[BZOJ2819]Nim（树链剖分）

题目描述

题解

代码

#include<iostream>
#include<cstring>
#include<cstdio>
using namespace std;

const int max_n=5e5+5;
const int max_m=max_n*2;
const int max_tree=max_n*4;

int n,m,x,y,u,t,ans,q,N,a[max_n];
int tot,point[max_n],nxt[max_m],v[max_m];
int size[max_n],h[max_n],father[max_n],son[max_n],top[max_n],num[max_n],val[max_n];
int tree[max_tree];

inline void addedge(int x,int y)
{
++tot; nxt[tot]=point[x]; point[x]=tot; v[tot]=y;
++tot; nxt[tot]=point[y]; point[y]=tot; v[tot]=x;
}
inline void dfs_1(int x,int fa,int dep)
{
size[x]=1; h[x]=dep; father[x]=fa;
int maxson=0;
for (int i=point[x];i;i=nxt[i])
if (v[i]!=fa)
{
dfs_1(v[i],x,dep+1);
size[x]+=size[v[i]];
if (size[v[i]]>maxson)
{
maxson=size[v[i]];
son[x]=v[i];
}
}
}
inline void dfs_2(int x,int fa)
{
if (son[fa]!=x) top[x]=x;
else top[x]=top[fa];
num[x]=++N; val
=a[x];
if (son[x]) dfs_2(son[x],x);
for (int i=point[x];i;i=nxt[i])
if (v[i]!=fa&&v[i]!=son[x])
dfs_2(v[i],x);
}
inline void update(int now)
{
tree[now]=tree[now<<1]^tree[now<<1|1];
}
inline void build(int now,int l,int r)
{
int mid=(l+r)>>1;
if (l==r)
{
tree[now]=val[l];
return;
}
build(now<<1,l,mid);
build(now<<1|1,mid+1,r);
update(now);
}
inline void point_change(int now,int l,int r,int x,int v)
{
int mid=(l+r)>>1;
if (l==r)
{
tree[now]=v;
return;
}
if (x<=mid)
point_change(now<<1,l,mid,x,v);
else
point_change(now<<1|1,mid+1,r,x,v);
update(now);
}
inline int query(int now,int l,int r,int lrange,int rrange)
{
int mid=(l+r)>>1,ans=0;
if (lrange<=l&&r<=rrange)
return tree[now];
if (lrange<=mid)
ans^=query(now<<1,l,mid,lrange,rrange);
if (mid+1<=rrange)
ans^=query(now<<1|1,mid+1,r,lrange,rrange);
return ans;
}
int main()
{
scanf("%d",&n);
for (int i=1;i<=n;++i) scanf("%d",&a[i]);
for (int i=1;i<n;++i)
{
scanf("%d%d",&x,&y);
addedge(x,y);
}
dfs_1(1,0,1);
dfs_2(1,0);
build(1,1,N);
scanf("%d",&q);
for (int i=1;i<=q;++i)
{
char opt=getchar();
while (opt!='Q'&&opt!='C') opt=getchar();
if (opt=='C')
{
scanf("%d%d",&x,&y);
point_change(1,1,N,num[x],y);
}
else
{
scanf("%d%d",&u,&t);
ans=0;
int f1=top[u],f2=top[t];
while (f1!=f2)
{
if (h[f1]<h[f2])
{
swap(u,t);
swap(f1,f2);
}
ans^=query(1,1,N,num[f1],num[u]);
u=father[f1];
f1=top[u];
}
if (num[u]>num[t]) swap(u,t);
ans^=query(1,1,N,num[u],num[t]);
if (!ans) printf("No\n");
else printf("Yes\n");
}
}
}

#include<iostream>
#include<cstring>
#include<cstdio>
using namespace std;

const int max_n=5e5+5;
const int max_m=max_n;
const int max_e=max_m*2;
const int max_tree=max_n*4;

int n,m,x,y,u,t,ans,q,N,a[max_n];
int tot,point[max_n],nxt[max_e],v[max_e];
int size[max_n],h[max_n],father[max_n],son[max_n],top[max_n],num[max_n],val[max_n];
int strack[max_n],cur[max_n],use[max_n];
int tree[max_tree];

inline void addedge(int x,int y)
{
++tot; nxt[tot]=point[x]; point[x]=tot; v[tot]=y;
++tot; nxt[tot]=point[y]; point[y]=tot; v[tot]=x;
}
inline void dfs_1()
{
int temp=0; h[1]=1;
strack[++temp]=1; size[1]=1;
for (int i=1;i<=n;++i) cur[i]=point[i];
while (temp)
{
int x=strack[temp];
if (v[cur[x]]==father[x]) cur[x]=nxt[cur[x]];
if (!cur[x])
{
temp--;
if (father[x])
{
size[father[x]]+=size[x];
if (size[x]>size[son[father[x]]]) son[father[x]]=x;
}
continue;
}
int vt=v[cur[x]];
strack[++temp]=vt;
size[vt]=1; h[vt]=h[x]+1; father[vt]=x;
cur[x]=nxt[cur[x]];
}
}
inline void dfs_2()
{
int temp=0;
strack[++temp]=1; top[1]=1; num[1]=++N; val
=a[1];
for (int i=1;i<=n;++i) cur[i]=point[i];
while (temp)
{
int x=strack[temp];
if (!use[x])
{
use[x]=1;
int vt=son[x];
if (vt)
{
strack[++temp]=vt;
top[vt]=top[x];
num[vt]=++N;
val
=a[vt];
}
continue;
}
while (cur[x]&&(v[cur[x]]==father[x]||v[cur[x]]==son[x])) cur[x]=nxt[cur[x]];
if (!cur[x])
{
temp--;
continue;
}
else
{
int vt=v[cur[x]];
strack[++temp]=vt;
top[vt]=vt; num[vt]=++N; val
=a[vt];
cur[x]=nxt[cur[x]];
}
}
}
inline void update(int now)
{
tree[now]=tree[now<<1]^tree[now<<1|1];
}
inline void build(int now,int l,int r)
{
int mid=(l+r)>>1;
if (l==r)
{
tree[now]=val[l];
return;
}
build(now<<1,l,mid);
build(now<<1|1,mid+1,r);
update(now);
}
inline void point_change(int now,int l,int r,int x,int v)
{
int mid=(l+r)>>1;
if (l==r)
{
tree[now]=v;
return;
}
if (x<=mid)
point_change(now<<1,l,mid,x,v);
else
point_change(now<<1|1,mid+1,r,x,v);
update(now);
}
inline int query(int now,int l,int r,int lrange,int rrange)
{
int mid=(l+r)>>1,ans=0;
if (lrange<=l&&r<=rrange)
return tree[now];
if (lrange<=mid)
ans^=query(now<<1,l,mid,lrange,rrange);
if (mid+1<=rrange)
ans^=query(now<<1|1,mid+1,r,lrange,rrange);
return ans;
}
int main()
{
scanf("%d",&n);
for (int i=1;i<=n;++i) scanf("%d",&a[i]);
for (int i=1;i<n;++i)
{
scanf("%d%d",&x,&y);
addedge(x,y);
}
dfs_1();
dfs_2();
build(1,1,N);
scanf("%d",&q);
for (int i=1;i<=q;++i)
{
char opt=getchar();
while (opt!='Q'&&opt!='C') opt=getchar();
if (opt=='C')
{
scanf("%d%d",&x,&y);
point_change(1,1,N,num[x],y);
}
else
{
scanf("%d%d",&u,&t);
ans=0;
int f1=top[u],f2=top[t];
while (f1!=f2)
{
if (h[f1]<h[f2])
{
swap(u,t);
swap(f1,f2);
}
ans^=query(1,1,N,num[f1],num[u]);
u=father[f1];
f1=top[u];
}
if (num[u]>num[t]) swap(u,t);
ans^=query(1,1,N,num[u],num[t]);
if (!ans) printf("No\n");
else printf("Yes\n");
}
}
}