luogu P3178 [HAOI2015]树上操作 题解

Posted 2020-12-27 misakaazusa

题目链接：https://www.luogu.org/problemnew/show/P3178
模板题 菜

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#define lson left, mid, rt<<1
#define rson mid + 1, right, rt<<1|1
#define ll long long
using namespace std;
const int maxn = 200000 + 10;
ll n, m, root, mod;
ll node[maxn], num; 
ll fa[maxn], dep[maxn], size[maxn], son[maxn], top[maxn], seg[maxn], rev[maxn];
ll res;
struct edge{
    ll from, to, next;  
}e[maxn<<2];
ll head[maxn], cnt;
//-------------------------------------------------------
ll tree[maxn<<2], lazy[maxn<<2];
void PushUP(ll rt)
{
    tree[rt] = (tree[rt<<1] + tree[rt<<1|1]);
}
void build(ll left, ll right, ll rt)
{
    if(left == right)
    {
        tree[rt] = rev[left];
        tree[rt] = tree[rt];
        return;
    }
    ll mid = (left + right) >> 1;
    build(lson);
    build(rson);
    PushUP(rt);
}
void PushDOWN(ll left, ll right, ll rt, ll mid)
{
    lazy[rt<<1] += lazy[rt]; 
    lazy[rt<<1|1] += lazy[rt];
    tree[rt<<1] += (mid - left + 1)*lazy[rt];
    tree[rt<<1|1] += (right - mid)*lazy[rt];
    lazy[rt] = 0;
}
ll query(ll l, ll r, ll left, ll right, ll rt)
{
    ll res = 0;
    if(l <= left && r >= right)
    {
        return tree[rt];
    }
    ll mid = (left + right)>>1;
    if(lazy[rt]) PushDOWN(left, right, rt, mid);
    if(l <= mid) res += query(l, r, lson);
    if(r > mid) res += query(l, r, rson);
    return res;
}
void update(ll l, ll r, ll add, ll left, ll right, ll rt)
{
    if(l <= left && r >= right)
    {
        lazy[rt] += add;
        tree[rt] += (right - left + 1)*add;
        return;
    }
    ll mid = (left + right)>>1;
    PushDOWN(left, right, rt, mid);
    if(l <= mid) update(l, r, add, lson);
    if(r > mid) update(l, r, add, rson);
    PushUP(rt);
}
//------------------------------------------------
void add(ll u, ll v)
{
    e[++cnt].from = u;
    e[cnt].next = head[u];
    e[cnt].to = v;
    head[u] = cnt;
}
void dfs1(ll u, ll f, ll d)
{
    ll maxson = -1;
    size[u] = 1;
    fa[u] = f;
    dep[u] = d;
    for(ll i = head[u]; i != -1; i = e[i].next)
    {
        ll v = e[i].to;
        if(v != f)
        {
            dfs1(v, u, d + 1);
            size[u] += size[v];
            if(size[v] > maxson) son[u] = v, maxson = size[v];
        }
    }
}
void dfs2(ll u, ll t)
{
    seg[u] = ++num;
    rev[num] = node[u];
    top[u] = t;
    if(!son[u]) return;
    dfs2(son[u], t);
    for(ll i = head[u]; i != -1; i = e[i].next)
    {
        ll v = e[i].to;
        if(fa[u] == v || son[u] == v) continue;
        dfs2(v, v);
    }
}
ll qRange(ll x, ll y)
{
    ll ans = 0;
    while(top[x] != top[y])
    {
        if(dep[top[x]] < dep[top[y]]) swap(x, y);
        res = 0;
        res = query(seg[top[x]], seg[x], 1, n, 1);
        ans = ans + res;
        x = fa[top[x]];
    }
    if(dep[x] > dep[y]) swap(x, y);
    res = 0;
    res = query(seg[x], seg[y], 1, n, 1);
    ans = ans + res;
    return ans;
}
void updRange(ll x, ll y, ll k)
{
    while(top[x] != top[y])
    {
        if(dep[top[x]] < dep[top[y]]) swap(x, y);
        update(seg[top[x]], seg[x], k, 1, n, 1);
        x = fa[top[x]];
    }
    if(dep[x] > dep[y]) swap(x, y);
    update(seg[x], seg[y], k, 1, n, 1);
}
ll qSon(ll x)
{
    res = 0;
    res = query(seg[x], seg[x]+size[x]-1, 1, n, 1);
    return res;
}
ll updSon(ll x, ll k)
{
    update(seg[x], seg[x]+size[x]-1, k, 1, n, 1);
}
int main()
{
    memset(head, -1, sizeof(head));
    scanf("%lld%lld",&n,&m);
    root = 1;
    for(ll i = 1; i <= n; i++)
    scanf("%lld",&node[i]);
    for(ll i = 1; i < n; i++)
    {
        ll u, v;
        scanf("%lld%lld",&u,&v);
        add(u, v), add(v, u);
    }
    dfs1(root, 0, 1);
    dfs2(root, root);
    build(1,n,1);
    for(ll i = 1; i <= m; i++)
    {
        ll opt, x, y, z;
        scanf("%lld",&opt);
        if(opt == 1)
        {
            scanf("%lld%lld%",&x,&y);
            updRange(x, x, y);
        }
        if(opt == 2)
        {
            scanf("%lld%lld",&x,&y);
            updSon(x, y);
        }
        if(opt == 3)
        {
            scanf("%lld",&x);
            printf("%lld
",qRange(x, 1));
        }
    }
    return 0;
}