[THUWC2017]在美妙的数学王国中畅游

description

BZOJ

solution

(LCT)+泰勒展开。
顺便练了一下(LCT)。

求导数错了一个地方改了好久，果然还是数学不行啊。

Code

#include<bits/stdc++.h>
#include<algorithm>
#include<iostream>
#include<cstdlib>
#include<iomanip>
#include<cstring>
#include<complex>
#include<vector>
#include<cstdio>
#include<string>
#include<bitset>
#include<ctime>
#include<cmath>
#include<queue>
#include<stack>
#include<map>
#include<set>
#define Cpy(x,y) memcpy(x,y,sizeof(x))
#define Set(x,y) memset(x,y,sizeof(x))
#define FILE "a"
#define mp make_pair
#define pb push_back
#define RG register
#define il inline
using namespace std;
typedef unsigned long long ull;
typedef vector<int>VI;
typedef long long ll;
typedef double dd;
const dd eps=1e-7;
const int mod=1e9+7;
const int N=100010;
const int M=1000010;
const int inf=2147483647;
const ll INF=1e18+1;
const ll P=100000;
il ll read(){
	RG ll data=0,w=1;RG char ch=getchar();
	while(ch!='-'&&(ch<'0'||ch>'9'))ch=getchar();
	if(ch=='-')w=-1,ch=getchar();
	while(ch<='9'&&ch>='0')data=data*10+ch-48,ch=getchar();
	return data*w;
}

il void file(){
	srand(time(NULL)+rand());
	freopen(FILE".in","r",stdin);
	freopen(FILE".out","w",stdout);
}

const int K=17;
int n,m;ll fac[K];char st[20];
int fa[N],s[2][N],rv[N],cal[N],top;
dd v[N][20],sum[N][20];
#define isr(i) (s[1][fa[i]]==i)
#define isroot(i) (s[0][fa[i]]!=i&&s[1][fa[i]]!=i)
il void update(int i){
	for(RG int k=0;k<K;k++)
		sum[i][k]=v[i][k]+sum[s[0][i]][k]+sum[s[1][i]][k];
}
il void reverse(int i){swap(s[0][i],s[1][i]);rv[i]^=1;}
il void pushdown(int i){
	if(!rv[i])return;rv[i]=0;
	if(s[0][i])reverse(s[0][i]);
	if(s[1][i])reverse(s[1][i]);
}
il void rot(int i){
	int j=fa[i],k=fa[j];bool b=isr(i);
	if(!isroot(j))s[isr(j)][k]=i;fa[i]=k;
	if(s[!b][i])fa[s[!b][i]]=j;s[b][j]=s[!b][i];
	s[!b][i]=j;fa[j]=i;update(j);
}
il void splay(int i){
	cal[++top]=i;
	for(RG int x=i;!isroot(x);x=fa[x])cal[++top]=fa[x];
	while(top)pushdown(cal[top--]);
	for(RG int j=fa[i];!isroot(i);rot(i),j=fa[i])
		if(!isroot(j))isr(i)^isr(j)?rot(i):rot(j);
	update(i);
}
il void access(int x){
	for(RG int y=0;x;y=x,x=fa[x])splay(x),s[1][x]=y,update(x);
}
il void makeroot(int x){access(x);splay(x);reverse(x);}
il int findroot(int x){
	access(x);splay(x);while(s[0][x])x=s[0][x];return x;
}
il void split(int x,int y){makeroot(x);access(y);splay(y);}
il void link(int x,int y){makeroot(x);fa[x]=y;}
il void cut(int x,int y){split(x,y);fa[x]=s[0][y]=0;update(y);}

il void func(int f,dd a,dd b,dd *g){
	dd r=1,s,c;if(f==1)c=cos(b),s=sin(b);if(f==2)c=exp(b);
	for(RG int i=0;i<K;i++){
		if(f==1){g[i]=((i&1)?c:s)*r;if(i%4>=2)g[i]=-g[i];}
		else if(f==2)g[i]=c*r;
		else if(f==3){g[i]=0;if(!i)g[i]=b;if(i==1)g[i]=a;}
		if(f!=3)g[i]/=fac[i];r*=a;
	}
}
il void modify(int u,int f,dd a,dd b){
	access(u);splay(u);func(f,a,b,v[u]);update(u);
}
il dd query(int u,int v,dd x){
	RG dd ret=0,r=1;split(u,v);
	for(RG int i=0;i<K;i++,r=r*x)ret+=sum[v][i]*r;
	return ret;
}

int main()
{
	fac[0]=1;for(RG int i=1;i<K;i++)fac[i]=fac[i-1]*i;
	n=read();m=read();scanf("%s",st+1);
	RG dd a,b,x,as;
	for(RG int i=1,f;i<=n;i++){
		f=read();scanf("%lf%lf",&a,&b);func(f,a,b,v[i]);
	}
	for(RG int i=1,u,v,c,f;i<=m;i++){
		scanf("%s",st+1);
		if(st[1]=='a'){u=read()+1;v=read()+1;link(u,v);}
		if(st[1]=='d'){u=read()+1;v=read()+1;cut(u,v);}
		if(st[1]=='m'){
			c=read()+1;f=read();scanf("%lf%lf",&a,&b);
			modify(c,f,a,b);
		}
		if(st[1]=='t'){
			u=read()+1;v=read()+1;scanf("%lf",&x);
			if(findroot(u)!=findroot(v))puts("unreachable");
			else printf("%.8lf
",query(u,v,x));
		}
	}
	return 0;
}