Steven_MengのBlog

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树链剖分模板题,用支持区间加,区间覆盖,查询区间最大的线段树实现。

注意覆盖标记$cotag$优先级比加标记$tag$要高,所以覆盖时直接设$tag=0$

需要把$Change$操作转化为顶点$U[k]$和$V[k]$的覆盖操作

其他没什么好说的,注意细节即可

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// luogu-judger-enable-o2
#include <bits/stdc++.h>
#define MAXN 2000005
#define HA 19260817
#define INF 0x3f3f3f3f
using namespace std;
inline int read(){
int x=0,f=1;
char ch=getchar();
while (ch<'0'||ch>'9'){
if (ch=='-') f=-1;
ch=getchar();
}
while (ch>='0'&&ch<='9'){
x=(x<<3)+(x<<1)+(ch^'0');
ch=getchar();
}
return x*f;
}
struct Edge{
int to,len;
};
vector<Edge>G[MAXN];
inline void AddEdge(int u,int v,int w){
G[u].push_back(Edge{v,w});
}
int sz[MAXN],big[MAXN],fa[MAXN],top[MAXN],dep[MAXN],tofa[MAXN];
void dfs1(int u,int father){
fa[u]=father;sz[u]=1;
for (register int i=0;i<G[u].size();++i){
int v=G[u][i].to;
if (v!=father){
dep[v]=dep[u]+1;
tofa[v]=G[u][i].len;
dfs1(v,u);
sz[u]+=sz[v];
if (sz[big[u]]<sz[v]) big[u]=v;
}
}
}
int ql[MAXN],alb[MAXN],cnt;
void dfs2(int u,int t){
alb[ql[u]=++cnt]=u;
top[u]=t;
if (big[u]) dfs2(big[u],t);
for (register int i=0;i<(int)G[u].size();++i){
int v=G[u][i].to;
if (v!=fa[u]&&v!=big[u]){
dfs2(v,v);
}
}
}
namespace SegmentTree{
struct node{
int l,r;
int maxn,tag,cotag;
}tree[MAXN<<2];
#define lc i<<1
#define rc i<<1|1
inline void pushup(int i){
tree[i].maxn=max(tree[lc].maxn,tree[rc].maxn);
}
inline void Add(int i,int val){
tree[i].maxn+=val;
tree[i].tag+=val;
}
inline void Cover(int i,int val){
tree[i].maxn=val;
tree[i].cotag=val;
tree[i].tag=0;
}
inline void pushdown(int i){
if (tree[i].cotag!=HA){
Cover(lc,tree[i].cotag);
Cover(rc,tree[i].cotag);
tree[i].cotag=HA;
}
if (tree[i].tag){
Add(lc,tree[i].tag);
Add(rc,tree[i].tag);
tree[i].tag=0;
}
}
void Build(int i,int l,int r){
tree[i].l=l,tree[i].r=r;
tree[i].cotag=HA,tree[i].tag=0;
if (l==r){
tree[i].maxn=tofa[alb[l]];
return ;
}
int mid=(l+r)>>1;
Build(lc,l,mid);
Build(rc,mid+1,r);
pushup(i);
}
int Query(int i,int L,int R){
if (L<=tree[i].l&&tree[i].r<=R){
return tree[i].maxn;
}
int mid=(tree[i].l+tree[i].r)>>1,ans=-INF;
pushdown(i);
if (L<=mid) ans=max(ans,Query(lc,L,R));
if (mid<R) ans=max(ans,Query(rc,L,R));
return ans;
}
void CoverInterval(int i,int L,int R,int val){
if (L<=tree[i].l&&tree[i].r<=R){
Cover(i,val);
return ;
}
int mid=(tree[i].l+tree[i].r)>>1;
pushdown(i);
if (L<=mid) CoverInterval(lc,L,R,val);
if (mid<R) CoverInterval(rc,L,R,val);
pushup(i);
}
void AddInterval(int i,int L,int R,int val){
if (L<=tree[i].l&&tree[i].r<=R){
Add(i,val);
return ;
}
int mid=(tree[i].l+tree[i].r)>>1;
pushdown(i);
if (L<=mid) AddInterval(lc,L,R,val);
if (mid<R) AddInterval(rc,L,R,val);
pushup(i);
}
}
using namespace SegmentTree;
inline void Add_Chain(int u,int v,int w){
while (top[u]!=top[v]){
if (dep[top[u]]<dep[top[v]]){
swap(u,v);
}
AddInterval(1,ql[top[u]],ql[u],w);
u=fa[top[u]];
}
if (dep[u]>dep[v]) swap(u,v);
AddInterval(1,ql[u]+1,ql[v],w);
}
inline void Cover_Chain(int u,int v,int w){
while (top[u]!=top[v]){
if (dep[top[u]]<dep[top[v]]){
swap(u,v);
}
CoverInterval(1,ql[top[u]],ql[u],w);
u=fa[top[u]];
}
if (dep[u]>dep[v]) swap(u,v);
CoverInterval(1,ql[u]+1,ql[v],w);
}
inline int Query_Chain(int u,int v){
int ans=-INF;
while (top[u]!=top[v]){
if (dep[top[u]]<dep[top[v]]){
swap(u,v);
}
ans=max(ans,Query(1,ql[top[u]],ql[u]));
u=fa[top[u]];
}
if (dep[u]>dep[v]) swap(u,v);
return max(ans,Query(1,ql[u]+1,ql[v]));
}
int U[MAXN],V[MAXN];
inline void Init(){
dfs1(1,0);
dfs2(1,1);
}
int main(){
int n=read();
for (register int i=1;i<n;++i){
int u=read(),v=read(),w=read();
AddEdge(u,v,w);
AddEdge(v,u,w);
U[i]=u,V[i]=v;
}
Init();
Build(1,1,n);
while (true){
char ch[10];
scanf("%s",ch);
if (ch[0]=='C'&&ch[1]=='h'){
int k=read(),w=read();
Cover_Chain(U[k],V[k],w);
}
else if (ch[0]=='C'&&ch[1]=='o'){
int u=read(),v=read(),w=read();
Cover_Chain(u,v,w);
}
else if (ch[0]=='A'){
int u=read(),v=read(),w=read();
Add_Chain(u,v,w);
}
else if (ch[0]=='M'){
int u=read(),v=read();
printf("%d\n",Query_Chain(u,v));
}
else {
break;
}
}
}

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