y]==x && !ch[y][0]) ch[x][1]=fa[y]=0,pushup(x);
}

inline void modify(int x,int y)
{
splay(x);
s[x]^=val[x];
val[x]=y;
s[x]^=val[x];
}

inline void split(int x,int y)
{
makeroot(x);access(y);splay(y);
}

inline int query(int x,int y){split(x,y);return s[y];}

int main()
{
int n,m;
scanf("%d%d",&n,&m);
for (int i=1;i<=n;++i)
scanf("%d",val+i);
for (int i=1,opt,x,y;i<=m;++i)
{
scanf("%d%d%d",&opt,&x,&y);
switch (opt)
{
case 0:printf("%d\n",query(x,y));break;
case 1:link(x,y);break;
case 2:cut(x,y);break;
case 3:modify(x,y);break;
}
}
}

K-D Tree

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#include <cstdio>
#include <algorithm>

using std::nth_element;
using std::min;
using std::max;

const int maxn=1e6+100;
const int INF=0x3f3f3f3f;

struct Point
{
int x,y;
Point(){}
Point(int x,int y):x(x),y(y){}
};

struct KDTree
{
static constexpr double alpha=0.75;
int root;
struct Node
{
int val,siz,sum;
int ch[2];
Point mn,mx,now;
}t[maxn];
int top,has_rebuild,fa_rebuild,k_rebuild;
KDTree(){t[0].mn=Point(INF,INF);t[0].mx=Point(-INF,-INF);}
int trash[maxn],Trash;
inline bool isbad(int o){return t[t[o].ch[0]].siz>t[o].siz*alpha || t[t[o].ch[1]].siz>t[o].siz*alpha;}
inline void pushup(int o)
{
t[o].siz=t[t[o].ch[0]].siz+t[t[o].ch[1]].siz+1;
t[o].sum=t[t[o].ch[0]].sum+t[t[o].ch[1]].sum+t[o].val;
t[o].mn.x=min({t[o].now.x,t[t[o].ch[0]].mn.x,t[t[o].ch[1]].mn.x});
t[o].mn.y=min({t[o].now.y,t[t[o].ch[0]].mn.y,t[t[o].ch[1]].mn.y});
t[o].mx.y=max({t[o].now.y,t[t[o].ch[0]].mx.y,t[t[o].ch[1]].mx.y});
t[o].mx.x=max({t[o].now.x,t[t[o].ch[0]].mx.x,t[t[o].ch[1]].mx.x});
}
inline void dfs(int o)
{
if (!o) return;
if (t[o].ch[0]) dfs(t[o].ch[0]);
trash[++Trash]=o;
if (t[o].ch[1]) dfs(t[o].ch[1]);
}
inline int _rebuild(int l,int r,int k)
{
if (l>r) return 0;
int mid=(l+r)>>1;
int x=trash[mid];
if (l==r)
{
t[x].ch[0]=t[x].ch[1]=0;
t[x].mn=t[x].mx=t[x].now;
t[x].siz=1;
t[x].sum=t[x].val;
return x;
}
if (k==1) nth_element(trash+l,trash+mid+1,trash+r+1,[this](const int x,const int y) ->bool {return t[x].now.x<t[y].now.x;});
else nth_element(trash+l,trash+mid+1,trash+r+1,[this](const int x,const int y) ->bool {return t[x].now.y<t[y].now.y;});
x=trash[mid];
t[x].ch[0]=_rebuild(l,mid-1,k^1);
t[x].ch[1]=_rebuild(mid+1,r,k^1);
pushup(x);
return x;
}
inline int rebuild(int o,int k)
{
Trash=0;
dfs(o);
if (Trash) return _rebuild(1,Trash,k);
return 0;
}
void _insert(const Point& p,const int x,int& o,int k)
{
if (!o)
{
o=++top;
t[o].sum=t[o].val=x;
t[o].mn=t[o].mx=t[o].now=p;
t[o].siz=1;
return;
}
if (k&1) _insert(p,x,t[o].ch[t[o].now.x<=p.x],0);
else _insert(p,x,t[o].ch[t[o].now.y<=p.y],1);
pushup(o);
if (isbad(t[o].ch[0])) has_rebuild=t[o].ch[0],fa_rebuild=o,k_rebuild=k^1;
else if (isbad(t[o].ch[1])) has_rebuild=t[o].ch[1],fa_rebuild=o,k_rebuild=k^1;
}
inline void insert(const Point& p,const int x)
{
_insert(p,x,root,0);
if (isbad(root)) root=rebuild(root,0);
else if (has_rebuild) t[fa_rebuild].ch[t[fa_rebuild].ch[1]==has_rebuild]=rebuild(has_rebuild,k_rebuild);
has_rebuild=fa_rebuild=k_rebuild=0;
}
inline bool check_range(int o,const Point& l,const Point& r)
{
return t[o].mn.x>=l.x && t[o].mn.y>=l.y && t[o].mx.x<=r.x && t[o].mx.y<=r.y;
}
inline bool check_point(int o,const Point& l,const Point& r)
{
return (t[o].now.x>=l.x && t[o].now.x<=r.x) && (t[o].now.y>=l.y && t[o].now.y<=r.y);
}
inline bool check_have(int o,const Point& l,const Point& r)
{
return !((t[o].mx.x<l.x) || (t[o].mx.y<l.y) || (t[o].mn.x>r.x) || (t[o].mn.y>r.y));
}
inline int query(const Point& l,const Point& r,int o)
{
if (!o) return 0;
if (check_range(o,l,r)) return t[o].sum;
int ans=0;
if (check_point(o,l,r)) ans+=t[o].val;
if (check_have(t[o].ch[0],l,r)) ans+=query(l,r,t[o].ch[0]);
if (check_have(t[o].ch[1],l,r)) ans+=query(l,r,t[o].ch[1]);
return ans;
}
}T;

int main()
{
int n;
scanf("%d",&n);
int opt,x,lastans=0;
Point a,b;
while (scanf("%d",&opt) && opt!=3 && "STO LCH OTZ")
{
if (opt==1)
{
scanf("%d%d%d",&a.x,&a.y,&x);
a.x^=lastans;a.y^=lastans;x^=lastans;
T.insert(a,x);
}
else
{
scanf("%d%d%d%d",&a.x,&a.y,&b.x,&b.y);
a.x^=lastans;a.y^=lastans;b.x^=lastans;b.y^=lastans;
printf("%d\n",lastans=T.query(a,b,T.root));
}
}
}

平衡树

Treap

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struct Treap
{
struct Node
{
int v,s,r,cnt;
Node* ch[2];
Node(int v,int s=1):s(s),cnt(s),r(rand()*rand()),v(v){ch[0]=ch[1]=0;}
inline void pushup()
{
s=cnt;
if (ch[0]) s+=ch[0]->s;
if (ch[1]) s+=ch[1]->s;
}
inline int cmp(int x)
{
return v==x?-1:v<x;
}
};
private:
int __prec,__succ;
public:
Treap():__prec(0),__succ(0),root(0){}
Node *root;
inline void rotate(Node* &o,int d)
{
Node *k=o->ch[d^1];
o->ch[d^1]=k->ch[d];
k->ch[d]=o;
o->pushup();
k->pushup();
o=k;
}

inline void _insert(Node* &o,int x,int t=1)
{
if (!o){o=new Node(x,t);return;}
int d=o->cmp(x);
if (d==-1) {o->cnt+=t;o->s+=t;return;}
_insert(o->ch[d],x,t);
if (o->ch[d]->r > o->r) rotate(o,d^1);
o->pushup();
}
inline void insert(int x,int k=1){_insert(root,x,k);}

inline void _remove(Node* &o,int x)
{
if (!o) return;
int d=o->cmp(x);
if (d==-1)
{
if (o->cnt>1) {--o->cnt;--o->s;return;}
if (!(o->ch[0])){Node* k=o;o=o->ch[1];delete k;return;}
else if (!(o->ch[1])){Node* k=o;o=o->ch[0];delete k;return;}
else
{
int d2=(o->ch[0]->r > o->ch[1]->r);
rotate(o,d2);
_remove(o->ch[d2],x);
}
}
else _remove(o->ch[d],x);
if (o) o->pushup();
}
inline void remove(int x){_remove(root,x);}

inline int _kth(Node* o,int k)
{
if (!o || k<=0) return INT_MIN;
int s=o->ch[0]?o->ch[0]->s:0;
if (k>=s+1 && k<=s+o->cnt) return o->v;
if (k<=s) return _kth(o->ch[0],k);
return _kth(o->ch[1],k-s-o->cnt);
}
inline int kth(int k){return _kth(root,k);}

inline int _rank(Node* o,int x)
{
if (!o) return 1;
int s=o->ch[0]?o->ch[0]->s:0;
if (o->v==x) return s+1;
if (o->v<x) return s+o->cnt+_rank(o->ch[1],x);
return _rank(o->ch[0],x);
}
inline int rank(int x){return _rank(root,x);}

inline int _count(Node* o,int x)
{
if (!o) return 0;
int d=o->cmp(x);
if (~d) return _count(o->ch[d],x);
return o->cnt;
}
inline int count(int x){return _count(root,x);}

inline void _prec(Node* o,int x)
{
if (!o) return;
if (o->v<x) __prec=max(__prec,o->v);
if (o->v>=x) _prec(o->ch[0],x);
else _prec(o->ch[1],x);
}
inline void _succ(Node* o,int x)
{
if (!o) return;
if (o->v>x) __succ=min(__succ,o->v);
if (o->v<=x) _succ(o->ch[1],x);
else _succ(o->ch[0],x);
}
inline int prec(int x){__prec=INT_MIN+1;_prec(root,x);return __prec;}
inline int succ(int x){__succ=INT_MAX ;_succ(root,x);return __succ;}
}T;

替罪羊树

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#include <cstdio>
#include <vector>
#include <cassert>

using std::vector;

const int maxn=1e5+1000;

struct Scapegoat_Tree
{
int root,has_rebuild,fa;
#if __cplusplus >= 201103L
static constexpr double alpha=0.75;
#else
static const double alpha=0.75;
#endif
struct Node
{
int siz,cnt,val;
bool deleted;
int ch[2];
}t[maxn];
inline bool isbad(int x){return t[t[x].ch[0]].cnt>t[x].cnt*alpha || t[t[x].ch[1]].cnt>t[x].cnt*alpha;}
inline void maintain(int x){t[x].siz=t[t[x].ch[0]].siz+t[t[x].ch[1]].siz+!t[x].deleted;t[x].cnt=t[t[x].ch[0]].cnt+t[t[x].ch[1]].cnt+1;}
int pool[maxn],top;
vector<int> tmp;
Scapegoat_Tree(){for (int i=1;i<maxn;++i) pool[++top]=i;}
void dfs(int o)
{
if (t[o].ch[0]) dfs(t[o].ch[0]);
if (!t[o].deleted) tmp.push_back(o);
else pool[++top]=o;
if (t[o].ch[1]) dfs(t[o].ch[1]);
}
int _rebuild(int l,int r)
{
if (l>r) return 0;
int mid=(l+r)>>1,o=tmp[mid];
if (l==r) t[o].siz=t[o].cnt=1;
t[o].ch[0]=_rebuild(l,mid-1);
t[o].ch[1]=_rebuild(mid+1,r);
maintain(o);
return o;
}
int rebuild(int o)
{
tmp.clear();
dfs(o);
return _rebuild(0,tmp.size()-1);
}
void _insert(int x,int &o)
{
if (!o)
{
o=pool[top--];
t[o].siz=t[o].cnt=1;
t[o].val=x;
t[o].deleted=false;
t[o].ch[0]=t[o].ch[1]=0;
return;
}
++t[o].siz;++t[o].cnt;
int d=(t[o].val<=x);
_insert(x,t[o].ch[d]);
// if (isbad(o)) o=rebuild(o);//need repair?
if (isbad(t[o].ch[0])) has_rebuild=t[o].ch[0],fa=o;
else if (isbad(t[o].ch[1])) has_rebuild=t[o].ch[1],fa=o;
// maintain(o);
}
void insert(int x)
{
_insert(x,root);
if (has_rebuild) t[fa].ch[t[fa].ch[1]==has_rebuild]=rebuild(has_rebuild);
fa=has_rebuild=0;
}
void _remove_kth(int x,int o)
{
if (t[t[o].ch[0]].siz+1==x && !t[o].deleted)
{
t[o].deleted=true;
t[o].siz--;
return;
}
--t[o].siz;
if (t[t[o].ch[0]].siz>=x) _remove_kth(x,t[o].ch[0]);
else _remove_kth(x-t[t[o].ch[0]].siz-!t[o].deleted,t[o].ch[1]);
// maintain(o);
}
void remove_kth(int x)
{
_remove_kth(x,root);
if (t[root].cnt*alpha>t[root].siz) root=rebuild(root);
fa=has_rebuild=0;
}
int rank(int x)
{
int ans=1;
int o=root;
while (o)
if (t[o].val>=x) o=t[o].ch[0];
else ans+=t[t[o].ch[0]].siz+!t[o].deleted,o=t[o].ch[1];
return ans;
}
int kth(int k)
{
int o=root;
while (1)
{
int s=t[t[o].ch[0]].siz;
if (!t[o].deleted && s+1==k) return t[o].val;
if (s>=k) o=t[o].ch[0];
else k-=s+!t[o].deleted,o=t[o].ch[1];
}
}
void print(int o)
{
if (!o) return;
print(t[o].ch[0]);
// printf("sizls=%d sizrs=%d ,siz=%d\n",t[t[o].ch[0]].siz,t[t[o].ch[1]].siz,t[o].siz);
if (!t[o].deleted) printf("%d ",t[o].val);
print(t[o].ch[1]);
}
/* data */
}T;

int main()
{
int n;
scanf("%d",&n);
for (int i=1,opt,x;i<=n;++i)
{
scanf("%d%d",&opt,&x);
switch (opt)
{
case 1:
T.insert(x);
break;
case 2:
T.remove_kth(T.rank(x));
break;
case 3:
printf("%d\n",T.rank(x));
break;
case 4:
printf("%d\n",T.kth(x));
break;
case 5:
printf("%d\n",T.kth(T.rank(x)-1));
break;
case 6:
printf("%d\n",T.kth(T.rank(x+1)));
break;
}
// T.print(T.root);putchar('\n');
// T.root=T.rebuild(T.root);
}
}

Splay

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struct Splay
{
int root,cnt;
struct Node
{
int val,size,ff,ch[2],cnt;
}t[maxn];

inline void pushup(int x)
{
t[x].size=t[x].cnt+t[t[x].ch[0]].size+t[t[x].ch[1]].size;
}

inline void rotate(int x)
{
int y=t[x].ff,z=t[y].ff;
int k=(t[y].ch[1]==x);
t[z].ch[t[z].ch[1]==y]=x;
t[x].ff=z;
t[y].ch[k]=t[x].ch[k^1];
t[t[x].ch[k^1]].ff=y;
t[y].ff=x;
t[x].ch[k^1]=y;
pushup(y);pushup(x);
}

inline void splay(int x,int goal)
{
while (t[x].ff!=goal)
{
int y=t[x].ff,z=t[y].ff;
if (z!=goal) rotate((t[z].ch[1]==y)^(t[y].ch[1]==x)?x:y);
rotate(x);
}
if (!goal) root=x;
}

inline void insert(int x)
{
int u=root,ff=0;
while (t[u].val!=x && u)
{
ff=u;
u=t[u].ch[t[u].val<x];
}
if (u) {++t[u].cnt;splay(u,0);return;}
u=++cnt;
if (ff) t[ff].ch[x>t[ff].val]=u;
t[u].ff=ff;
t[u].ch[0]=t[u].ch[1]=0;
t[u].size=1;
t[u].cnt=1;
t[u].val=x;
splay(u,0);
}

inline void find(int x)
{
int u=root;
if (!u) return;
while (t[u].ch[t[u].val<x] && t[u].val!=x) u=t[u].ch[t[u].val<x];
splay(u,0);
}

inline int Next(int x,int type)
{
find(x);
int u=root;
if (t[u].val>x && type) return u;
if (t[u].val<x && !type) return u;
u=t[u].ch[type];
while (t[u].ch[type^1])u=t[u].ch[type^1];
splay(u,0);
return u;
}

inline void Delete(int x)
{
int prev=Next(x,0),succ=Next(x,1);
splay(prev,0);splay(succ,prev);
int u=t[succ].ch[0];
if (t[u].cnt>1){--t[u].cnt;splay(u,0);return;}
else t[succ].ch[0]=0;
}

inline int kth(int k)
{
int u=root;
if (t[u].size<k) return inf;
while (19260817)
{
int s=t[t[u].ch[0]].size;
if (s+t[u].cnt<k)
k-=s+t[u].cnt,u=t[u].ch[1];
else if (k<=s)
u=t[u].ch[0];
else {splay(u,0);return t[u].val;}
}
}
}T;

权值线段树

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void insert(int x,int l=1,int r=n,int o=1)
{
++sumv[o];
if (l==r) return;
int m=(l+r)>>1;
if (x<=m) insert(x,ls);
else insert(x,rs);
}

inline void remove(int x,int l=1,int r=n,int o=1)
{
--sumv[o];
if (l==r) return;
int m=(l+r)>>1;
if (x<=m) remove(x,ls);
else remove(x,rs);
}

inline int count(int x,int l=1,int r=n,int o=1)
{
if (l==r) return sumv[o];
int m=(l+r)>>1;
if (x<=m) return count(x,ls);
else return count(x,rs);
}

inline int rank(int x,int l=1,int r=n,int o=1)
{
if (l==r) return 1;
int m=(l+r)>>1;
if (x<=m) return rank(x,ls);
else return rank(x,rs)+sumv[o<<1];
}

inline int kth(int k,int l=1,int r=n,int o=1)
{
if (l==r) return l;
int m=(l+r)>>1;
if (k<=sumv[o<<1]) return kth(k,ls);
return kth(k-sumv[o<<1],rs);
}

inline int prec(int x)
{
return kth(rank(x)-1);
}

inline int succ(int x)
{
return kth(rank(x)+count(x));
}

inline int get_rnk(int i)
{
return lower_bound(b+1,b+n+1,i)-b;
}

树套树

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struct Node
{
int v,s,r,cnt;
Node* ch[2];
Node(int v,int s=1):s(s),cnt(s),r(rand()*rand()),v(v){ch[0]=ch[1]=0;}
inline void pushup()
{
s=cnt;
if (ch[0]) s+=ch[0]->s;
if (ch[1]) s+=ch[1]->s;
}
inline int cmp(int x)
{
return v==x?-1:v<x;
}
};

struct Treap
{
private:
int __prec,__succ;
public:
Treap():__prec(0),__succ(0),root(0){}
Node *root;
inline void rotate(Node* &o,int d)
{
Node *k=o->ch[d^1];
o->ch[d^1]=k->ch[d];
k->ch[d]=o;
o->pushup();
k->pushup();
o=k;
}

inline void _insert(Node* &o,int x,int t=1)
{
if (!o){o=new Node(x,t);return;}
int d=o->cmp(x);
if (d==-1) {o->cnt+=t;o->s+=t;return;}
_insert(o->ch[d],x,t);
if (o->ch[d]->r > o->r) rotate(o,d^1);
o->pushup();
}
inline void insert(int x,int k=1){_insert(root,x,k);}

inline void _remove(Node* &o,int x)
{
if (!o) return;
int d=o->cmp(x);
if (d==-1)
{
if (o->cnt>1) {--o->cnt;--o->s;return;}
if (!(o->ch[0])){Node* k=o;o=o->ch[1];delete k;return;}
else if (!(o->ch[1])){Node* k=o;o=o->ch[0];delete k;return;}
else
{
int d2=(o->ch[0]->r > o->ch[1]->r);
rotate(o,d2);
_remove(o->ch[d2],x);
}
}
else _remove(o->ch[d],x);
if (o) o->pushup();
}
inline void remove(int x){_remove(root,x);}

inline int _kth(Node* o,int k)
{
if (!o || k<=0) return INT_MIN;
int s=o->ch[0]?o->ch[0]->s:0;
if (k>=s+1 && k<=s+o->cnt) return o->v;
if (k<=s) return _kth(o->ch[0],k);
return _kth(o->ch[1],k-s-o->cnt);
}
inline int kth(int k){return _kth(root,k);}

inline int _rank(Node* o,int x)
{
if (!o) return 1;
int s=o->ch[0]?o->ch[0]->s:0;
if (o->v==x) return s+1;
if (o->v<x) return s+o->cnt+_rank(o->ch[1],x);
return _rank(o->ch[0],x);
}
inline int rank(int x){return _rank(root,x);}

inline int _count(Node* o,int x)
{
if (!o) return 0;
int d=o->cmp(x);
if (~d) return _count(o->ch[d],x);
return o->cnt;
}
inline int count(int x){return _count(root,x);}

inline void _prec(Node* o,int x)
{
if (!o) return;
if (o->v<x) __prec=max(__prec,o->v);
if (o->v>=x) _prec(o->ch[0],x);
else _prec(o->ch[1],x);
}
inline void _succ(Node* o,int x)
{
if (!o) return;
if (o->v>x) __succ=min(__succ,o->v);
if (o->v<=x) _succ(o->ch[1],x);
else _succ(o->ch[0],x);
}
inline int prec(int x){__prec=INT_MIN+1;_prec(root,x);return __prec;}
inline int succ(int x){__succ=INT_MAX ;_succ(root,x);return __succ;}
}tree[maxn<<2];

inline void insert_tree(Treap& t,Node* rt)
{
if (!rt) return;
t.insert(rt->v,rt->cnt);
insert_tree(t,rt->ch[0]);
insert_tree(t,rt->ch[1]);
}

inline void pushup(int o)
{
insert_tree(tree[o],tree[o<<1].root);
insert_tree(tree[o],tree[o<<1|1].root);
}

inline void build(int l,int r,int o)
{
if (l==r) {tree[o].insert(a[l]);return;}
int m=(l+r)>>1;
build(ls);
build(rs);
pushup(o);
}

inline int rank(int L,int R,int k,int l,int r,int o)
{
if (L<=l && R>=r) return tree[o].rank(k);
const int m=(l+r)>>1;
int tot=0;
if (L<=m) tot+=rank(L,R,k,ls);
if (R> m) tot+=rank(L,R,k,rs);
if (L<=m && R>m) --tot;
return tot;
}

inline int count(int L,int R,int x,int l,int r,int o)
{
if (L<=l && R>=r) return tree[o].count(x);
const int m=(l+r)>>1;
int tot=0;
if (L<=m) tot+=count(L,R,x,ls);
if (R> m) tot+=count(L,R,x,rs);
return tot;
}

inline void update(int p,int x,int l,int r,int o)
{
tree[o].remove(a[p]);
tree[o].insert(x);
if (l==r) return;
int m=(l+r)>>1;
if (p<=m) update(p,x,ls);
else update(p,x,rs);
}

inline int prec(int L,int R,int x,int l,int r,int o)
{
if (L<=l && R>=r) return tree[o].prec(x);
int m=(l+r)>>1,ans=INT_MIN+1;
if (L<=m) ans=prec(L,R,x,ls);
if (R>m) ans=max(ans,prec(L,R,x,rs));
return ans;
}

inline int succ(int L,int R,int x,int l,int r,int o)
{
if (L<=l && R>=r) return tree[o].succ(x);
int m=(l+r)>>1,ans=INT_MAX;
if (L<=m) ans=succ(L,R,x,ls);
if (R> m) ans=min(ans,succ(L,R,x,rs));
return ans;
}

inline int kth(int L,int R,int k,int n)
{
int l=1,r=tree[1].root->s;
while (l<=r)
{
int m=(l+r)>>1;
int t=tree[1].kth(m);
int K=rank(L,R,t,1,n,1);
int cnt=count(L,R,t,1,n,1);
if (K==k && !cnt) return succ(L,R,t,1,n,1);
if (K+cnt-1>=k && K<=k && cnt) return t;
if (cnt)
if (K+cnt-1<k) l=m+1;
else r=m-1;
else
if (K<k) l=m+1;
else r=m-1;
}
return INT_MAX;
}

DSU ON TREE(CF600E)

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#include <cstdio>
#include <cstring>
#include <algorithm>

const int maxn=1e5+1000;

typedef long long ll;

ll ans[maxn],tot;
int head[maxn],_cnt,n,mx;
int fa[maxn],siz[maxn],son[maxn],cnt[maxn],col[maxn],isson[maxn];

struct Edge
{
int to,next;
}edge[maxn<<1];

inline int max(int a,int b){return a<b?b:a;}

inline void add(int u,int v)
{
edge[++_cnt].next=head[u];
edge[_cnt].to=v;
head[u]=_cnt;
}

void dfs(int u,int f)
{
fa[u]=f;
siz[u]=1;
int maxs=-1;
for (int i=head[u];i;i=edge[i].next)
{
int v=edge[i].to;
if (v!=f)
{
dfs(v,u);siz[u]+=siz[v];
if (siz[v]>maxs) maxs=siz[v],son[u]=v;
}
}
if (son[u]) isson[son[u]]=true;
}

void AddAns(int u,int x,int Son)
{
if((cnt[col[u]]+=x)>mx) mx=cnt[col[u]],tot=col[u];
else if(cnt[col[u]]==mx) tot+=(ll)col[u];
for (int i=head[u];i;i=edge[i].next)
{
int v=edge[i].to;
if (v!=fa[u] && v!=Son) AddAns(v,x,Son);
}
}

void solve(int u,int f,int keep)
{
for (int i=head[u];i;i=edge[i].next)
{
int v=edge[i].to;
if (v!=f && v!=son[u]) solve(v,u,0);
}
if (son[u]) solve(son[u],u,1);
AddAns(u,1,son[u]);
ans[u]=tot;
// int t=0;
// for (int i=1;i<=n;++i) t=max(t,cnt[i]);
// for (int i=1;i<=n;++i) if (cnt[i]==t) ans[u]=ans[u]+(ll)i;
if (!keep) AddAns(u,-1,0),mx=tot=0;
}

int main()
{
scanf("%d",&n);
for (int i=1;i<=n;++i) scanf("%d",col+i);
for (int i=1,u,v;i<n;++i)
{
scanf("%d%d",&u,&v);
add(u,v);add(v,u);
}
dfs(1,1);
solve(1,0,0);
for (int i=1;i<=n;++i) printf("%lld ",ans[i]);
}

珂朵莉树

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struct Node
{
int l,r;
mutable int x;
Node(int l,int r=-1,int x=0):l(l),r(r),x(x){}
bool operator< (const Node &nd) const {return l<nd.l;}
};

typedef long long ll;
typedef set<Node>::iterator It;

struct Cmp
{
bool operator() (const It& a,const It& b) const {return a->x<b->x;}
};

int a[maxn];
int seed,n,m,vmax;
set<Node> s;

inline void swap(int& a,int& b){a^=b^=a^=b;}

inline int Rand()
{
int ret=seed;
seed=((ll)seed*7+13)%1000000007;
return ret;
}

inline void init()
{
for (int i=1;i<=n;++i)
s.insert(Node(i,i,a[i]));
s.insert(Node(n+1,n+1,0));
}

inline ll pow_mod(ll a,ll b,ll p)
{
ll ans=1%p;a%=p;
for (;b;b>>=1)
{
if (b&1) ans=ans*a%p;
a=a*a%p;
}
return ans;
}

inline It split(int pos)
{
It it=s.lower_bound(Node(pos));
if (it!=s.end() && it->l==pos) return it;
--it;
int l=it->l,r=it->r,v=it->x;
s.erase(it);
s.insert(Node(l,pos-1,v));
return s.insert(Node(pos,r,v)).first;
}

inline void assign(int l,int r,int x)
{
It it2=split(r+1),it1=split(l);
s.erase(it1,it2);
s.insert(Node(l,r,x));
}

inline void add(int l,int r,int x)
{
It it2=split(r+1),it1=split(l);
for (It i=it1;i!=it2;++i) i->x+=x;
}

inline int kth(int l,int r,int x)
{
vector<It> v;
It it2=split(r+1),it1=split(l);
for (It i=it1;i!=it2;++i) v.push_back(i);
sort(v.begin(),v.end(),Cmp());
for (int i=0;i<v.size();++i)
{
// assert(v[i]->r>=v[i]->l);//Assertion Failed...Fixed....
x-=v[i]->r-v[i]->l+1;
if (x<=0) return v[i]->x;
}
return -1;
}

inline int power(int l,int r,int x,int p)
{
ll ans=0;
It it2=split(r+1),it1=split(l);
for (It it=it1;it!=it2;++it) ans=((ll)ans+(ll)pow_mod(it->x,x,p)*(it->r-it->l+1)%p)%p;
return ans;
}