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// input: undirected (un)weighted tree as
// adjacency list containing pair<neighbour,weight>s
// (To remove weights, remove every "w" and fix errors)
// output[r] = dp[r], where dp[v] :=
// fin(Sum_{child c of v, regarding root r} from_child( dp[c] ))
struct Reroot {
using D = todo; // dp value
using A = todo (often D); // value from a vertex's child(ren)
// (A,agg,e) commutative monoid
A e = todo;
A from_child(z v, z c, auto w, D dp_c) { todo }
static A agg(A a, A b) { todo }
D fin(z v, A chils_agg) { todo }
vector<D> dp;
D dfs0(z v, z p, auto& g) {
A ca = e;
for (auto [c, w] : g[v]) if(c-p) {
ca = agg(ca, from_child(v, c, w, dfs0(c, v, g)));
}
return dp[v] = fin(v, ca);
}
void dfs1(z v, z p, auto& g) {
vector ps = {e};
for (auto [c, w] : g[v]) {
ps.push_back(from_child(v, c, w, dp[c]));
}
auto ss = ps;
exclusive_scan(ps.begin(), ps.end(), ps.begin(), e, agg);
exclusive_scan(ss.rbegin(),ss.rend(),ss.rbegin(),e, agg);
z i = 0;
for (auto [c, w] : g[v]) if(++i, c-p) {
dp[v] = fin(v, agg(ss[i], ps[i]));
dfs1(c, v, g);
}
dp[v] = fin(v, s[0]);
}
auto solve(auto g) {
dp.resize(sz(g));
dfs0(0, 0, g);
dfs1(0, 0, g);
return dp;
}
};
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