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// output[r] = dp[r], where dp[v] :=
// fin(Sum_{child c of v, regarding root r} fromChild( dp[c] ))
// To remove weights, remove every "w" and "W" and fix errors
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 fromChild(int v, int c, auto w, D dp_c) { /todo/ }
static A agg(A a, A b) { /todo/ }
D fin(int v, A chilsAgg) { /todo/ }
vector<D> dp;
D dfs0(auto& g, int v, int from = -1) {
A ca = e;
for (auto [c, w] : g[v]) {
if (c == from) continue;
ca = agg(ca, fromChild(v, c, w, dfs0(c, v, g)));
}
return dp[v] = fin(v, ca);
}
void dfs1(auto& g, int v, int from = -1) {
vector ps = {e};
for (auto [c, w] : g[v]) {
ps.push_back(fromChild(v, c, w, dp[c]));
}
auto ss = ps;
exclusive_scan(be(ps), ps.begin(), e, agg);
exclusive_scan(ss.rbegin(), ss.rend(), ss.rbegin(), e, agg);
int i = 0;
for (auto [c, w] : g[v]) {
++i;
if (c == from) continue;
dp[v] = fin(v, agg(ss[i], ps[i]));
dfs1(c, v, g);
}
dp[v] = fin(v, ss[0]);
}
template<typename W>
auto solve(vector<vector<pair<int, W>>> g) {
dp.resize(sz(g));
dfs0(g, 0);
dfs1(g, 0);
return dp;
}
};
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