4034: [HAOI2015]树上操作

4034: [HAOI2015]树上操作

链接

思路：

　　树链剖分。操作：单点修改，路径查询，子树修改。

代码：

#include<cstdio>
#include<algorithm>
#include<cstring>
#include<iostream>
#include<cmath>
#include<cctype>

using namespace std;

const int N = 100100;
typedef long long LL;

struct Edge{
    int to,nxt;
    Edge() {}
    Edge(int a,int b) {to = a,nxt = b;}
}e[N<<1];
int head[N],tot;
LL sum[N<<2],tag[N<<2],w[N],data[N];
int pos[N],siz[N],son[N],bel[N],deth[N],fa[N];
int tn;

inline int read() {
    int x = 0,f = 1;char ch = getchar();
    for (; !isdigit(ch); ch=getchar()) if(ch=='-') f = -1;
    for (; isdigit(ch); ch=getchar()) x = x*10+ch-'0';
    return x * f;
}
void add_edge(int u,int v) {
    e[++tot] = Edge(v,head[u]);head[u] = tot;
    e[++tot] = Edge(u,head[v]);head[v] = tot;
}
void dfs1(int u,int pa) {
    siz[u] = 1;
    deth[u] = deth[pa] + 1;
    fa[u] = pa;
    for (int i=head[u]; i; i=e[i].nxt) {
        int v = e[i].to;
        if (v==pa) continue;
        dfs1(v,u);
        siz[u] += siz[v];
        if (!son[u] || siz[son[u]]<siz[v]) son[u] = v;
    }
}
void dfs2(int u,int top) {
    bel[u] = top;
    pos[u] = ++tn;
    data[pos[u]] = w[u];
    if (!son[u]) return; 
    dfs2(son[u],top);
    for (int i=head[u]; i; i=e[i].nxt) {
        int v = e[i].to;
        if (v==fa[u] || v==son[u]) continue;
        dfs2(v,v);
    }
}

#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1

void pushup(int rt) {
    sum[rt] = sum[rt<<1] + sum[rt<<1|1];
}
void pushdown(int rt,int len) {
    if (tag[rt]) {
        sum[rt<<1] += 1ll * tag[rt] * (len-len/2);tag[rt<<1] += tag[rt];
        sum[rt<<1|1] += 1ll * tag[rt] * (len/2);tag[rt<<1|1] += tag[rt];
        tag[rt] = 0;
    }
}
void build(int l,int r,int rt) {
    if (l==r) {
        sum[rt] = data[l];
        return ;
    }
    int mid = (l + r) / 2;
    build (lson);
    build (rson);
    pushup(rt);
}
void update(int l,int r,int rt,int L,int R,LL x) {
    if (L <= l && r <= R) {
        sum[rt] += 1ll * (r - l + 1) * x;
        tag[rt] += x;
        return ;
    }
    pushdown(rt,r-l+1);
    int mid = (l + r) / 2;
    if (L <= mid) update(lson,L,R,x);
    if (R > mid)  update(rson,L,R,x);
    pushup(rt);
}
LL query(int l,int r,int rt,int L,int R) {
    if (L <= l && r <= R) {
        return sum[rt];
    }
    int mid = (l + r) / 2;
    LL ret = 0;
    pushdown(rt,r-l+1);
    if (L <= mid) ret += query(lson,L,R);
    if (R > mid)  ret += query(rson,L,R);
    return ret;
}
void Ask(int x,int y) {
    LL ans = 0;
    while (bel[x] != bel[y]) {
        if (deth[bel[x]] < deth[bel[y]]) swap(x,y);
        ans += query(1,tn,1,pos[bel[x]],pos[x]);
        x = fa[bel[x]];
    }
    if (deth[x] < deth[y]) swap(x,y);
    ans += query(1,tn,1,pos[y],pos[x]);
    printf("%lld
",ans);
}
int main() {
    int n = read(),m = read();
    for (int i=1; i<=n; ++i) w[i] = read();
    for (int i=1; i<n; ++i) {
        int u = read(),v = read();
        add_edge(u,v);
    }
    dfs1(1,0);
    dfs2(1,1);
    build(1,tn,1);
    LL a;
    while (m--) {
        int opt = read(),x = read();
        if (opt == 1) {
            a = read();
            update(1,tn,1,pos[x],pos[x],a);    
        }
        else if (opt==2) {
            a = read();
            update(1,tn,1,pos[x],pos[x]+siz[x]-1,a);
        }
        else Ask(x,1);
    }
    return 0;
}