洛谷 P4546 & bzoj 5020 在美妙的数学王国中畅游 —— LCT+泰勒展开

题目：https://www.luogu.org/problemnew/show/P4546

先写了个55分的部分分，直接用LCT维护即可，在洛谷上拿了60分；

注意各处 pushup，而且 splay 维护的是一条链但其形态不一定是一条链！

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;
int rd()
{
  int ret=,f=; char ch=getchar();
  while(ch<''||ch>''){if(ch=='-')f=; ch=getchar();}
  while(ch>=''&&ch<='')ret=ret*+ch-'',ch=getchar();
  return f?ret:-ret;
}
typedef double db;
int const xn=1e5+;
int n,m,hd[xn],f[xn],fa[xn],c[xn][],rev[xn];
db A[xn],B[xn],sum[xn];
char tp[],op[];
bool isroot(int x){return c[fa[x]][]!=x&&c[fa[x]][]!=x;}
db cal(int x,db v){db y=A[x]*v+B[x]; if(f[x]==)return sin(y); if(f[x]==)return exp(y); return y;}
void pushup(int x){sum[x]=cal(x,)+sum[c[x][]]+sum[c[x][]];}
void rotate(int x)
{
  int y=fa[x],z=fa[y],d=(c[y][]==x);
  if(!isroot(y))c[z][c[z][]==y]=x;
  fa[x]=z; fa[y]=x; fa[c[x][!d]]=y;
  c[y][d]=c[x][!d]; c[x][!d]=y;
  pushup(y); pushup(x);
}
int sta[xn],top;
void rever(int x)
{
  if(!rev[x])return;
  rev[c[x][]]^=; rev[c[x][]]^=;
  swap(c[x][],c[x][]); rev[x]=;
}
void splay(int x)
{
  sta[top=]=x;
  for(int i=x;!isroot(i);i=fa[i])sta[++top]=fa[i];//i!
  for(int i=top;i;i--)rever(sta[i]);
  while(!isroot(x))
    {
      int y=fa[x],z=fa[y];
      if(!isroot(y))
    ((c[y][]==x)^(c[z][]==y))?rotate(x):rotate(y);
      rotate(x);
    }
}
void access(int x)
{
  for(int t=;x;c[x][]=t,pushup(x),t=x,x=fa[x])splay(x);//pushup
}
void makeroot(int x)
{
  access(x); splay(x); rev[x]^=;
}
int find(int x)
{
  access(x); splay(x); while(c[x][])x=c[x][]; return x;
}
void link(int x,int y)
{
  makeroot(x); fa[x]=y;
}
void cut(int x,int y)
{
  makeroot(x); access(y); splay(y);
  fa[x]=; c[y][]=; pushup(y);
}
db dfs(int x,db v)
{
  db ret=cal(x,v);
  if(c[x][])ret+=dfs(c[x][],v);
  if(c[x][])ret+=dfs(c[x][],v);
  return ret;
}
void query1(int x,int y,db v)
{
  if(find(x)!=find(y)){puts("unreachable"); return;}
  makeroot(x); access(y); splay(y); db ret=;
  //for(int t=x;t!=fa[y];t=fa[t])ret+=cal(t,v);
  //printf("%.8e\n",ret);
  printf("%.8e\n",dfs(y,v));
}
void query2(int x,int y)
{
  if(find(x)!=find(y)){puts("unreachable"); return;}
  makeroot(x); access(y); splay(y);
  printf("%.8e\n",sum[y]);
}
int main()
{
  n=rd(); m=rd(); scanf("%s",tp);
  for(int i=;i<=n;i++)f[i]=rd(),scanf("%lf%lf",&A[i],&B[i]);
  for(int i=,u,v;i<=m;i++)
    {
      scanf("%s",op);
      if(op[]=='a'){u=rd()+; v=rd()+; link(u,v);}
      else if(op[]=='d'){u=rd()+; v=rd()+; cut(u,v);}
      else if(op[]=='m'){int x=rd()+; access(x); splay(x); f[x]=rd(); scanf("%lf%lf",&A[x],&B[x]); pushup(x);}//a,s,p
      else
    {
      u=rd()+; v=rd()+; db x; scanf("%lf",&x);
      if(tp[]=='')query2(u,v);
      else query1(u,v,x);
    }
    }
}

55(60)分

参考了博客：https://www.cnblogs.com/zhoushuyu/p/8148732.html

A[x] 写成 A[i] 看了一个小时...

代码如下：

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;
typedef double db;
int rd()
{
  int ret=,f=; char ch=getchar();
  while(ch<''||ch>''){if(ch=='-')f=; ch=getchar();}
  while(ch>=''&&ch<='')ret=ret*+ch-'',ch=getchar();
  return f?ret:-ret;
}
int const xn=1e5+;
int n,m,f[xn],fa[xn],c[xn][],jc[],rev[xn];
db A[xn],B[xn],g[xn][];
char tp[],op[];
bool isroot(int x){return c[fa[x]][]!=x&&c[fa[x]][]!=x;}
db t[];
void pushup(int x)
{
  db p=;
  if(f[x]==)
    {
      t[]=sin(B[x]); t[]=cos(B[x]); t[]=-t[]; t[]=-t[];
      for(int i=;i<=;i++,p=p*A[x])
    g[x][i]=p*t[i%]+g[c[x][]][i]+g[c[x][]][i];
    }
  if(f[x]==)
    {
      db tmp=exp(B[x]);
      for(int i=;i<=;i++,p=p*A[x])
    g[x][i]=p*tmp+g[c[x][]][i]+g[c[x][]][i];
    }
  if(f[x]==)
    {
      g[x][]=B[x]+g[c[x][]][]+g[c[x][]][];
      g[x][]=A[x]+g[c[x][]][]+g[c[x][]][];
      for(int i=;i<=;i++)g[x][i]=g[c[x][]][i]+g[c[x][]][i];
    }
}
void rotate(int x)
{
  int y=fa[x],z=fa[y],d=(c[y][]==x);
  if(!isroot(y))c[z][c[z][]==y]=x;
  fa[x]=z; fa[y]=x; fa[c[x][!d]]=y;
  c[y][d]=c[x][!d]; c[x][!d]=y;
  pushup(y); pushup(x);
}
int sta[xn],top;
void rever(int x)
{if(!rev[x])return; rev[c[x][]]^=; rev[c[x][]]^=; swap(c[x][],c[x][]); rev[x]=;}
void splay(int x)
{
  sta[top=]=x;
  for(int i=x;!isroot(i);i=fa[i])sta[++top]=fa[i];
  for(int i=top;i;i--)rever(sta[i]);
  while(!isroot(x))
    {
      int y=fa[x],z=fa[y];
      if(!isroot(y))
    ((c[y][]==x)^(c[z][]==y))?rotate(x):rotate(y);
      rotate(x);
    }
}
void access(int x)
{
  for(int t=;x;c[x][]=t,pushup(x),t=x,x=fa[x])splay(x);
}
void makeroot(int x)
{
  access(x); splay(x); rev[x]^=;
}
int find(int x)
{
  access(x); splay(x); while(c[x][])x=c[x][]; return x;
}
void link(int x,int y)
{
  makeroot(x); fa[x]=y;
}
void cut(int x,int y)
{
  makeroot(x); access(y); splay(y); fa[x]=c[y][]=; pushup(y);
}
void query(int x,int y,db v)
{
  if(find(x)!=find(y)){puts("unreachable"); return;}
  makeroot(x); access(y); splay(y);
  db ret=,p=; for(int i=;i<=;i++,p=p*v)ret+=g[y][i]*p/jc[i];
  printf("%.8e\n",ret);
}
int main()
{
  n=rd(); m=rd(); scanf("%s",tp);
  for(int i=;i<=n;i++)f[i]=rd(),scanf("%lf%lf",&A[i],&B[i]);
  jc[]=; for(int i=;i<=;i++)jc[i]=jc[i-]*i;
  for(int i=,u,v;i<=m;i++)
    {
      scanf("%s",op);
      if(op[]=='a'){u=rd()+; v=rd()+; link(u,v);}
      if(op[]=='d'){u=rd()+; v=rd()+; cut(u,v);}
      if(op[]=='m'){int x=rd()+; splay(x); f[x]=rd(); scanf("%lf%lf",&A[x],&B[x]); pushup(x);}//A[x] not A[i]!
      if(op[]=='t'){u=rd()+; v=rd()+; db x; scanf("%lf",&x); query(u,v,x);}
    }
  return ;
}