树链剖分+线段树区间修改区间查询

蓝桥守护者

• 进行树链剖分，按照dfs2的遍历顺序依次标号
• 对的最短路径进行修改时，通过树链，将区间拆为一个个小区间
• 由于每个链内序号为一个区间，符合线段树
• 对子树进行修改时，子树区间即为
• 对于所有点进行修改，整合时要乘区间长度

import java.io.*;
import java.math.BigInteger;
import java.util.StringTokenizer;


//implements Runnable
public class Main{
    static long md=(long)1e9+7;
    static long Linf=Long.MAX_VALUE/2;
    static int inf=Integer.MAX_VALUE/2;
    static int N=100010;
    static int n=0;
    static int m=0;
    static long ans=0;
    static
    class Edge{
        int fr,to,nxt;
        public Edge(int u,int v){
            fr=u;to=v;
        }
    }
    static Edge[] e;
    static int[] head;
    static int cnt=0;
    static void addEdge(int fr,int to){
        cnt++;
        e[cnt]=new Edge(fr,to);
        e[cnt].nxt=head[fr];
        head[fr]=cnt;
    }
    static int[] dep,siz,son,fa,top,id;
    static long[] v,A,add,tr;
//    static int[] ls,rs;
    static void init(){
        e=new Edge[2*n+1];
        head=new int[n+1];
        cnt=0;id=new int[n+1];
        dep=new int[n+1];siz=new int[n+1];son=new int[n+1];fa=new int[n+1];top=new int[n+1];
        v=new long[n+1];A=new long[n+1];add=new long[n<<2];tr=new long[n<<2];
//        ls=new int[n+1];rs=new int[n+1];
    }
    static void dfs1(int x,int f){
        dep[x]=dep[f]+1;fa[x]=f;siz[x]=1;
        for(int i=head[x];i>0;i=e[i].nxt){
            int y=e[i].to;
            if(y==f)continue;
            dfs1(y,x);
            siz[x]+=siz[y];
            if(son[x]==0||siz[son[x]]<siz[y]){
                son[x]=y;
            }
        }
    }
    static int o=0;
    static void dfs2(int x,int tp){
        o++;id[x]=o;A[o]=v[x];
        top[x]=tp;
        if(son[x]!=0)dfs2(son[x],tp);
        for(int i=head[x];i>0;i=e[i].nxt){
            int y=e[i].to;
            if(y==fa[x]||y==son[x])continue;
            dfs2(y,y);
        }
    }
    static void pushup(int x){
        tr[x]=tr[x<<1]+tr[x<<1|1];
    }
    static void addtag(int x,int l,int r,long d){
        add[x]+=d;
        tr[x]+=(r-l+1)*d;
    }
    static void pushdown(int x,int l,int r){
        if(add[x]!=0){
            int mid=(l+r)>>1;
            addtag(x<<1,l,mid,add[x]);
            addtag(x<<1|1,mid+1,r,add[x]);
            add[x]=0;
        }
    }
    static void build(int x,int l,int r){
        if(l==r){
            tr[x]=A[l];
            return;
        }
        int mid=(l+r)>>1;
        build(x<<1,l,mid);
        build(x<<1|1,mid+1,r);
        pushup(x);
    }
    static void update(int x,int l,int r,int ql,int qr,long d){
        if(ql<=l&&r<=qr){
            addtag(x,l,r,d);
            return;
        }
        pushdown(x,l,r);
        int mid=(l+r)>>1;
        if(ql<=mid)update(x<<1,l,mid,ql,qr,d);
        if(qr>mid)update(x<<1|1,mid+1,r,ql,qr,d);
        pushup(x);
    }
    static long query(int x,int l,int r,int ql,int qr){
        if(ql<=l&&r<=qr){
            return tr[x];
        }
        pushdown(x,l,r);
        long res=0;
        int mid=(l+r)>>1;
        if(ql<=mid)res+=query(x<<1,l,mid,ql,qr);
        if(qr>mid)res+=query(x<<1|1,mid+1,r,ql,qr);
        return res;
    }
    static void update_road(int x,int y,long d){
        while(top[x]!=top[y]){
            if(dep[top[x]]<dep[top[y]]){
                int t=x;x=y;y=t;
            }
            update(1,1,n,id[top[x]],id[x],d);
            x=fa[top[x]];
        }
        if(dep[x]<dep[y]){
            int t=x;x=y;y=t;
        }
        update(1,1,n,id[y],id[x],d);
    }
    static long query_road(int x,int y){
        long res=0;
        while(top[x]!=top[y]){
            if(dep[top[x]]<dep[top[y]]){
                int t=x;x=y;y=t;
            }
            res+=query(1,1,n,id[top[x]],id[x]);
            x=fa[top[x]];
        }
        if(dep[x]<dep[y]){
            int t=x;x=y;y=t;
        }
        res+=query(1,1,n,id[y],id[x]);
        return res;
    }
    static void update_sonTree(int x,long d){
        update(1,1,n,id[x],id[x]+siz[x]-1,d);
    }
    static long query_sonTree(int x){
        return query(1,1,n,id[x],id[x]+siz[x]-1);
    }
    static void solve() throws Exception{
        //快读快输
        AReader input=new AReader();
//        Scanner input=new Scanner(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
        String al="abcdefghijklmnopqrstuvwxyz";
        char[] ac=al.toCharArray();
        n=input.nextInt();
        init();
        for(int i=1;i<=n;++i)v[i]=input.nextInt();
        for(int i=1;i<n;++i){
            int u=input.nextInt();
            int v=input.nextInt();
            addEdge(u,v);addEdge(v,u);
        }
        dfs1(1,0);
        dfs2(1,1);
        build(1,1,n);
        m=input.nextInt();
        while(m>0){
            m--;
            int op=input.nextInt();
            if(op==1){
                int u=input.nextInt();
                int v=input.nextInt();
                int w=input.nextInt();
                update_road(u,v,w);
            }else if(op==2){
                int u=input.nextInt();
                long w=input.nextInt();
                update_sonTree(u,w);
            }else if(op==3){
                int u=input.nextInt();
                int v=input.nextInt();
                long ans=query_road(u,v);
                out.write(ans+"\n");
            }else{
                int u=input.nextInt();
                long ans=query_sonTree(u);
                out.write(ans+"\n");
            }
        }

        out.flush();
        out.close();
    }
    public static void main(String[] args) throws Exception{
        solve();
    }
//    public static final void main(String[] args) throws Exception {
//        new Thread(null, new Main(), "线程名字", 1 << 27).start();
//    }
//    @Override
//    public void run() {
//        try {
//            //原本main函数的内容
//            solve();
//
//        } catch (Exception e) {
//        }
//    }
    static//快读模板，不用管
    class AReader{
        BufferedReader bf;
        StringTokenizer st;

        public AReader(){
            bf=new BufferedReader(new InputStreamReader(System.in));
            st=new StringTokenizer("");
        }
        public String nextLine() throws IOException{
            return bf.readLine();
        }
        public String next() throws IOException{
            while(!st.hasMoreTokens()){
                st=new StringTokenizer(bf.readLine());
            }
            return st.nextToken();
        }
        public char nextChar() throws IOException{
            //确定下一个token只有一个字符的时候再用
            return next().charAt(0);
        }
        public int nextInt() throws IOException{
            return Integer.parseInt(next());
        }
        public long nextLong() throws IOException{
            return Long.parseLong(next());
        }
        public double nextDouble() throws IOException{
            return Double.parseDouble(next());
        }
        public float nextFloat() throws IOException{
            return Float.parseFloat(next());
        }
        public byte nextByte() throws IOException{
            return Byte.parseByte(next());
        }
        public short nextShort() throws IOException{
            return Short.parseShort(next());
        }
        public BigInteger nextBigInteger() throws IOException{
            return new BigInteger(next());
        }
    }
}