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=0,f=1; char ch=getchar();
  while(ch<'0'||ch>'9'){if(ch=='-')f=0; ch=getchar();}
  while(ch>='0'&&ch<='9')ret=ret*10+ch-'0',ch=getchar();
  return f?ret:-ret;
}
typedef double db;
int const xn=1e5+5;
int n,m,hd[xn],f[xn],fa[xn],c[xn][2],rev[xn];
db A[xn],B[xn],sum[xn];
char tp[10],op[15];
bool isroot(int x){return c[fa[x]][0]!=x&&c[fa[x]][1]!=x;}
db cal(int x,db v){db y=A[x]*v+B[x]; if(f[x]==1)return sin(y); if(f[x]==2)return exp(y); return y;}
void pushup(int x){sum[x]=cal(x,1)+sum[c[x][0]]+sum[c[x][1]];}
void rotate(int x)
{
  int y=fa[x],z=fa[y],d=(c[y][1]==x);
  if(!isroot(y))c[z][c[z][1]==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][0]]^=1; rev[c[x][1]]^=1;
  swap(c[x][0],c[x][1]); rev[x]=0;
}
void splay(int x)
{
  sta[top=1]=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][0]==x)^(c[z][0]==y))?rotate(x):rotate(y);
      rotate(x);
    }
}
void access(int x)
{
  for(int t=0;x;c[x][1]=t,pushup(x),t=x,x=fa[x])splay(x);//pushup
}
void makeroot(int x)
{
  access(x); splay(x); rev[x]^=1;
}
int find(int x)
{
  access(x); splay(x); while(c[x][0])x=c[x][0]; 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]=0; c[y][0]=0; pushup(y);
}
db dfs(int x,db v)
{
  db ret=cal(x,v);
  if(c[x][0])ret+=dfs(c[x][0],v);
  if(c[x][1])ret+=dfs(c[x][1],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=0;
  //for(int t=x;t!=fa[y];t=fa[t])ret+=cal(t,v);
  //printf("%.8e
",ret);
  printf("%.8e
",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
",sum[y]);
}
int main()
{
  n=rd(); m=rd(); scanf("%s",tp);
  for(int i=1;i<=n;i++)f[i]=rd(),scanf("%lf%lf",&A[i],&B[i]);
  for(int i=1,u,v;i<=m;i++)
    {
      scanf("%s",op);
      if(op[0]=='a'){u=rd()+1; v=rd()+1; link(u,v);}
      else if(op[0]=='d'){u=rd()+1; v=rd()+1; cut(u,v);}
      else if(op[0]=='m'){int x=rd()+1; access(x); splay(x); f[x]=rd(); scanf("%lf%lf",&A[x],&B[x]); pushup(x);}//a,s,p
      else
    {
      u=rd()+1; v=rd()+1; db x; scanf("%lf",&x);
      if(tp[1]=='0')query2(u,v);
      else query1(u,v,x);
    }
    }
}

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=0,f=1; char ch=getchar();
  while(ch<'0'||ch>'9'){if(ch=='-')f=0; ch=getchar();}
  while(ch>='0'&&ch<='9')ret=ret*10+ch-'0',ch=getchar();
  return f?ret:-ret;
}
int const xn=1e5+5;
int n,m,f[xn],fa[xn],c[xn][2],jc[15],rev[xn];
db A[xn],B[xn],g[xn][15];
char tp[10],op[15];
bool isroot(int x){return c[fa[x]][0]!=x&&c[fa[x]][1]!=x;}
db t[5];
void pushup(int x)
{
  db p=1;
  if(f[x]==1)
    {
      t[0]=sin(B[x]); t[1]=cos(B[x]); t[2]=-t[0]; t[3]=-t[1];
      for(int i=0;i<=12;i++,p=p*A[x])
    g[x][i]=p*t[i%4]+g[c[x][0]][i]+g[c[x][1]][i];
    }
  if(f[x]==2)
    {
      db tmp=exp(B[x]);
      for(int i=0;i<=12;i++,p=p*A[x])
    g[x][i]=p*tmp+g[c[x][0]][i]+g[c[x][1]][i];
    }
  if(f[x]==3)
    {
      g[x][0]=B[x]+g[c[x][0]][0]+g[c[x][1]][0];
      g[x][1]=A[x]+g[c[x][0]][1]+g[c[x][1]][1];
      for(int i=2;i<=12;i++)g[x][i]=g[c[x][0]][i]+g[c[x][1]][i];
    }
}
void rotate(int x)
{
  int y=fa[x],z=fa[y],d=(c[y][1]==x);
  if(!isroot(y))c[z][c[z][1]==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][0]]^=1; rev[c[x][1]]^=1; swap(c[x][0],c[x][1]); rev[x]=0;}
void splay(int x)
{
  sta[top=1]=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][0]==x)^(c[z][0]==y))?rotate(x):rotate(y);
      rotate(x);
    }
}
void access(int x)
{
  for(int t=0;x;c[x][1]=t,pushup(x),t=x,x=fa[x])splay(x);
}
void makeroot(int x)
{
  access(x); splay(x); rev[x]^=1;
}
int find(int x)
{
  access(x); splay(x); while(c[x][0])x=c[x][0]; 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][0]=0; 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=0,p=1; for(int i=0;i<=12;i++,p=p*v)ret+=g[y][i]*p/jc[i];
  printf("%.8e
",ret);
}
int main()
{
  n=rd(); m=rd(); scanf("%s",tp);
  for(int i=1;i<=n;i++)f[i]=rd(),scanf("%lf%lf",&A[i],&B[i]);
  jc[0]=1; for(int i=1;i<=12;i++)jc[i]=jc[i-1]*i;
  for(int i=1,u,v;i<=m;i++)
    {
      scanf("%s",op);
      if(op[0]=='a'){u=rd()+1; v=rd()+1; link(u,v);}
      if(op[0]=='d'){u=rd()+1; v=rd()+1; cut(u,v);}
      if(op[0]=='m'){int x=rd()+1; splay(x); f[x]=rd(); scanf("%lf%lf",&A[x],&B[x]); pushup(x);}//A[x] not A[i]!
      if(op[0]=='t'){u=rd()+1; v=rd()+1; db x; scanf("%lf",&x); query(u,v,x);}
    }
  return 0;
}