add rerooting dp template

1 files changed, 59 insertions, 0 deletions

diff --git a/graph/reroot.cpp b/graph/reroot.cpp
new file mode 100644
index 0000000..eeca43e
--- /dev/null
+++ b/graph/reroot.cpp
@@ -0,0 +1,59 @@
+// Usual Tree DP can be broken down in 4 steps:
+// - Initialize dp[v] = identity
+// - Iterate over all children w and take a value for w 
+//   by looking at dp[w] and possibly the edge label of v -> w
+// - combine the values of those children
+//   usually, this operation should be commutative and associative
+// - finalize the value of dp[v] after iterating over all children
+struct Reroot{
+	using T = ll;
+
+	// identity element
+	T E(){}
+	// x: dp value of child
+	// e: index of edge going to child
+	T takeChild(T x, int e){}
+	T combine(T x, T y){}
+	// called after combining all dp values of children
+	T finalize(T x, int v){}
+
+	vector<vector<pair<int, int>>> g;
+	vector<int> ord, pae;
+	vector<T> dp;
+
+	T dfs(int v){
+		ord.push_back(v);
+		for(auto [w, e] : g[v]){
+			g[w].erase(find(all(g[w]), pair(v, e^1)));
+			pae[w] = e^1;
+			dp[v] = combine(dp[v], takeChild(dfs(w), e));
+		}
+		return dp[v] = finalize(dp[v], v);
+	}
+
+	vector<T> solve(int n, vector<pair<int, int>> edges){
+		g.resize(n);
+		for(int i = 0; i < n-1; i++){
+			g[edges[i].first].emplace_back(edges[i].second, 2*i);
+			g[edges[i].second].emplace_back(edges[i].first, 2*i+1);
+		}
+		pae.assign(n, -1);
+		dp.assign(n, E());
+		dfs(0);
+		vector<T> updp(n, E()), res(n, E());
+		for(int v : ord){
+			vector<T> pref(sz(g[v])+1), suff(sz(g[v])+1);
+			if(v != 0) pref[0] = takeChild(updp[v], pae[v]);
+			for(int i = 0; i < sz(g[v]); i++){
+				pref[i+1] = suff[i] = takeChild(dp[g[v][i].first], g[v][i].second);
+				pref[i+1] = combine(pref[i], pref[i+1]);
+			}
+			for(int i = sz(g[v])-1; i >= 0; i--)
+				suff[i] = combine(suff[i], suff[i+1]);
+			for(int i = 0; i < sz(g[v]); i++)
+				updp[g[v][i].first] = finalize(combine(pref[i], suff[i+1]), v);
+			res[v] = finalize(pref.back(), v);
+		}
+		return res;
+	}
+};
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