/
rerooting_dp.hpp
76 lines (70 loc) · 2.11 KB
/
rerooting_dp.hpp
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#pragma once
#include "graph/base.hpp"
#include "graph/tree.hpp"
template <typename TREE, typename Data>
struct Rerooting_dp {
static_assert(!TREE::Graph_type::is_directed);
TREE& tree;
vc<Data> dp_1; // 辺 pv に対して、部分木 v
vc<Data> dp_2; // 辺 pv に対して、部分木 p
vc<Data> dp; // full tree
template <typename F1, typename F2, typename F3>
Rerooting_dp(TREE& tree, F1 f_ee, F2 f_ev, F3 f_ve, const Data unit)
: tree(tree) {
build(f_ee, f_ev, f_ve, unit);
}
// v を根としたときの full tree
Data operator[](int v) { return dp[v]; }
// root を根としたときの部分木 v
Data get(int v, int root) {
if (root == v) return dp[v];
if (!tree.in_subtree(root, v)) { return dp_1[v]; }
int w = tree.jump(v, root, 1);
return dp_2[w];
}
template <typename F1, typename F2, typename F3>
void build(F1 f_ee, F2 f_ev, F3 f_ve, const Data unit) {
int N = tree.N;
// dp1: subtree
dp_1.assign(N, unit);
FOR_R(i, N) {
int v = tree.V[i];
for (auto&& e: tree.G[v]) {
if (e.to == tree.parent[v]) continue;
dp_1[v] = f_ee(dp_1[v], f_ve(dp_1[e.to], e));
}
dp_1[v] = f_ev(dp_1[v], v);
}
// dp2[v]: subtree of p, rooted at v
dp_2.assign(N, unit);
// dp[v]: fulltree, rooted at v
dp.assign(N, unit);
FOR(i, N) {
int p = tree.V[i];
vc<int> ch;
vc<Data> ch_data;
Data x = unit;
for (auto&& e: tree.G[p]) {
if (e.to == tree.parent[p]) {
x = f_ve(dp_2[p], e);
} else {
ch.eb(e.to);
ch_data.eb(f_ve(dp_1[e.to], e));
}
}
int n = len(ch);
if (!n) {
dp[p] = f_ev(x, p);
continue;
}
vc<Data> prod_left(n, x);
FOR(i, n - 1) prod_left[i + 1] = f_ee(prod_left[i], ch_data[i]);
Data prod_right = unit;
FOR_R(i, n) {
dp_2[ch[i]] = f_ev(f_ee(prod_left[i], prod_right), p);
prod_right = f_ee(prod_right, ch_data[i]);
}
dp[p] = f_ev(f_ee(x, prod_right), p);
}
}
};