FZU - 2277(树链剖分或dfs序+线段树)

There is a rooted tree with n nodes, number from 1-n. Root’s number is 1.Each node has a value ai.

Initially all the node’s value is 0.

We have q operations. There are two kinds of operations.

1 v x k : a[v]+=x , a[v’]+=x-k (v’ is child of v) , a[v’’]+=x-2*k (v’’ is child of v’) and so on.

2 v : Output a[v] mod 1000000007(10^9 + 7).

Input

First line contains an integer T (1 ≤ T ≤ 3), represents there are T test cases.

In each test case:

The first line contains a number n.

The second line contains n-1 number, p2,p3,…,pn . pi is the father of i.

The third line contains a number q.

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Next q lines, each line contains an operation. (“1 v x k” or “2 v”)

1 ≤ n ≤ 3*10^5

1 ≤ pi < i

1 ≤ q ≤ 3*10^5

1 ≤ v ≤ n; 0 ≤ x < 10^9 + 7; 0 ≤ k < 10^9 + 7

Output

For each operation 2, outputs the answer.

Sample Input

Sample Output

2
1

看了网上的题解博客，弄懂思路，经过不断调试和修改，终于在规定时间ac了。

思路：

树链剖分。

用dfs序分割出每一颗子树，编号自动从1到n，不用操作，在一条链上的点都是连续的，而且可以一一对应到线段树上，因为题目刚开始没有初始值，所以也不用建树，最后的查询也不是对某一条链进行查询，直接是单点查询，所以，应该也称不上熟练剖分吧，都说是dfs序+线段树。

总之还是dfs序好些，以后再写一写熟练剖分的代码吧。

代码：

#include <iostream>
#include <cstdio>
#include <cstring>
#include <vector>
#define lson rt1<<1,l,m
#define rson rt1<<1|1,m+1,r
#define LL long long
using namespace std;
const LL maxn=310000;
const LL mod=1e9+7;
vector<LL>G[maxn];
LL deep[maxn];
LL st[maxn],en[maxn];
LL ans=0;
LL tem=0;
//****************
LL sum[maxn*4],sumk[maxn*4];
void dfs(LL x)
{
    deep[x]=ans;
    st[x]=tem++;
    ans++;
    for(LL i=0;i<G[x].size();i++)
    {
        LL v=G[x][i];
        dfs(v);
    }
    ans--;
    en[x]=tem-1;
}
void update(LL u,LL x,LL k,LL lt,LL rt,LL rt1,LL l,LL r)
{
    if(lt<=l&&r<=rt)
    {
        sum[rt1]=(sum[rt1]+x+deep[u]*k)%mod;
        sumk[rt1]=(sumk[rt1]+k)%mod;
        return;
    }
    LL m=(r+l)>>1;
    if(lt<=m)update(u,x,k,lt,rt,lson);
    if(rt>m)update(u,x,k,lt,rt,rson);

}
LL quert(LL u,LL L,LL R,LL rt1,LL l,LL r)
{
    if(L<=l&&r<=R)
    {
        return (sum[rt1]-(sumk[rt1]*deep[u])%mod)%mod;
    }
    LL m=(l+r)>>1;
    if(L<=m)return(quert(u,L,R,lson)+sum[rt1]-(sumk[rt1]*deep[u])%mod)%mod;
    else return(quert(u,L,R,rson)+sum[rt1]-(sumk[rt1]*deep[u])%mod)%mod;
}
int main()
{
    LL t;
    scanf("%I64d",&t);
    while(t--)
    {
        memset(deep,0,sizeof(deep));
        memset(sum,0,sizeof(sum));
        memset(sumk,0,sizeof(sumk));
        memset(st,0,sizeof(st));
        memset(en,0,sizeof(en));
        ans=0,tem=1;
        LL n;
        scanf("%I64d",&n);
        for(int i=1;i<=n;i++)G[i].clear();
        LL u;
        for(int i=2;i<=n;i++)
        {
            scanf("%I64d",&u);
            G[u].push_back(i);
        }
        LL m,f,x,k;
        LL lt,rt;
        scanf("%I64d",&m);
        ans=0;
        dfs(1);
        while(m--)
        {

            scanf("%I64d",&f);
            if(f==1)
            {
                scanf("%I64d%I64d%I64d",&u,&x,&k);
                lt=st[u];
                rt=en[u];
                update(u,x,k,lt,rt,1,1,n);
            }
            else
            {
                scanf("%I64d",&u);
                lt=st[u];
                rt=st[u];
                printf("%I64d\n",(quert(u,lt,rt,1,1,n)+mod)%mod);
            }
        }
    }
   return 0;
}

FZU - 2277(树链剖分或dfs序+线段树)

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