HDU 5296 Annoying problem （樹狀數組+dfs序+倍增）

題意：一顆n節點的帶權無向樹，一個初始爲空的集合S，有兩種操作：1 x 如果S中沒有x，加入x ；2 x 如果S中存在x，刪除x。每次操作完後求出使S集合連通的最小邊權和。

解析：設root爲S集合的LCA。點i的左右時間戳爲L[i],R[i]，ans爲當前的權重和。

當前集合S中添加節點x，如果x不在root的子樹中，那麼ans += dis[x]+dis[root]-2*dis[lca(x,root)]。如果x在root子樹中，那麼向上找到離x最近的且子樹中包含集合S中某些點的節點u，ans += dis[x] - dis[u];

當前集合S中刪除節點x，刪除後的集合爲S'，如果lca(S') != root，那麼ans -= dis[x] + dis[lca(S')] - 2*dis[root]。如果lca(S') = root，那麼向上找到離x最近的且子樹中包含集合S’中某些點的節點u，ans -= dis[x] - dis[u];

[code]:

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<vector>
#include<functional>
#include<queue>
#include<set>

#define lowbit(i) (i&-i)
using namespace std;
typedef pair<int,int> P;
const int maxn = 1e5+5;

inline bool read(int &ret){
    char c;int sgn;
    if(c = getchar(),c==EOF) return 0;
    while(c != '-'&&(c<'0'||c>'9')) c=getchar();
    sgn = (c=='-')?-1:1;
    ret = (c=='-')?0:(c-'0');
    while(c=getchar(),c>='0'&&c<='9') ret=ret*10+(c-'0');
    ret*=sgn;
    return 1;
}

struct Nod{
    int b,val,next;
    void init(int b,int val,int next){
        this->b=b;this->val=val;this->next=next;
    }
}buf[maxn<<1];
int n,m,len,E[maxn],ans;
int L[maxn],R[maxn],tot,root;
int par[maxn][20],dis[maxn],dep[maxn];
int bit[maxn<<1];
set<int> ms;

void add(int k,int x){
    for(;k<=tot;k+=lowbit(k)) bit[k]+=x;
}
int sum(int k){
    int ans = 0;
    for(;k;k-=lowbit(k)) ans += bit[k];
    return ans;
}

void init(){
    ms.clear();
    root = -1;
    len = tot = ans = 0;
    memset(E,-1,n*sizeof(int));
    memset(bit,0,(2*n+1)*sizeof(int));
}
void add_edge(int a,int b,int c){
    buf[len].init(b,c,E[a]);E[a]=len++;
    buf[len].init(a,c,E[b]);E[b]=len++;
}
void dfs(int u,int pre,int deep){
    int i,v;
    par[u][0] = pre;dep[u] = deep;
    L[u] = ++tot;
    for(i = E[u];i != -1;i = buf[i].next){
        v = buf[i].b;
        if(v == pre)continue;
        dis[v] = dis[u] + buf[i].val;
        dfs(v,u,deep+1);
    }
    R[u] = ++tot;
}
void preprocess(){
    int i,j;
    dfs(0,-1,0);
    for(i = 1;i < 20;i++){
        for(j = 0;j < n;j++){
            par[j][i] = par[j][i-1]!=-1?par[par[j][i-1]][i-1]:-1;
        }
    }
}
int GetVet(int u,int len){
    int i;
    for(i = 19;i >= 0;i--){
        if(len>=(1<<i)){
            u = par[u][i];
            len -= (1<<i);
            if(u == -1) return -1;
        }
    }
    return u;
}

void AddOp(int u){
    int i,j,v;
    if(root==-1){
        root = u;
        ans = 0;
        ms.insert(u);
        add(L[u],1);
        return;
    }
    int lb,rb,mid,vv;
    lb = -1,rb = n+1;
    while(rb-lb>1){
        mid = (lb+rb)>>1;
        vv = GetVet(u,mid);
        if(vv==-1||sum(R[vv])-sum(L[vv]-1)>0){
            rb = mid;
            v = vv;
        }else lb = mid;
    }
    if(L[u]>=L[root]&&L[u]<=R[root]){
        ans += dis[u]-dis[v];
    }else{
        ans += dis[root]+dis[u]-2*dis[v];
        root = v;
    }
    add(L[u],1);
    ms.insert(u);
}
void DelOp(int u){
    int i,j,v;
    add(L[u],-1);
    ms.erase(u);
    if(ms.size()==1){
        root = -1;
        ans = 0;
        //ms.erase(u);
        return;
    }
    int lb,rb,mid,vv;
    lb = -1,rb = n+1;
    while(rb-lb>1){
        mid = (lb+rb)>>1;
        vv = GetVet(*ms.begin(),mid);
        if(vv==-1||sum(R[vv])-sum(L[vv]-1)==ms.size()){
            rb = mid;
            v = vv;
        }else lb = mid;
    }
    if(v==root){
        lb = -1,rb = n+1;
        while(rb-lb>1){
            mid = (lb+rb)>>1;
            vv = GetVet(u,mid);
            if(vv==-1||sum(R[vv])-sum(L[vv]-1)>0){
                rb = mid;
                v = vv;
            }else lb = mid;
        }
        ans -= dis[u]-dis[v];
    }else{
        ans -= dis[v]+dis[u]-2*dis[root];
        root = v;
    }
}

int main(){
    int i,j,cas,u,v,w,op;
    scanf("%d",&cas);
    for(int T=1;T<=cas;T++){
        scanf("%d%d",&n,&m);
        init();
        for(i = 1;i < n;i++){
            //scanf("%d%d%d",&u,&v,&w);
            read(u);read(v);read(w);
            u--,v--;
            add_edge(u,v,w);
        }
        preprocess();
        printf("Case #%d:\n",T);
        while(m--){
            scanf("%d%d",&op,&u);u--;
            if(op == 1&&ms.find(u)==ms.end()) AddOp(u);
            else if(op==2&&ms.find(u)!=ms.end()) DelOp(u);
            printf("%d\n",ans);
        }
    }

    return 0;
}