Merge mzuenni changes

3 files changed, 89 insertions, 11 deletions

diff --git a/graph/2sat.cpp b/graph/2sat.cpp
index 8fb3d39..75e54e6 100644
--- a/graph/2sat.cpp
+++ b/graph/2sat.cpp
@@ -2,7 +2,7 @@ struct sat2 {
 	int n; // + scc variablen
 	vector<int> sol;
 
-	sat2(int vars) : n(vars*2), adj(vars*2) {};
+	sat2(int vars) : n(vars*2), adj(n) {}
 
 	static int var(int i) {return i << 1;} // use this!
 
@@ -18,20 +18,14 @@ struct sat2 {
 	void addAnd(int a, int b) {addTrue(a); addTrue(b);}
 	void addNand(int a, int b) {addOr(1^a, 1^b);}
 
-	bool solvable() {
+	bool solve() {
 		scc(); //scc code von oben
+		sol.assign(n, -1);
 		for (int i = 0; i < n; i += 2) {
 			if (idx[i] == idx[i + 1]) return false;
+			sol[i] = idx[i] < idx[i + 1];
+			sol[i + 1] = !sol[i];
 		}
 		return true;
 	}
-
-	void assign() {
-		sol.assign(n, -1);
-		for (int i = 0; i < sccCounter; i++) {
-			if (sol[sccs[i][0]] == -1) {
-				for (int v : sccs[i]) {
-					sol[v] = 1;
-					sol[1^v] = 0;
-	}}}}
 };
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;
+	}
+};
\ No newline at end of file
diff --git a/graph/virtualTree.cpp b/graph/virtualTree.cpp
new file mode 100644
index 0000000..f7a3cb1
--- /dev/null
+++ b/graph/virtualTree.cpp
@@ -0,0 +1,25 @@
+// needs dfs in- and out- time and lca function
+vector<int> in, out;
+
+void virtualTree(const vector<int>& a) { // takes indices of used nodes
+	auto ind = a;
+	sort(all(ind), [&](int x, int y) {return in[x] < in[y];});
+
+	for (int i=0; i<sz(a)-1; i++) {
+		ind.push_back(lca(ind[i], ind[i+1]));
+	}
+	sort(all(ind), [&](int x, int y) {return in[x] < in[y];});
+	ind.erase(unique(all(ind)), ind.end());
+
+	int n = ind.size();
+	vector<vector<int>> tree(n);
+	stack<int> st{{0}};
+	for (int i=1; i<n; i++) {
+		while (in[ind[i]] >= out[ind[st.top()]]) st.pop();
+		tree[st.top()].push_back(i);
+		st.push(i);
+	}
+
+	// virtual directed tree with n nodes, original indices in ind
+	// weights can be calculated if necessary, e.g. with binary lifting
+}