merge

1 files changed, 62 insertions, 0 deletions

diff --git a/graph/reroot.cpp b/graph/reroot.cpp
new file mode 100644
index 0000000..4c6a748
--- /dev/null
+++ b/graph/reroot.cpp
@@ -0,0 +1,62 @@
+// 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 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 comb(T x, T y) {}
+	// called after combining all dp values of children
+	T fin(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] = comb(dp[v], takeChild(dfs(w), e));
+		}
+		return dp[v] = fin(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++){
+				auto [u, w] = g[v][i];
+				pref[i+1] = suff[i] = takeChild(dp[u], w);
+				pref[i+1] = comb(pref[i], pref[i+1]);
+			}
+			for (int i = sz(g[v])-1; i >= 0; i--) {
+				suff[i] = comb(suff[i], suff[i+1]);
+			}
+			for (int i = 0; i < sz(g[v]); i++) {
+				updp[g[v][i].first] = fin(comb(pref[i], suff[i+1]), v);
+			}
+			res[v] = fin(pref.back(), v);
+		}
+		return res;
+	}
+};