bzoj 3052: [wc2013]糖果公园 带修改莫队

3052: [wc2013]糖果公园

Time Limit: 250 Sec Memory Limit: 512 MB
Submit: 506 Solved: 189
[Submit][Status]

Description

Input

Output

Sample Input

Sample Input

Sample Output

84

131

27

84

HINT

　　本来这道题想到了莫队算法，但是看到带修改就直接放弃了。结果看题解才发现带修改居然也能用莫队！！！之所以可以这样用，是因为修改的时间复杂度非常非常低，以至于可以在修改的时间轴上任意跳跃。具体细节自己去看其他题解啦。

　　写的有点长，但是跑的还算比较快。

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;
#define MAXN 100100
#define MAXB 2200
#define MAXQ 100100
#define MAXV MAXN
#define MAXE MAXV*2
typedef long long qword;
inline int nextInt()
{
register int x=0;
register int ch;
while (ch=getchar(),ch<'0' || ch>'9');
while (x=x*10+ch-'0',ch=getchar(),ch<='9' && ch>='0');
return x;
}
int n,m,q,sb;
struct Edge
{
int np;
Edge *next;
}E[MAXE],*V[MAXV];
int tope=-1;
int que[MAXN];
void addedge(int x,int y)
{
E[++tope].np=y;
E[tope].next=V[x];
V[x]=&E[tope];
}
int depth[MAXN];
int pnt[MAXN];
int top[MAXN],bsiz[MAXN];
int belong[MAXN];
int topb=0;
void bfs1()
{
Edge *ne;
int now;
int head=-1,tail=0;
que[0]=1;
pnt[1]=1;
belong[1]=++topb;
top[1]=1;
bsiz[1]=1;
depth[1]=1;
while (head<tail)
{
now=que[++head];
for (ne=V[now];ne;ne=ne->next)
{
if (ne->np==pnt[now])continue;
que[++tail]=ne->np;
pnt[ne->np]=now;
depth[ne->np]=depth[now]+1;
if (bsiz[belong[now]]<sb)
{
bsiz[belong[now]]++;
belong[ne->np]=belong[now];
top[ne->np]=top[now];
}else
{
belong[ne->np]=++topb;
bsiz[topb]=1;
top[ne->np]=ne->np;
}
}
}
}
int jump[20][MAXN];
void init_lca()
{
for (int i=1;i<=n;i++)
jump[0][i]=pnt[i];
for (int j=1;j<20;j++)
for (int i=1;i<=n;i++)
jump[j][i]=jump[j-1][jump[j-1][i]];
}
int lca(int x,int y)
{
if (depth[x]<depth[y])swap(x,y);
int dep=depth[x]-depth[y];
for (int i=0;i<20;i++)
if (dep & (1<<i))
x=jump[i][x];
if (x==y)return x;
for (int i=19;i>=0;i--)
if (jump[i][x]!=jump[i][y])
x=jump[i][x],y=jump[i][y];
return pnt[x];
}
int get_dis(int x,int y)
{
return depth[x]+depth[y]-2*depth[lca(x,y)];
}
struct qur_t
{
int s,t,id;
int upper_pos;
qword ans;
}qur[MAXQ];
int topq=-1;
bool cmp_qur_block(qur_t a1,qur_t a2)
{
if (belong[a1.s]!=belong[a2.s])
return belong[a1.s]<belong[a2.s];
if (belong[a1.t]!=belong[a2.t])
return belong[a1.t]<belong[a2.t];
return a1.id<a2.id;
}
bool cmp_qur_id(qur_t a1,qur_t a2)
{
return a1.id<a2.id;
}
int sweet[MAXN];
qword suprise[MAXN];
int candy[MAXN];
struct mdfy_t
{
int pos,cnew,cold,id;
}mdfy[MAXN];
int topm=-1;
struct path
{
int s,t,a,ds;
path(int s,int t):s(s),t(t)
{
a=lca(s,t);
ds=depth[s]+depth[t]-2*depth[a];
}
path(){}
bool inside(int x)
{
return get_dis(x,s)+get_dis(x,t)==ds;
}
void get_path(int *step,int &tops)
{
tops=-1;
for (int x=s;x!=a;x=pnt[x])
step[++tops]=x;
tops=ds;
for (int x=t;x!=a;x=pnt[x])
step[tops--]=x;
step[tops--]=a;
tops=ds;
}
};
int tot[MAXN];
bool inside[MAXN];
int step[MAXN],tops;
int main()
{
//    freopen("input.txt","r",stdin);
//    freopen("output.txt","w",stdout);
int x,y,z;
n=nextInt(),m=nextInt(),q=nextInt();
sb=pow(n,2.0/3);
for (int i=1;i<=m;i++)
sweet[i]=nextInt();
for (int i=1;i<=n;i++)
suprise[i]=nextInt();
for (int i=1;i<=n;i++)suprise[i]+=suprise[i-1];
for (int i=1;i<n;i++)
{
x=nextInt(),y=nextInt();
addedge(x,y);
addedge(y,x);
}
for (int i=1;i<=n;i++)
candy[i]=nextInt();
int opt;
for (int i=1;i<=q;i++)
{
opt=nextInt();
if (opt==0)
{
x=nextInt(),y=nextInt();
++topm;
mdfy[topm].pos=x;
mdfy[topm].cnew=y;
mdfy[topm].cold=candy[x];
candy[x]=y;
mdfy[topm].id=i;
}else
{
x=nextInt(),y=nextInt();
++topq;
qur[topq].s=x;
qur[topq].t=y;
qur[topq].upper_pos=topm+1;
qur[topq].id=i;
}
}
for (int i=topm;i>=0;i--)
candy[mdfy[i].pos]=mdfy[i].cold;
bfs1();
init_lca();
sort(qur,qur+topq+1,cmp_qur_block);
for (int i=0;i<qur[0].upper_pos;i++)
candy[mdfy[i].pos]=mdfy[i].cnew;
int a;
a=lca(qur[0].s,qur[0].t);
qword nsum=0;
for (x=qur[0].s;x!=a;x=pnt[x])
{
inside[x]=true;
tot[candy[x]]++;
nsum+=(suprise[tot[candy[x]]]-suprise[tot[candy[x]]-1])*sweet[candy[x]];
}
for (y=qur[0].t;;y=pnt[y])
{
inside[y]=true;
tot[candy[y]]++;
nsum+=(suprise[tot[candy[y]]]-suprise[tot[candy[y]]-1])*sweet[candy[y]];
if (y==a)break;
}
qur[0].ans=nsum;
path pnow(qur[0].s,qur[0].t);
path pwalk;
for (int i=1;i<=topq;i++)
{
for (int kk=0;kk<2;kk++)
{
if (kk==0)
pwalk=path(qur[i-1].s,qur[i].s);
else
pwalk=path(qur[i-1].t,qur[i].t);
pwalk.get_path(step,tops);
bool flag=true;
for (int j=0;j<=tops+1;j++)
{
if (j!=tops+1 && inside[step[j]])
{
inside[step[j]]=false;
tot[candy[step[j]]]--;
nsum+=(suprise[tot[candy[step[j]]]]-suprise[tot[candy[step[j]]]+1])*sweet[candy[step[j]]];
}else
{
if (flag)
{
inside[step[j-1]]=true;
tot[candy[step[j-1]]]++;
nsum+=(suprise[tot[candy[step[j-1]]]]-suprise[tot[candy[step[j-1]]]-1])*sweet[candy[step[j-1]]];
flag=false;
}
if (j==tops+1)break;
inside[step[j]]=true;
tot[candy[step[j]]]++;
nsum+=(suprise[tot[candy[step[j]]]]-suprise[tot[candy[step[j]]]-1])*sweet[candy[step[j]]];
}
}
}
if (qur[i-1].upper_pos<qur[i].upper_pos)
{
for (int j=qur[i-1].upper_pos;j<qur[i].upper_pos;j++)
{
if (candy[mdfy[j].pos]!=mdfy[j].cold)throw;
candy[mdfy[j].pos]=mdfy[j].cnew;
if (inside[mdfy[j].pos])
{
tot[mdfy[j].cold]--;
nsum+=(suprise[tot[mdfy[j].cold]]-suprise[tot[mdfy[j].cold]+1])*sweet[mdfy[j].cold];
tot[mdfy[j].cnew]++;
nsum+=(suprise[tot[mdfy[j].cnew]]-suprise[tot[mdfy[j].cnew]-1])*sweet[mdfy[j].cnew];
}
}
}else
{
for (int j=qur[i-1].upper_pos-1;j>=qur[i].upper_pos;j--)
{
if (candy[mdfy[j].pos]!=mdfy[j].cnew)throw;
candy[mdfy[j].pos]=mdfy[j].cold;
if (inside[mdfy[j].pos])
{
tot[mdfy[j].cnew]--;
nsum+=(suprise[tot[mdfy[j].cnew]]-suprise[tot[mdfy[j].cnew]+1])*sweet[mdfy[j].cnew];
tot[mdfy[j].cold]++;
nsum+=(suprise[tot[mdfy[j].cold]]-suprise[tot[mdfy[j].cold]-1])*sweet[mdfy[j].cold];
}
}
}
qur[i].ans=nsum;
}
sort(qur,qur+topq+1,cmp_qur_id);
for (int i=0;i<=topq;i++)
printf("%lld\n",qur[i].ans);
}