Merge pull request #338 from hitonanode/rename-rerooting

Rename rerooting

Author: hitonanode

tree/rerooting.hpp

@@ -8,77 +8,83 @@
 // Reference:
 // - https://atcoder.jp/contests/abc222/editorial/2749
 // - https://null-mn.hatenablog.com/entry/2020/04/14/124151
-template <class Edge, class St, class Ch, Ch (*merge)(Ch, Ch), Ch (*f)(St, int, Edge),
-          St (*g)(Ch, int), Ch (*e)()>
+template <class Edge, class Subtree, class Children, Children (*rake)(Children, Children),
+          Children (*add_edge)(Subtree, int, Edge), Subtree (*add_vertex)(Children, int),
+          Children (*e)()>
 struct rerooting {
     int n_;
     std::vector<int> par, visited;
     std::vector<std::vector<std::pair<int, Edge>>> to;
-    std::vector<St> dp_subtree;
-    std::vector<St> dp_par;
-    std::vector<St> dpall;
+
+    // dp_subtree[i] = DP(root=i, edge (i, par[i]) is removed).
+    std::vector<Subtree> dp_subtree;
+
+    // dp_par[i] = DP(root=par[i], edge (i, par[i]) is removed). dp_par[root] is meaningless.
+    std::vector<Subtree> dp_par;
+
+    // dpall[i] = DP(root=i, all edges exist).
+    std::vector<Subtree> dpall;
+
     rerooting(const std::vector<std::vector<std::pair<int, Edge>>> &to_)
         : n_(to_.size()), par(n_, -1), visited(n_, 0), to(to_) {
-        for (int i = 0; i < n_; ++i) dp_subtree.push_back(g(e(), i));
+        for (int i = 0; i < n_; ++i) dp_subtree.push_back(add_vertex(e(), i));
         dp_par = dpall = dp_subtree;
     }
 
     void run_connected(int root) {
-        if (visited[root]) return;
-        visited[root] = 1;
+        if (visited.at(root)) return;
+        visited.at(root) = 1;
         std::vector<int> visorder{root};
 
         for (int t = 0; t < int(visorder.size()); ++t) {
-            int now = visorder[t];
-            for (const auto &edge : to[now]) {
-                int nxt = edge.first;
-                if (visited[nxt]) continue;
+            int now = visorder.at(t);
+            for (const auto &[nxt, _] : to[now]) {
+                if (visited.at(nxt)) continue;
                 visorder.push_back(nxt);
-                visited[nxt] = 1;
-                par[nxt] = now;
+                visited.at(nxt) = 1;
+                par.at(nxt) = now;
             }
         }
 
         for (int t = int(visorder.size()) - 1; t >= 0; --t) {
-            int now = visorder[t];
-            Ch ch = e();
-            for (const auto &edge : to[now]) {
-                int nxt = edge.first;
-                if (nxt == par[now]) continue;
-                ch = merge(ch, f(dp_subtree[nxt], nxt, edge.second));
+            const int now = visorder.at(t);
+            Children ch = e();
+            for (const auto &[nxt, edge] : to.at(now)) {
+                if (nxt != par.at(now)) ch = rake(ch, add_edge(dp_subtree.at(nxt), nxt, edge));
             }
-            dp_subtree[now] = g(ch, now);
+            dp_subtree.at(now) = add_vertex(ch, now);
         }
 
-        std::vector<Ch> left;
+        std::vector<Children> left;
         for (int now : visorder) {
-            int m = int(to[now].size());
+            const int m = to.at(now).size();
             left.assign(m + 1, e());
             for (int j = 0; j < m; j++) {
-                int nxt = to[now][j].first;
-                const St &st = (nxt == par[now] ? dp_par[now] : dp_subtree[nxt]);
-                left[j + 1] = merge(left[j], f(st, nxt, to[now][j].second));
+                const auto &[nxt, edge] = to.at(now).at(j);
+                const Subtree &st = (nxt == par.at(now) ? dp_par.at(now) : dp_subtree.at(nxt));
+                left.at(j + 1) = rake(left.at(j), add_edge(st, nxt, edge));
             }
-            dpall[now] = g(left.back(), now);
+            dpall.at(now) = add_vertex(left.back(), now);
 
-            Ch rprod = e();
+            Children rprod = e();
             for (int j = m - 1; j >= 0; --j) {
-                int nxt = to[now][j].first;
-                if (nxt != par[now]) dp_par[nxt] = g(merge(left[j], rprod), now);
+                const auto &[nxt, edge] = to.at(now).at(j);
+
+                if (nxt != par.at(now)) dp_par.at(nxt) = add_vertex(rake(left.at(j), rprod), now);
 
-                const St &st = (nxt == par[now] ? dp_par[now] : dp_subtree[nxt]);
-                rprod = merge(f(st, nxt, to[now][j].second), rprod);
+                const Subtree &st = (nxt == par.at(now) ? dp_par.at(now) : dp_subtree.at(nxt));
+                rprod = rake(add_edge(st, nxt, edge), rprod);
             }
         }
     }
 
     void run() {
         for (int i = 0; i < n_; ++i) {
-            if (!visited[i]) run_connected(i);
+            if (!visited.at(i)) run_connected(i);
         }
     }
 
-    const St &get_subtree(int root_, int par_) const {
+    const Subtree &get_subtree(int root_, int par_) const {
         if (par_ < 0) return dpall.at(root_);
         if (par.at(root_) == par_) return dp_subtree.at(root_);
         if (par.at(par_) == root_) return dp_par.at(par_);
@@ -87,13 +93,13 @@ struct rerooting {
 };
 /* Template:
 struct Subtree {};
-struct Child {};
+struct Children {};
 struct Edge {};
-Child e() { return Child(); }
-Child merge(Child x, Child y) { return Child(); }
-Child f(Subtree x, int ch_id, Edge edge) { return Child(); }
-Subtree g(Child x, int v_id) { return Subtree(); }
+Children e() { return Children(); }
+Children rake(Children x, Children y) { return Children(); }
+Children add_edge(Subtree x, int ch_id, Edge edge) { return Children(); }
+Subtree add_vertex(Children x, int v_id) { return Subtree(); }
 
 vector<vector<pair<int, Edge>>> to;
-rerooting<Edge, Subtree, Child, merge, f, g, e> tree(to);
+rerooting<Edge, Subtree, Children, rake, add_edge, add_vertex, e> tree(to);
 */

tree/rerooting.md

@@ -7,12 +7,12 @@ documentation_of: ./rerooting.hpp
 
 - ここに記述する内容はリンク [1] で説明されていることとほぼ同等．
 - 木の各頂点・各辺になんらかのデータ構造が載っている．
-- 根付き木について，各頂点 $v$ を根とする部分木に対して計算される `St` 型の情報を $X_v$ とする．また，各辺 $uv$ が持つ `Edge` 型の情報を $e_{uv}$ とする．
-- $X_v$ は $X_v = g\left(\mathrm{merge}\left(f(X\_{c\_1}, c\_1, e\_{v c\_1}), \dots, f(X\_{c\_k}, c\_k, e\_{v c\_k})\right), v \right)$ を満たす．ここで $c\_1, \dots, c\_k$ は $v$ の子の頂点たち．
-  - $f(X\_v, v, e\_{uv})$ は $u$ の子 $v$ について `Ch` 型の情報を計算する関数．
-  - $\mathrm{merge}(y\_1, \dots, y\_k)$ は任意個の `Ch` 型の引数の積を計算する関数．
-  - $g(y, v)$ は `Ch` 型の引数 $y$ をもとに頂点 $v$ における `St` 型の情報を計算する関数．
-  - `Ch` 型には結合法則が成立しなければならない．また， `Ch` 型の単位元を `e()` とする．
+- 根付き木について，各頂点 $v$ を根とする部分木に対して計算される `Subtree` 型の情報を $X_v$ とする．また，各辺 $uv$ が持つ `Edge` 型の情報を $e_{uv}$ とする．
+- $X_v$ は $X_v = \mathrm{add\_vertex}\left(\mathrm{rake}\left(\mathrm{add\_edge}(X\_{c\_1}, c\_1, e\_{v c\_1}), \dots, \mathrm{add\_edge}(X\_{c\_k}, c\_k, e\_{v c\_k})\right), v \right)$ を満たす．ここで $c\_1, \dots, c\_k$ は $v$ の子の頂点たち．
+  - $\mathrm{add\_edge}(X\_v, v, e\_{uv})$ は $u$ の子 $v$ について `Children` 型の情報を計算する関数．
+  - $\mathrm{add\_vertex}(y, v)$ は `Children` 型の引数 $y$ をもとに頂点 $v$ における `Subtree` 型の情報を計算する関数．
+  - $\mathrm{rake}(y\_1, \dots, y\_k)$ は任意個の `Children` 型の引数の積を計算する関数．
+  - $\mathrm{rake}()$ には結合法則が成立しなければならない．また， `Children` 型の単位元を `e()` とする．
 - 以上のような性質を満たすデータ構造を考えたとき，本ライブラリは森の各頂点 $r$ を根とみなしたときの連結成分に関する $X_r$ の値を全ての $r$ について線形時間で計算する．
 
 ## 使用方法（例）
@@ -23,29 +23,29 @@ struct Subtree {
     bool exist;
     int oneway, round;
 };
-struct Child {
+struct Children {
     bool exist;
     int oneway, round;
 };
-Child merge(Child x, Child y) {
+Children rake(Children x, Children y) {
     if (!x.exist) return y;
     if (!y.exist) return x;
-    return Child{true, min(x.oneway + y.round, y.oneway + x.round), x.round + y.round};
+    return Children{true, min(x.oneway + y.round, y.oneway + x.round), x.round + y.round};
 }
-Child f(Subtree x, int, tuple<>) {
+Children add_edge(Subtree x, int, tuple<>) {
     if (!x.exist) return {false, 0, 0};
     return {true, x.oneway + 1, x.round + 2};
 }
-Subtree g(Child x, int v) {
+Subtree add_vertex(Children x, int v) {
     if (x.exist) return {true, x.oneway, x.round};
     return {inD[v], 0, 0};
     return {false, 0, 0};
 }
-Child e() { return {false, 0, 0}; }
+Children e() { return {false, 0, 0}; }
 
 
 vector<vector<pair<int, tuple<>>>> to;
-rerooting<tuple<>, Subtree, Child, merge, f, g, e> tree(to);
+rerooting<tuple<>, Subtree, Children, rake, add_edge, add_vertex, e> tree(to);
 tree.run();
 for (auto x : tree.dpall) cout << x.oneway << '\n';
 ```

tree/test/rerooting.aoj1595.test.cpp

@@ -9,19 +9,19 @@ using namespace std;
 struct Subtree {
     int oneway, round;
 };
-struct Child {
+struct Children {
     int oneway, round;
 };
 
-Child merge(Child x, Child y) {
-    return Child{min(x.oneway + y.round, y.oneway + x.round), x.round + y.round};
+Children merge(Children x, Children y) {
+    return Children{min(x.oneway + y.round, y.oneway + x.round), x.round + y.round};
 }
 
-Child f(Subtree x, int, tuple<>) { return {x.oneway + 1, x.round + 2}; }
+Children add_edge(Subtree x, int, tuple<>) { return {x.oneway + 1, x.round + 2}; }
 
-Subtree g(Child x, int) { return {x.oneway, x.round}; }
+Subtree add_vertex(Children x, int) { return {x.oneway, x.round}; }
 
-Child e() { return {0, 0}; }
+Children e() { return {0, 0}; }
 
 int main() {
     cin.tie(nullptr), ios::sync_with_stdio(false);
@@ -34,7 +34,7 @@ int main() {
         --u, --v;
         to[u].push_back({v, {}}), to[v].push_back({u, {}});
     }
-    rerooting<tuple<>, Subtree, Child, merge, f, g, e> tree(to);
+    rerooting<tuple<>, Subtree, Children, merge, add_edge, add_vertex, e> tree(to);
     tree.run();
     for (auto x : tree.dpall) cout << x.oneway << '\n';
 }

tree/test/rerooting.yuki1718.test.cpp

@@ -11,24 +11,24 @@ struct Subtree {
     bool exist;
     int oneway, round;
 };
-struct Child {
+struct Children {
     bool exist;
     int oneway, round;
 };
-Child e() { return {false, 0, 0}; }
+Children e() { return {false, 0, 0}; }
 
-Child merge(Child x, Child y) {
+Children merge(Children x, Children y) {
     if (!x.exist) return y;
     if (!y.exist) return x;
-    return Child{true, min(x.oneway + y.round, y.oneway + x.round), x.round + y.round};
+    return Children{true, min(x.oneway + y.round, y.oneway + x.round), x.round + y.round};
 }
 
-Child f(Subtree x, int, tuple<>) {
+Children add_edge(Subtree x, int, tuple<>) {
     if (!x.exist) return e();
     return {true, x.oneway + 1, x.round + 2};
 }
 
-Subtree g(Child x, int v) {
+Subtree add_vertex(Children x, int v) {
     if (x.exist or inD[v]) return {true, x.oneway, x.round};
     return {false, 0, 0};
 }
@@ -52,7 +52,7 @@ int main() {
         cin >> d;
         inD[d - 1] = 1;
     }
-    rerooting<tuple<>, Subtree, Child, merge, f, g, e> tree(to);
+    rerooting<tuple<>, Subtree, Children, merge, add_edge, add_vertex, e> tree(to);
     tree.run();
     for (auto x : tree.dpall) cout << x.oneway << '\n';
 }