[HDU3966]Aragorn's Story（树链剖分）

题目描述

题解

代码

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

const int max_n=5e4+5;
const int max_e=max_n*2;
const int max_N=max_n*4;

int w[max_n],h[max_n],father[max_n],son[max_n],size[max_n];
int tree[max_n],num[max_n],top[max_n];
int point[max_n],nxt[max_e],v[max_e],tot;
int sum[max_N],delta[max_N];
int n,m,p,f1,f2,u,t,x,y,c,ans,N;

inline void clear(){
memset(w,0,sizeof(w));
memset(h,0,sizeof(h));
memset(father,0,sizeof(father));
memset(son,0,sizeof(son));
memset(size,0,sizeof(size));
memset(tree,0,sizeof(tree));
memset(num,0,sizeof(num));
memset(v,0,sizeof(v));
tot=0;
memset(sum,0,sizeof(sum));
memset(delta,0,sizeof(delta));
memset(point,0,sizeof(point));
memset(nxt,0,sizeof(nxt));
memset(v,0,sizeof(v));
f1=f2=u=t=x=y=c=ans=N=0;
}

inline void add(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;
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){
sum[now]=sum[now<<1]+sum[now<<1|1];
}

inline void pushdown(int now,int l,int r,int mid){
if (delta[now]){
sum[now<<1]+=delta[now]*(mid-l+1);
delta[now<<1]+=delta[now];
sum[now<<1|1]+=delta[now]*(r-mid);
delta[now<<1|1]+=delta[now];
delta[now]=0;
}
}

inline void build(int now,int l,int r){
int mid=(l+r)>>1;
if (l==r){
sum[now]=w[tree[l]];
return;
}
build(now<<1,l,mid);
build(now<<1|1,mid+1,r);
update(now);
}

inline void interval_change(int now,int l,int r,int lrange,int rrange,int v){
int mid=(l+r)>>1;
if (lrange<=l&&r<=rrange){
sum[now]+=v*(r-l+1);
delta[now]+=v;
return;
}
pushdown(now,l,r,mid);
if (lrange<=mid)
interval_change(now<<1,l,mid,lrange,rrange,v);
if (mid+1<=rrange)
interval_change(now<<1|1,mid+1,r,lrange,rrange,v);
update(now);
}

inline int query(int now,int l,int r,int x){
int mid=(l+r)>>1,ans=0;
if (l==r) return sum[now];
pushdown(now,l,r,mid);
if (x<=mid)
ans+=query(now<<1,l,mid,x);
else
ans+=query(now<<1|1,mid+1,r,x);
return ans;
}

inline void ID(int u,int t,int x){
f1=top[u],f2=top[t];
while (f1!=f2){
if (h[f1]<h[f2]){
swap(f1,f2);
swap(u,t);
}
interval_change(1,1,N,num[f1],num[u],x);
u=father[f1];
f1=top[u];
}
if (num[u]>num[t]) swap(u,t);
interval_change(1,1,N,num[u],num[t],x);
}

int main(){
while (~scanf("%d%d%d",&n,&m,&p)){
clear();

for (int i=1;i<=n;++i)
scanf("%d",&w[i]);
for (int i=1;i<=m;++i){
scanf("%d%d",&x,&y);
add(x,y);
}

dfs_1(1,0,1);
dfs_2(1,0);
for (int i=1;i<=n;++i)
tree[num[i]]=i;

build(1,1,N);
for (int i=1;i<=p;++i){
char order=getchar();
while (order!='Q'&&order!='I'&&order!='D') order=getchar();
switch(order){
case 'Q':{
scanf("%d",&c);
ans=query(1,1,N,num[c]);
printf("%d\n",ans);
break;
}
case 'I':{
scanf("%d%d%d",&u,&t,&x);
ID(u,t,x);
break;
}
case 'D':{
scanf("%d%d%d",&u,&t,&x);
ID(u,t,-x);
break;
}
}
}
}
}

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

const int max_n=5e4+5;
const int max_e=max_n*2;
const int max_N=max_n*4;

int w[max_n],h[max_n],father[max_n],son[max_n],size[max_n];
int tree[max_n],num[max_n],top[max_n];
int point[max_n],nxt[max_e],v[max_e],tot;
int sum[max_N],delta[max_N];
int n,m,p,f1,f2,u,t,x,y,c,ans,N;
int strack[max_n],cur[max_n],use[max_n];

inline void clear(){
memset(w,0,sizeof(w));
memset(h,0,sizeof(h));
memset(father,0,sizeof(father));
memset(son,0,sizeof(son));
memset(size,0,sizeof(size));
memset(tree,0,sizeof(tree));
memset(num,0,sizeof(num));
memset(v,0,sizeof(v));
tot=0;
memset(sum,0,sizeof(sum));
memset(delta,0,sizeof(delta));
memset(point,0,sizeof(point));
memset(nxt,0,sizeof(nxt));
memset(v,0,sizeof(v));
memset(use,0,sizeof(use));
memset(strack,0,sizeof(strack));
memset(cur,0,sizeof(cur));
f1=f2=u=t=x=y=c=ans=N=0;
}

inline void add(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;
strack[++temp]=1; size[1]=1; h[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;
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;
}
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;
cur[x]=nxt[cur[x]];
}
}
}

inline void update(int now){
sum[now]=sum[now<<1]+sum[now<<1|1];
}

inline void pushdown(int now,int l,int r,int mid){
if (delta[now]){
sum[now<<1]+=delta[now]*(mid-l+1);
delta[now<<1]+=delta[now];
sum[now<<1|1]+=delta[now]*(r-mid);
delta[now<<1|1]+=delta[now];
delta[now]=0;
}
}

inline void build(int now,int l,int r){
int mid=(l+r)>>1;
if (l==r){
sum[now]=w[tree[l]];
return;
}
build(now<<1,l,mid);
build(now<<1|1,mid+1,r);
update(now);
}

inline void interval_change(int now,int l,int r,int lrange,int rrange,int v){
int mid=(l+r)>>1;
if (lrange<=l&&r<=rrange){
sum[now]+=v*(r-l+1);
delta[now]+=v;
return;
}
pushdown(now,l,r,mid);
if (lrange<=mid)
interval_change(now<<1,l,mid,lrange,rrange,v);
if (mid+1<=rrange)
interval_change(now<<1|1,mid+1,r,lrange,rrange,v);
update(now);
}

inline int query(int now,int l,int r,int x){
int mid=(l+r)>>1,ans=0;
if (l==r) return sum[now];
pushdown(now,l,r,mid);
if (x<=mid)
ans+=query(now<<1,l,mid,x);
else
ans+=query(now<<1|1,mid+1,r,x);
return ans;
}

inline void ID(int u,int t,int x){
f1=top[u],f2=top[t];
while (f1!=f2){
if (h[f1]<h[f2]){
swap(f1,f2);
swap(u,t);
}
interval_change(1,1,N,num[f1],num[u],x);
u=father[f1];
f1=top[u];
}
if (num[u]>num[t]) swap(u,t);
interval_change(1,1,N,num[u],num[t],x);
}

int main(){
while (~scanf("%d%d%d",&n,&m,&p)){
clear();

for (int i=1;i<=n;++i)
scanf("%d",&w[i]);
for (int i=1;i<=m;++i){
scanf("%d%d",&x,&y);
add(x,y);
}
dfs_1();
dfs_2();
for (int i=1;i<=n;++i)
tree[num[i]]=i;

build(1,1,N);
for (int i=1;i<=p;++i){
char order=getchar();
while (order!='Q'&&order!='I'&&order!='D') order=getchar();
switch(order){
case 'Q':{
scanf("%d",&c);
ans=query(1,1,N,num[c]);
printf("%d\n",ans);
break;
}
case 'I':{
scanf("%d%d%d",&u,&t,&x);
ID(u,t,x);
break;
}
case 'D':{
scanf("%d%d%d",&u,&t,&x);
ID(u,t,-x);
break;
}
}
}
}
}