LUOGU P1505 [国家集训队]旅游 (树链剖分+线段树)

Posted 2021-01-09 sdfzsyq

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解题思路

快被调死的码农题，，，其实就是一个边权下放到点权的线段树+树剖。

 

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cstdlib>

using namespace std;
const int MAXN = 100005;
const int inf = 0x3f3f3f3f;

inline int rd(){
    int x=0,f=1;char ch=getchar();
    while(!isdigit(ch)) {f=ch==‘-‘?0:1;ch=getchar();}
    while(isdigit(ch))  {x=(x<<1)+(x<<3)+ch-‘0‘;ch=getchar();}
    return f?x:-x;
}

int n,m,head[MAXN],cnt=1,to[MAXN<<1],nxt[MAXN<<1],val[MAXN<<1],num;
int w[MAXN],wt[MAXN],id[MAXN],top[MAXN],siz[MAXN],son[MAXN],fa[MAXN],dep[MAXN];
int Sum[MAXN<<2],Min[MAXN<<2],Max[MAXN<<2];
bool rev[MAXN<<2],lazy[MAXN<<2];

inline void add(int bg,int ed,int ww){
    to[++cnt]=ed,nxt[cnt]=head[bg],head[bg]=cnt,val[cnt]=ww;
}

void dfs1(int x,int f,int d){
    dep[x]=d,fa[x]=f,siz[x]=1;int maxson=-1,u;
    for(register int i=head[x];i;i=nxt[i]){
        u=to[i];if(u==f) continue;
        dfs1(u,x,d+1);siz[x]+=siz[u];w[u]=val[i];
        if(siz[u]>maxson) {maxson=siz[u];son[x]=u;}
    }
}

void dfs2(int x,int topf){
    top[x]=topf;id[x]=++num;wt[num]=w[x];
    if(!son[x]) return;dfs2(son[x],topf);int u;
    for(register int i=head[x];i;i=nxt[i]){
        u=to[i];if(u==fa[x] || u==son[x]) continue;
        dfs2(u,u);
    }
}

inline void pushdown(int x){
    rev[x<<1]^=1;rev[x<<1|1]^=1;rev[x]^=1;
    Sum[x<<1]=-Sum[x<<1];Sum[x<<1|1]=-Sum[x<<1|1];
    swap(Min[x<<1],Max[x<<1]);swap(Min[x<<1|1],Max[x<<1|1]);
    Min[x<<1]=-Min[x<<1];Min[x<<1|1]=-Min[x<<1|1];
    Max[x<<1]=-Max[x<<1];Max[x<<1|1]=-Max[x<<1|1];
}

void build(int x,int l,int r){
    if(l==r) {if(l==1) Min[x]=inf,Max[x]=-inf; else Sum[x]=Min[x]=Max[x]=wt[l];return;}
    int mid=(l+r)>>1;
    build(x<<1,l,mid);build(x<<1|1,mid+1,r);
    Sum[x]=Sum[x<<1]+Sum[x<<1|1];
    Min[x]=min(Min[x<<1],Min[x<<1|1]);
    Max[x]=max(Max[x<<1],Max[x<<1|1]);
}

void update(int x,int l,int r,int L,int R,int ww){
    if(L<=l && r<=R) {
        if(ww==-inf) {rev[x]^=1;Sum[x]=-Sum[x];swap(Min[x],Max[x]);Min[x]=-Min[x];Max[x]=-Max[x];}
        else Sum[x]=Min[x]=Max[x]=ww;
        return;
    }
    int mid=(l+r)>>1;if(rev[x]) pushdown(x);
    if(L<=mid) update(x<<1,l,mid,L,R,ww);
    if(mid<R)  update(x<<1|1,mid+1,r,L,R,ww);
    Sum[x]=Sum[x<<1]+Sum[x<<1|1];
    Min[x]=min(Min[x<<1],Min[x<<1|1]);
    Max[x]=max(Max[x<<1],Max[x<<1|1]);
}

int query_Sum(int x,int l,int r,int L,int R){
    if(L<=l && r<=R) return Sum[x];
    int mid=(l+r)>>1,ret=0;if(rev[x]) pushdown(x);
    if(L<=mid) ret+=query_Sum(x<<1,l,mid,L,R);
    if(mid<R)  ret+=query_Sum(x<<1|1,mid+1,r,L,R);
    return ret;
}

int query_Max(int x,int l,int r,int L,int R){
    if(L<=l && r<=R) return Max[x];
    int mid=(l+r)>>1,ret=-inf;if(rev[x]) pushdown(x);
    if(L<=mid) ret=max(ret,query_Max(x<<1,l,mid,L,R));
    if(mid<R)  ret=max(ret,query_Max(x<<1|1,mid+1,r,L,R));
    return ret;
}

int query_Min(int x,int l,int r,int L,int R){
    if(L<=l && r<=R) return Min[x];
    int mid=(l+r)>>1,ret=inf;if(rev[x]) pushdown(x);
    if(L<=mid) ret=min(ret,query_Min(x<<1,l,mid,L,R));
    if(mid<R)  ret=min(ret,query_Min(x<<1|1,mid+1,r,L,R));
    return ret;
}

void updRev(int x,int y){
    while(top[x]!=top[y]){
        if(dep[top[x]]<dep[top[y]]) swap(x,y);
        update(1,1,n,id[top[x]],id[x],-inf);
        x=fa[top[x]];
    }
    if(dep[x]>dep[y]) swap(x,y);
    if(x!=y) update(1,1,n,id[x]+1,id[y],-inf);
}

inline int qSum(int x,int y){
    int ret=0;
    while(top[x]!=top[y]){
        if(dep[top[x]]<dep[top[y]]) swap(x,y);
        ret+=query_Sum(1,1,n,id[top[x]],id[x]);
        x=fa[top[x]];
    }
    if(dep[x]>dep[y]) swap(x,y);
    if(x!=y) ret+=query_Sum(1,1,n,id[x]+1,id[y]);
    return ret;
}

inline int qMax(int x,int y){
    int ret=-inf;
    while(top[x]!=top[y]){
        if(dep[top[x]]<dep[top[y]]) swap(x,y);
        ret=max(ret,query_Max(1,1,n,id[top[x]],id[x]));
        x=fa[top[x]];
    }
    if(dep[x]>dep[y]) swap(x,y);
    if(x!=y) ret=max(ret,query_Max(1,1,n,id[x]+1,id[y]));
    return ret;
}

inline int qMin(int x,int y){
    int ret=inf;
    while(top[x]!=top[y]){
        if(dep[top[x]]<dep[top[y]]) swap(x,y);
        ret=min(ret,query_Min(1,1,n,id[top[x]],id[x]));
        x=fa[top[x]];
    }
    if(dep[x]>dep[y]) swap(x,y);if(x!=y) ret=min(ret,query_Min(1,1,n,id[x]+1,id[y]));
    return ret;
}

inline int pre(int x){
    return dep[to[x<<1]]>dep[to[x<<1^1]]?to[x<<1]:to[x<<1^1];
}

int main(){
//    freopen("wrong.out","w",stdout);
    n=rd();int x,y,z;char s[5];
    for(int i=1;i<n;i++){
        x=rd()+1,y=rd()+1,z=rd();
        add(x,y,z),add(y,x,z);
    }
    dfs1(1,0,1);dfs2(1,1);build(1,1,n);m=rd();
    while(m--){
        scanf("%s",s+1);x=rd(),y=rd();
        if(s[1]==‘C‘) update(1,1,n,id[pre(x)],id[pre(x)],y);
        else if(s[1]==‘N‘) updRev(x+1,y+1);
        else if(s[1]==‘S‘) printf("%d
",qSum(x+1,y+1));
        else if(s[2]==‘A‘) printf("%d
",qMax(x+1,y+1));
        else printf("%d
",qMin(x+1,y+1));
    }
    return 0;
}

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