Merge pull request #5 from f1or1an/new-master

shorter rerooting

1 files changed, 36 insertions, 50 deletions

diff --git a/content/graph/reroot.cpp b/content/graph/reroot.cpp
index 4c6a748..379c839 100644
--- a/content/graph/reroot.cpp
+++ b/content/graph/reroot.cpp
@@ -1,62 +1,48 @@
-// 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
+using W = ll; // edge weight type
+vector<vector<pair<int, W>>> adj;
+
 struct Reroot {
-	using T = ll;
+	using T = ll; // dp type
 
-	// 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) {}
+	static constexpr T E = 0; // neutral element
+	T takeChild(int v, int c, W w, T x) {} // move child along edge
+	static T comb(T x, T y) {}
+	T fin(int v, T x) {} // add v to own dp value x
 
-	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));
+	T dfs0(int v, int from = -1) {
+		T val = E;
+		for (auto [u, w] : adj[v]) {
+			if (u == from) continue;
+			val = comb(val, takeChild(v, u, w, dfs0(u, v)));
 		}
-		return dp[v] = fin(dp[v], v);
+		return dp[v] = fin(v, val);
 	}
 
-	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);
+	void dfs1(int v, int from = -1) {
+		vector<T> pref = {E};
+		for (auto [u, w] : adj[v]) {
+			pref.push_back(takeChild(v, u, w, dp[u]));
 		}
-		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);
+		auto suf = pref;
+		partial_sum(all(pref), pref.begin(), comb);
+		exclusive_scan(suf.rbegin(), suf.rend(),
+		               suf.rbegin(), E, comb);
+
+		for (int i = 0; i < sz(adj[v]); i++) {
+			auto [u, w] = adj[v][i];
+			if (u == from) continue;
+			dp[v] = fin(v, comb(pref[i], suf[i + 1]));
+			dfs1(u, v);
 		}
-		return res;
+		dp[v] = fin(v, suf[0]);
+	}
+
+	auto solve() {
+		dp.assign(sz(adj), E);
+		dfs0(0);
+		dfs1(0);
+		return dp;
 	}
 };