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  • 【Luogu】P3979遥远的国度(树链剖分)

      题目链接

      不会换根从暑假开始就困扰我了……拖到现在……

      会了还是很激动的。

      换根操作事实上不需要(也不能)改树剖本来的dfs序……只是在query上动动手脚……

      设全树的集合为G,以root为根,u在原根到新根的链上的子树集合为G',则有查询区间=G-G'……

      然后查询的时候就查G-G'就行

      

    #include<cstdio>
    #include<cstdlib>
    #include<cctype>
    #include<algorithm>
    #include<cstring>
    #define left (rt<<1)
    #define right (rt<<1|1)
    #define mid ((l+r)>>1)
    #define lson l,mid,left
    #define rson mid+1,r,right
    #define maxn 100020
    using namespace std;
    inline long long read(){
        long long num=0,f=1;
        char ch=getchar();
        while(!isdigit(ch)){
            if(ch=='-')    f=-1;
            ch=getchar();
        }
        while(isdigit(ch)){
            num=num*10+ch-'0';
            ch=getchar();
        }
        return num*f;
    }
    
    struct Edge{
        int next,to;
    }edge[maxn*3];
    int head[maxn],num;
    inline void add(int from,int to){
        edge[++num]=(Edge){head[from],to};
        head[from]=num;
    }
    
    int tree[maxn*5];
    int tag[maxn*5];
    int size[maxn];
    int deep[maxn];
    int son[maxn];
    int father[maxn];
    int top[maxn];
    int dfn[maxn];
    int back[maxn],ID;
    int q[maxn];
    int s[maxn][22];
    int n,m;
    
    
    void find(int x,int fa){
        deep[x]=deep[fa]+1;    size[x]=1;
        for(int i=head[x];i;i=edge[i].next){
            int to=edge[i].to;
            if(to==fa)    continue;
            father[to]=x;
            s[to][0]=x;
            find(to,x);
            size[x]+=size[to];
            if(son[x]==0||size[son[x]]<size[to])    son[x]=to;
        }
    }
    
    void unionn(int x,int Top){
        dfn[x]=++ID;    back[ID]=x;
        top[x]=Top;
        if(!son[x])    return;
        unionn(son[x],Top);
        for(int i=head[x];i;i=edge[i].next){
            int to=edge[i].to;
            if(to==father[x]||to==son[x])    continue;
            unionn(to,to);
        }
    }
    
    inline void pushup(int rt){
        tree[rt]=min(tree[left],tree[right]);
    }
    
    void pushdown(int rt){
        if(tag[rt]==-1)    return;
        tag[left]=tag[right]=tag[rt];
        tree[left]=tree[right]=tag[rt];
        tag[rt]=-1;
        return;
    }
    
    void build(int l,int r,int rt){
        tag[rt]=-1;
        if(l==r){
            tree[rt]=q[back[l]];
            return;
        }
        build(lson);
        build(rson);
        pushup(rt);
    }
    
    void memseg(int from,int to,int num,int l,int r,int rt){
        if(from<=l&&to>=r){
            tree[rt]=tag[rt]=num;
            //printf("%d %d l=%d r=%d %d
    ",from,to,l,r,num);
            return;
        }
        pushdown(rt);
        if(from<=mid)    memseg(from,to,num,lson);
        if(to>mid)        memseg(from,to,num,rson);
        pushup(rt);
        return;
    }
    
    int query(int from,int to,int l,int r,int rt){
        if(from<=l&&to>=r)    return tree[rt];
        pushdown(rt);
        int ans=0x7fffffff;
        if(from<=mid)    ans=min(ans,query(from,to,lson));
        if(to>mid)        ans=min(ans,query(from,to,rson));
        return ans;
    }
    
    int root;
    
    void update(int from,int to,int num){
        while(top[from]!=top[to]){
            if(deep[top[from]]<deep[top[to]])    swap(from,to);
            memseg(dfn[top[from]],dfn[from],num,1,n,1);
            from=father[top[from]];
        }
        if(deep[from]>deep[to])    swap(from,to);
        memseg(dfn[from],dfn[to],num,1,n,1);
        return;
    }
    
    int LCA(int from,int to){
        if(deep[from]<deep[to])    swap(from,to);
        int f=deep[from]-deep[to];
        for(int i=0;(1<<i)<=f;++i)
            if(f&(1<<i))    from=s[from][i];
        if(from==to)    return from;
        for(int i=20;i>=0;--i){
            if(s[from][i]==s[to][i])    continue;
            from=s[from][i];
            to=s[to][i];
        }
        return s[from][0];
    }
    
    inline void prepare(){
        for(int j=1;j<=20;++j)
            for(int i=1;i<=n;++i)    s[i][j]=s[s[i][j-1]][j-1];
    }
    
    int ask(int o){
        if(root==1)    return query(dfn[o],dfn[o]+size[o]-1,1,n,1);
        int lca=LCA(root,o);
        if(lca!=o)    return query(dfn[o],dfn[o]+size[o]-1,1,n,1);
        else{
            int now=root;
            for(int i=20;i>=0;--i)
                if(deep[s[now][i]]>deep[o])    now=s[now][i];
            int ans=0x7fffffff;
            if(dfn[now]>1)                ans=min(ans,query(1,dfn[now]-1,1,n,1));
            if(dfn[now]+size[now]<=n)    ans=min(ans,query(dfn[now]+size[now],n,1,n,1));
            return ans;
        }
    }
    
    int main(){
        n=read(),m=read();
        for(int i=1;i<n;++i){
            int from=read(),to=read();
            add(from,to);
            add(to,from);
        }
        for(int i=1;i<=n;++i)    q[i]=read();
        root=read();
        find(1,1);
        unionn(1,1);
        build(1,n,1);
        prepare();
        for(int i=1;i<=m;++i){
            int opt=read();
            if(opt==1)    root=read();
            else if(opt==2){
                int x=read(),y=read(),z=read();
                update(x,y,z);
            }
            else{
                int x=read();
                printf("%d
    ",ask(x));
            }
        }
        return 0;
    }
    /*
    10 10
    1 2
    2 3
    2 4
    1 5
    5 6
    5 10
    5 7
    7 8
    7 9
    5 1 2 3 6 4 7 8 9 10
    1
    */

      话说写博客超简略的我简直是业界毒瘤啊……

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  • 原文地址:https://www.cnblogs.com/cellular-automaton/p/8349578.html
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