E. Jamie and Tree

思路

• 直接$root=v$；

• 找$lca$，$lca=lca(root,u),lca(root,v),lca(u,v)$中$dep$最深的：

  • $root$不在$lca$的子树上:

    直接$[l[lca],r[lca]]$区间更新$x$

  • $root$在$lca$的子树上:

    先把整棵树更新一遍+x，然后找到$root->lca$路径上与$lca$的儿子节点，然后更新他的子树-x

• 操作三:

  • $root$不在$v$的子树上：

    直接$sum(l[v],r[v])$

  • $root$在$v$的子树上:

    $+sum(1,n)$

    $-sum(nex{t}_{sonoflca})$类似操作二。

最后，操作二要特判一下$root==lca$和操作三要特判一下$root=v$，这个时候直接修改或者查询整个$[1,n]$的区间。

代码

/*Author : lifehappy
*/
#pragma GCC optimize(2)
#pragma GCC optimize(3)
#include <bits/stdc++.h>#define mp make_pair
#define pb push_back
#define endl '\n'
#define mid (l + r >> 1)
#define lson rt << 1, l, mid
#define rson rt << 1 | 1, mid + 1, r
#define ls rt << 1
#define rs rt << 1 | 1using namespace std;typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pii;const double pi = acos(-1.0);
const double eps = 1e-7;
const int inf = 0x3f3f3f3f;inline ll read() {ll f = 1, x = 0;char c = getchar();while(c < '0' || c > '9') {if(c == '-')    f = -1;c = getchar();}while(c >= '0' && c <= '9') {x = (x << 1) + (x << 3) + (c ^ 48);c = getchar();}return f * x;
}const int N = 1e5 + 10;int head[N], to[N << 1], nex[N << 1], cnt = 1, root;int son[N], sz[N], dep[N], fa[N], top[N], rk[N], id[N], l[N], r[N], tot;ll sum[N << 2], lazy[N << 2], value[N], n, m;void add(int x, int y) {to[cnt] = y;nex[cnt] = head[x];head[x] = cnt++;
}void dfs1(int rt, int f) {dep[rt] = dep[f] + 1;sz[rt] = 1, fa[rt] = f;for(int i = head[rt]; i; i = nex[i]) {if(to[i] == f) continue;dfs1(to[i], rt);sz[rt] += sz[to[i]];if(!son[rt] || sz[to[i]] > sz[son[rt]]) son[rt] = to[i];}
}void dfs2(int rt, int tp) {rk[++tot] = rt, id[rt] = tot;top[rt] = tp;l[rt] = r[rt] = tot;if(!son[rt]) return ;dfs2(son[rt], tp);for(int i = head[rt]; i; i = nex[i]) {if(to[i] == fa[rt] || to[i] == son[rt]) continue;dfs2(to[i], to[i]);}r[rt] = tot;
}void push_down(int rt, int l, int r) {if(lazy[rt]) {lazy[ls] += lazy[rt], lazy[rs] += lazy[rt];sum[ls] += 1ll * (mid - l + 1) * lazy[rt];sum[rs] += 1ll * (r - mid) * lazy[rt];lazy[rt] = 0;}
}void push_up(int rt) {sum[rt] = sum[ls] + sum[rs];
}void build(int rt, int l, int r) {if(l == r) {sum[rt] = value[rk[l]];return ;}build(lson);build(rson);push_up(rt);
}void update(int rt, int l, int r, int L, int R, int w) {if(l >= L && r <= R) {lazy[rt] += w;sum[rt] += 1ll * (r - l + 1) * w;return ;}push_down(rt, l, r);if(L <= mid) update(lson, L, R, w);if(R > mid)  update(rson, L, R, w);push_up(rt);
}ll query(int rt, int l, int r, int L, int R) {if(l >= L && r <= R) return sum[rt];push_down(rt, l, r);ll ans = 0;if(L <= mid) ans += query(lson, L, R);if(R > mid)  ans += query(rson, L, R);return ans;
}int Lca(int x, int y) {while(top[x] != top[y]) {if(dep[top[x]] < dep[top[y]]) swap(x, y);x = fa[top[x]];}return dep[x] < dep[y] ? x : y;
}int Max(int x, int y) {return dep[x] > dep[y] ? x : y;
}void update(int x, int y, int value) {while(top[x] != top[y]) {if(dep[top[x]] < dep[top[y]]) swap(x, y);update(1, 1, n, id[x], id[top[x]], value);x = fa[top[x]];}if(dep[x] > dep[y]) swap(x, y);update(1, 1, n, id[x], id[y], value);
}ll query(int x, int y) {ll ans = 0;while(top[x] != top[y]) {if(dep[top[x]] < dep[top[y]]) swap(x, y);ans += query(1, 1, n, id[x], id[top[x]]);x = fa[top[x]];}if(dep[x] > dep[y]) swap(x, y);ans += query(1, 1, n, id[x], id[y]);return ans;
}int get(int u) {int v = root;while(top[v] != top[u]) {if(fa[top[v]] == u) return top[v];v = fa[top[v]];}return son[u];
}int main() {// freopen("in.txt", "r", stdin);// freopen("out.txt", "w", stdout);// ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);n = read(), m = read();for(int i = 1; i <= n; i++) {value[i] = read();}for(int i = 1; i < n; i++) {int x = read(), y = read();add(x, y);add(y, x);}dfs1(1, 0);dfs2(1, 1);build(1, 1, n);root = 1;for(int i = 1; i <= m; i++) {int op = read();if(op == 1) {root = read();}else if(op == 2) {int u = read(), v = read(), x = read();int lca = Max(Max(Lca(u, v), Lca(root, v)), Lca(root, u));if(lca == root) {update(1, 1, n, 1, n, x);}else {if(id[root] < l[lca] || id[root] > r[lca]) {update(1, 1, n, l[lca], r[lca], x);}else {lca = get(lca);update(1, 1, n, 1, n, x);update(1, 1, n, l[lca], r[lca], -x);}}}else {int v = read();if(v == root) {printf("%lld\n", query(1, 1, n, 1, n));}else {if(id[root] < l[v] || id[root] > r[v]) {printf("%lld\n", query(1, 1, n, l[v], r[v]));}else {ll ans = query(1, 1, n, 1, n);v = get(v);ans -= query(1, 1, n, l[v], r[v]);printf("%lld\n", ans);}}}}return 0; 
}