E. Jamie and Tree
思路
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直接 r o o t = v root = v root=v;
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找 l c a lca lca, l c a = l c a ( r o o t , u ) , l c a ( r o o t , v ) , l c a ( u , v ) lca = {lca(root, u), lca(root, v), lca(u, v)} lca=lca(root,u),lca(root,v),lca(u,v)中 d e p dep dep最深的:
-
r o o t root root不在 l c a lca lca的子树上:
直接 [ l [ l c a ] , r [ l c a ] ] [l[lca], r[lca]] [l[lca],r[lca]]区间更新 x x x
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r o o t root root在 l c a lca lca的子树上:
先把整棵树更新一遍+x,然后找到 r o o t − > l c a root -> lca root−>lca路径上与 l c a lca lca的儿子节点,然后更新他的子树-x
-
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操作三:
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r o o t root root不在 v v v的子树上:
直接 s u m ( l [ v ] , r [ v ] ) sum({l[v], r[v]}) sum(l[v],r[v])
-
r o o t root root在 v v v的子树上:
+ s u m ( 1 , n ) + sum(1, n) +sum(1,n)
− s u m ( n e x t s o n o f l c a ) -sum(next_{son\ of\ lca}) −sum(nextson of lca)类似操作二。
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最后,操作二要特判一下 r o o t = = l c a root == lca root==lca和操作三要特判一下 r o o t = v root = v root=v,这个时候直接修改或者查询整个 [ 1 , n ] [1, n] [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 | 1
using 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;
}