我永远喜欢洛天依
给定一张图世末积雨云，你需要维护其支配树：
单点修改，子树修改，树链修改
子树求和，树链求和，多条树链的并集求和
撤销之前的操作
可以先用 Lengauer-Tarjan 算法 求出图的支配树，然后把它树剖，开一个线段树维护
至于多条树链的并集求和（有点像虚树的那种操作），现将所有点按照 dfn 排序，然后按照 dfn 的顺序依次加点
枚举节点a[i]，每次假装a[1..i]的答案中除了a[i]到根的路径没有求值之外其它的都求值了，那么转移的时候需要加上当前点到lca的距离。
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UuRbksXKeRJA8ZTGPou3Av6mQxjaEQQKjzqHQ88JiuuiaKYxDXsSBvET0PGUxi6LvvT1QaMo2hUCFUAk1R7IJvECR927ZtJMSERGZZyGAKQ599f9Qrie7LJIZKCiF7klUIGNoqiSqAJlVWF0PfLff4YbKFodK+erKeL1UChjiDm1bLMrk3oS6GPlvuMT4yLPJimNtNpREQ70xV9E3DTWHooxGBttw7TXx0N/zWJSDvGjEcn2Cy/JMFQxeGy2M+OpmMPdGs3KYVMWtJCbNi6Pp+fGXf1utJIiUIpW2/NM9Nw7YLviXIpcnsfzIIb8YQf2laAAAAAElFTkSuQmCC" alt="">
如图，我们从1转移到2时候，要加上绿色的链这一段的值
最后转移完后，我们再加上最后一个点到根的距离即可
至于撤销操作，我们可以考虑建立主席树，当然也可以不建主席树暴力撤销，因为每一步操作最多只会被撤销一次。
代码：
#include <cstdio>
#include <vector>
#include <algorithm>
using namespace std;
int n, m;
namespace dominate_tree
{
vector<int> g[50010], g1[50010], g2[50010];
int sdom[50010], bel[50010], val[50010], idom[50010];
int dfn[50010], dfntot, id[50010], fa[50010];
void dfs(int x)
{
dfn[x] = ++dfntot, id[dfntot] = x;
for (int i : g[x]) if (dfn[i] == 0) fa[i] = x, dfs(i);
}
int getf(int x)
{
if (x == bel[x]) return x;
int rt = getf(bel[x]);
if (dfn[sdom[val[bel[x]]]] < dfn[sdom[val[x]]])
val[x] = val[bel[x]];
return bel[x] = rt;
}
void work()
{
for (int i = 1; i <= n; i++) sdom[i] = bel[i] = val[i] = i;
dfs(1);
for (int i = n; i >= 2; i--)
{
int x = id[i];
for (int j : g1[x])
if (dfn[j])
{
getf(j);
if (dfn[sdom[val[j]]] < dfn[sdom[x]])
sdom[x] = sdom[val[j]];
}
g2[sdom[x]].push_back(x);
x = bel[x] = fa[x];
for (int j : g2[x])
{
getf(j);
if (sdom[val[j]] == x) idom[j] = x;
else idom[j] = val[j];
}
}
for (int i = 2; i <= n; i++)
{
int x = id[i];
if (idom[x] != sdom[x]) idom[x] = idom[idom[x]];
}
}
}
vector<int> out[50010];
int fa[50010], depth[50010], wson[50010], weight[50010];
int dfn[50010], top[50010], tot, val[50010], stop, tmp[50010];
long long tree[200010], lazy[200010];
struct ch { int type, u, w; } s[100010];
void pushdown(int x, int cl, int mid, int cr)
{
lazy[x * 2] += lazy[x], lazy[x * 2 + 1] += lazy[x];
tree[x * 2] += lazy[x] * (mid - cl + 1);
tree[x * 2 + 1] += lazy[x] * (cr - mid);
lazy[x] = 0;
}
void chenge(int x, int cl, int cr, int L, int R, int k)
{
if (cr < L || R < cl) return;
if (L <= cl && cr <= R) { lazy[x] += k, tree[x] += (cr - cl + 1) * (long long)k; return; }
int mid = (cl + cr) / 2;
pushdown(x, cl, mid, cr);
chenge(x * 2, cl, mid, L, R, k), chenge(x * 2 + 1, mid + 1, cr, L, R, k);
tree[x] = tree[x * 2] + tree[x * 2 + 1];
}
long long query(int x, int cl, int cr, int L, int R)
{
if (cr < L || R < cl) return 0;
if (L <= cl && cr <= R) return tree[x];
int mid = (cl + cr) / 2;
pushdown(x, cl, mid, cr);
return query(x * 2, cl, mid, L, R) + query(x * 2 + 1, mid + 1, cr, L, R);
}
void dfs1(int x)
{
wson[x] = -1, weight[x] = 1;
for (int i : out[x])
{
fa[i] = x, depth[i] = depth[x] + 1, dfs1(i), weight[x] += weight[i];
if (wson[x] == -1 || weight[i] > weight[wson[x]]) wson[x] = i;
}
}
void dfs2(int x, int topf)
{
dfn[x] = ++tot, top[x] = topf;
if (wson[x] != -1)
{
dfs2(wson[x], topf);
for (int i : out[x]) if (i != wson[x]) dfs2(i, i);
}
}
int lca(int x, int y)
{
while (top[x] != top[y])
{
if (depth[top[x]] < depth[top[y]]) swap(x, y);
x = fa[top[x]];
}
if (depth[x] > depth[y]) swap(x, y);
return x;
}
long long getans(int x)
{
long long res = 0;
while (x)
res += query(1, 1, n, dfn[top[x]], dfn[x]), x = fa[top[x]];
return res;
}
int main()
{
scanf("%d%d", &n, &m);
for (int i = 1; i <= n; i++) scanf("%d", &val[i]);
for (int x, y, i = 1; i <= m; i++)
scanf("%d%d", &x, &y), dominate_tree::g[x].push_back(y), dominate_tree::g1[y].push_back(x);
dominate_tree::work();
for (int i = 2; i <= n; i++) out[dominate_tree::idom[i]].push_back(i);
dfs1(1), dfs2(1, 1);
for (int i = 1; i <= n; i++) chenge(1, 1, n, dfn[i], dfn[i], val[i]);
int q; scanf("%d", &q);
for (int i = 1; i <= q; i++)
{
char tp;
scanf(" %c", &tp);
if (tp == 'C')
{
int opd, u, w;
scanf("%d%d%d", &opd, &u, &w);
s[++stop] = (ch){opd, u, w};
if (opd == 1) chenge(1, 1, n, dfn[u], dfn[u], w);
if (opd == 2) chenge(1, 1, n, dfn[u], dfn[u] + weight[u] - 1, w);
if (opd == 3)
while (u) chenge(1, 1, n, dfn[top[u]], dfn[u], w), u = fa[top[u]];
}
else if (tp == 'Q')
{
int opd, u;
scanf("%d%d", &opd, &u);
if (opd == 1) printf("%lld\n", query(1, 1, n, dfn[u], dfn[u] + weight[u] - 1));
if (opd == 2) printf("%lld\n", getans(u));
if (opd == 3)
{
long long res = 0;
for (int j = 1; j <= u; j++) scanf("%d", &tmp[j]);
sort(tmp + 1, tmp + 1 + u, [](int x, int y) { return dfn[x] < dfn[y]; });
for (int j = 2; j <= u; j++)
{
int lc = lca(tmp[j - 1], tmp[j]);
if (lc != tmp[j - 1])
res += getans(tmp[j - 1]) - getans(lc);
}
res += getans(tmp[u]);
printf("%lld\n", res);
}
}
else
{
int k;
scanf("%d", &k);
while (stop > 0 && k > 0)
{
int opd = s[stop].type, u = s[stop].u, w = -s[stop].w;
if (opd == 1) chenge(1, 1, n, dfn[u], dfn[u], w);
if (opd == 2) chenge(1, 1, n, dfn[u], dfn[u] + weight[u] - 1, w);
if (opd == 3)
while (u) chenge(1, 1, n, dfn[top[u]], dfn[u], w), u = fa[top[u]];
stop--, k--;
}
}
}
return 0;
}