From ab663a553fb64b6339a19bf1fc466cec3c9c5e1b Mon Sep 17 00:00:00 2001 From: GitHub Date: Sun, 5 May 2024 06:15:19 +0000 Subject: [PATCH] [auto-verifier] docs commit 4ab18443641837e473bf118fb6d7e0b0195c9b9f --- tree/rerooting.hpp.md | 184 ++++++++++++----------- tree/test/rerooting.aoj1595.test.cpp.md | 123 ++++++++------- tree/test/rerooting.yuki1718.test.cpp.md | 133 ++++++++-------- 3 files changed, 233 insertions(+), 207 deletions(-) diff --git a/tree/rerooting.hpp.md b/tree/rerooting.hpp.md index 37bdb21a..68bfde99 100644 --- a/tree/rerooting.hpp.md +++ b/tree/rerooting.hpp.md @@ -19,92 +19,104 @@ data: bundledCode: "#line 2 \"tree/rerooting.hpp\"\n#include \n#include \n\ #include \n#include \n\n// Rerooting\n// Reference:\n// - https://atcoder.jp/contests/abc222/editorial/2749\n\ // - https://null-mn.hatenablog.com/entry/2020/04/14/124151\ntemplate \nstruct rerooting {\n int n_;\n std::vector\ - \ par, visited;\n std::vector>> to;\n std::vector\ - \ dp_subtree;\n std::vector dp_par;\n std::vector dpall;\n rerooting(const\ + \ class Subtree, class Children, Children (*rake)(Children, Children),\n \ + \ Children (*add_edge)(Subtree, int, Edge), Subtree (*add_vertex)(Children,\ + \ int),\n Children (*e)()>\nstruct rerooting {\n int n_;\n std::vector\ + \ par, visited;\n std::vector>> to;\n\n \ + \ // dp_subtree[i] = DP(root=i, edge (i, par[i]) is removed).\n std::vector\ + \ dp_subtree;\n\n // dp_par[i] = DP(root=par[i], edge (i, par[i]) is removed).\ + \ dp_par[root] is meaningless.\n std::vector dp_par;\n\n // dpall[i]\ + \ = DP(root=i, all edges exist).\n std::vector dpall;\n\n rerooting(const\ \ std::vector>> &to_)\n : n_(to_.size()),\ \ par(n_, -1), visited(n_, 0), to(to_) {\n for (int i = 0; i < n_; ++i)\ - \ dp_subtree.push_back(g(e(), i));\n dp_par = dpall = dp_subtree;\n \ - \ }\n\n void run_connected(int root) {\n if (visited[root]) return;\n\ - \ visited[root] = 1;\n std::vector visorder{root};\n\n \ - \ for (int t = 0; t < int(visorder.size()); ++t) {\n int now = visorder[t];\n\ - \ for (const auto &edge : to[now]) {\n int nxt = edge.first;\n\ - \ if (visited[nxt]) continue;\n visorder.push_back(nxt);\n\ - \ visited[nxt] = 1;\n par[nxt] = now;\n \ - \ }\n }\n\n for (int t = int(visorder.size()) - 1; t >= 0; --t)\ - \ {\n int now = visorder[t];\n Ch ch = e();\n \ - \ for (const auto &edge : to[now]) {\n int nxt = edge.first;\n\ - \ if (nxt == par[now]) continue;\n ch = merge(ch,\ - \ f(dp_subtree[nxt], nxt, edge.second));\n }\n dp_subtree[now]\ - \ = g(ch, now);\n }\n\n std::vector left;\n for (int\ - \ now : visorder) {\n int m = int(to[now].size());\n left.assign(m\ - \ + 1, e());\n for (int j = 0; j < m; j++) {\n int nxt\ - \ = to[now][j].first;\n const St &st = (nxt == par[now] ? dp_par[now]\ - \ : dp_subtree[nxt]);\n left[j + 1] = merge(left[j], f(st, nxt,\ - \ to[now][j].second));\n }\n dpall[now] = g(left.back(),\ - \ now);\n\n Ch rprod = e();\n for (int j = m - 1; j >= 0;\ - \ --j) {\n int nxt = to[now][j].first;\n if (nxt\ - \ != par[now]) dp_par[nxt] = g(merge(left[j], rprod), now);\n\n \ - \ const St &st = (nxt == par[now] ? dp_par[now] : dp_subtree[nxt]);\n \ - \ rprod = merge(f(st, nxt, to[now][j].second), rprod);\n }\n\ + \ dp_subtree.push_back(add_vertex(e(), i));\n dp_par = dpall = dp_subtree;\n\ + \ }\n\n void run_connected(int root) {\n if (visited.at(root)) return;\n\ + \ visited.at(root) = 1;\n std::vector visorder{root};\n\n \ + \ for (int t = 0; t < int(visorder.size()); ++t) {\n int now\ + \ = visorder.at(t);\n for (const auto &[nxt, _] : to[now]) {\n \ + \ if (visited.at(nxt)) continue;\n visorder.push_back(nxt);\n\ + \ visited.at(nxt) = 1;\n par.at(nxt) = now;\n \ + \ }\n }\n\n for (int t = int(visorder.size()) - 1; t >=\ + \ 0; --t) {\n const int now = visorder.at(t);\n Children\ + \ ch = e();\n for (const auto &[nxt, edge] : to.at(now)) {\n \ + \ if (nxt != par.at(now)) ch = rake(ch, add_edge(dp_subtree.at(nxt),\ + \ nxt, edge));\n }\n dp_subtree.at(now) = add_vertex(ch,\ + \ now);\n }\n\n std::vector left;\n for (int now\ + \ : visorder) {\n const int m = to.at(now).size();\n left.assign(m\ + \ + 1, e());\n for (int j = 0; j < m; j++) {\n const\ + \ auto &[nxt, edge] = to.at(now).at(j);\n const Subtree &st = (nxt\ + \ == par.at(now) ? dp_par.at(now) : dp_subtree.at(nxt));\n left.at(j\ + \ + 1) = rake(left.at(j), add_edge(st, nxt, edge));\n }\n \ + \ dpall.at(now) = add_vertex(left.back(), now);\n\n Children rprod\ + \ = e();\n for (int j = m - 1; j >= 0; --j) {\n const\ + \ auto &[nxt, edge] = to.at(now).at(j);\n\n if (nxt != par.at(now))\ + \ dp_par.at(nxt) = add_vertex(rake(left.at(j), rprod), now);\n\n \ + \ const Subtree &st = (nxt == par.at(now) ? dp_par.at(now) : dp_subtree.at(nxt));\n\ + \ rprod = rake(add_edge(st, nxt, edge), rprod);\n }\n\ \ }\n }\n\n void run() {\n for (int i = 0; i < n_; ++i) {\n\ - \ if (!visited[i]) run_connected(i);\n }\n }\n\n const\ - \ St &get_subtree(int root_, int par_) const {\n if (par_ < 0) return dpall.at(root_);\n\ - \ if (par.at(root_) == par_) return dp_subtree.at(root_);\n if (par.at(par_)\ - \ == root_) return dp_par.at(par_);\n std::exit(1);\n }\n};\n/* Template:\n\ - struct Subtree {};\nstruct Child {};\nstruct Edge {};\nChild e() { return Child();\ - \ }\nChild merge(Child x, Child y) { return Child(); }\nChild f(Subtree x, int\ - \ ch_id, Edge edge) { return Child(); }\nSubtree g(Child x, int v_id) { return\ - \ Subtree(); }\n\nvector>> to;\nrerooting tree(to);\n*/\n" + \ if (!visited.at(i)) run_connected(i);\n }\n }\n\n const\ + \ Subtree &get_subtree(int root_, int par_) const {\n if (par_ < 0) return\ + \ dpall.at(root_);\n if (par.at(root_) == par_) return dp_subtree.at(root_);\n\ + \ if (par.at(par_) == root_) return dp_par.at(par_);\n std::exit(1);\n\ + \ }\n};\n/* Template:\nstruct Subtree {};\nstruct Children {};\nstruct Edge\ + \ {};\nChildren e() { return Children(); }\nChildren rake(Children x, Children\ + \ y) { return Children(); }\nChildren add_edge(Subtree x, int ch_id, Edge edge)\ + \ { return Children(); }\nSubtree add_vertex(Children x, int v_id) { return Subtree();\ + \ }\n\nvector>> to;\nrerooting tree(to);\n*/\n" code: "#pragma once\n#include \n#include \n#include \n\ #include \n\n// Rerooting\n// Reference:\n// - https://atcoder.jp/contests/abc222/editorial/2749\n\ // - https://null-mn.hatenablog.com/entry/2020/04/14/124151\ntemplate \nstruct rerooting {\n int n_;\n std::vector\ - \ par, visited;\n std::vector>> to;\n std::vector\ - \ dp_subtree;\n std::vector dp_par;\n std::vector dpall;\n rerooting(const\ + \ class Subtree, class Children, Children (*rake)(Children, Children),\n \ + \ Children (*add_edge)(Subtree, int, Edge), Subtree (*add_vertex)(Children,\ + \ int),\n Children (*e)()>\nstruct rerooting {\n int n_;\n std::vector\ + \ par, visited;\n std::vector>> to;\n\n \ + \ // dp_subtree[i] = DP(root=i, edge (i, par[i]) is removed).\n std::vector\ + \ dp_subtree;\n\n // dp_par[i] = DP(root=par[i], edge (i, par[i]) is removed).\ + \ dp_par[root] is meaningless.\n std::vector dp_par;\n\n // dpall[i]\ + \ = DP(root=i, all edges exist).\n std::vector dpall;\n\n rerooting(const\ \ std::vector>> &to_)\n : n_(to_.size()),\ \ par(n_, -1), visited(n_, 0), to(to_) {\n for (int i = 0; i < n_; ++i)\ - \ dp_subtree.push_back(g(e(), i));\n dp_par = dpall = dp_subtree;\n \ - \ }\n\n void run_connected(int root) {\n if (visited[root]) return;\n\ - \ visited[root] = 1;\n std::vector visorder{root};\n\n \ - \ for (int t = 0; t < int(visorder.size()); ++t) {\n int now = visorder[t];\n\ - \ for (const auto &edge : to[now]) {\n int nxt = edge.first;\n\ - \ if (visited[nxt]) continue;\n visorder.push_back(nxt);\n\ - \ visited[nxt] = 1;\n par[nxt] = now;\n \ - \ }\n }\n\n for (int t = int(visorder.size()) - 1; t >= 0; --t)\ - \ {\n int now = visorder[t];\n Ch ch = e();\n \ - \ for (const auto &edge : to[now]) {\n int nxt = edge.first;\n\ - \ if (nxt == par[now]) continue;\n ch = merge(ch,\ - \ f(dp_subtree[nxt], nxt, edge.second));\n }\n dp_subtree[now]\ - \ = g(ch, now);\n }\n\n std::vector left;\n for (int\ - \ now : visorder) {\n int m = int(to[now].size());\n left.assign(m\ - \ + 1, e());\n for (int j = 0; j < m; j++) {\n int nxt\ - \ = to[now][j].first;\n const St &st = (nxt == par[now] ? dp_par[now]\ - \ : dp_subtree[nxt]);\n left[j + 1] = merge(left[j], f(st, nxt,\ - \ to[now][j].second));\n }\n dpall[now] = g(left.back(),\ - \ now);\n\n Ch rprod = e();\n for (int j = m - 1; j >= 0;\ - \ --j) {\n int nxt = to[now][j].first;\n if (nxt\ - \ != par[now]) dp_par[nxt] = g(merge(left[j], rprod), now);\n\n \ - \ const St &st = (nxt == par[now] ? dp_par[now] : dp_subtree[nxt]);\n \ - \ rprod = merge(f(st, nxt, to[now][j].second), rprod);\n }\n\ + \ dp_subtree.push_back(add_vertex(e(), i));\n dp_par = dpall = dp_subtree;\n\ + \ }\n\n void run_connected(int root) {\n if (visited.at(root)) return;\n\ + \ visited.at(root) = 1;\n std::vector visorder{root};\n\n \ + \ for (int t = 0; t < int(visorder.size()); ++t) {\n int now\ + \ = visorder.at(t);\n for (const auto &[nxt, _] : to[now]) {\n \ + \ if (visited.at(nxt)) continue;\n visorder.push_back(nxt);\n\ + \ visited.at(nxt) = 1;\n par.at(nxt) = now;\n \ + \ }\n }\n\n for (int t = int(visorder.size()) - 1; t >=\ + \ 0; --t) {\n const int now = visorder.at(t);\n Children\ + \ ch = e();\n for (const auto &[nxt, edge] : to.at(now)) {\n \ + \ if (nxt != par.at(now)) ch = rake(ch, add_edge(dp_subtree.at(nxt),\ + \ nxt, edge));\n }\n dp_subtree.at(now) = add_vertex(ch,\ + \ now);\n }\n\n std::vector left;\n for (int now\ + \ : visorder) {\n const int m = to.at(now).size();\n left.assign(m\ + \ + 1, e());\n for (int j = 0; j < m; j++) {\n const\ + \ auto &[nxt, edge] = to.at(now).at(j);\n const Subtree &st = (nxt\ + \ == par.at(now) ? dp_par.at(now) : dp_subtree.at(nxt));\n left.at(j\ + \ + 1) = rake(left.at(j), add_edge(st, nxt, edge));\n }\n \ + \ dpall.at(now) = add_vertex(left.back(), now);\n\n Children rprod\ + \ = e();\n for (int j = m - 1; j >= 0; --j) {\n const\ + \ auto &[nxt, edge] = to.at(now).at(j);\n\n if (nxt != par.at(now))\ + \ dp_par.at(nxt) = add_vertex(rake(left.at(j), rprod), now);\n\n \ + \ const Subtree &st = (nxt == par.at(now) ? dp_par.at(now) : dp_subtree.at(nxt));\n\ + \ rprod = rake(add_edge(st, nxt, edge), rprod);\n }\n\ \ }\n }\n\n void run() {\n for (int i = 0; i < n_; ++i) {\n\ - \ if (!visited[i]) run_connected(i);\n }\n }\n\n const\ - \ St &get_subtree(int root_, int par_) const {\n if (par_ < 0) return dpall.at(root_);\n\ - \ if (par.at(root_) == par_) return dp_subtree.at(root_);\n if (par.at(par_)\ - \ == root_) return dp_par.at(par_);\n std::exit(1);\n }\n};\n/* Template:\n\ - struct Subtree {};\nstruct Child {};\nstruct Edge {};\nChild e() { return Child();\ - \ }\nChild merge(Child x, Child y) { return Child(); }\nChild f(Subtree x, int\ - \ ch_id, Edge edge) { return Child(); }\nSubtree g(Child x, int v_id) { return\ - \ Subtree(); }\n\nvector>> to;\nrerooting tree(to);\n*/\n" + \ if (!visited.at(i)) run_connected(i);\n }\n }\n\n const\ + \ Subtree &get_subtree(int root_, int par_) const {\n if (par_ < 0) return\ + \ dpall.at(root_);\n if (par.at(root_) == par_) return dp_subtree.at(root_);\n\ + \ if (par.at(par_) == root_) return dp_par.at(par_);\n std::exit(1);\n\ + \ }\n};\n/* Template:\nstruct Subtree {};\nstruct Children {};\nstruct Edge\ + \ {};\nChildren e() { return Children(); }\nChildren rake(Children x, Children\ + \ y) { return Children(); }\nChildren add_edge(Subtree x, int ch_id, Edge edge)\ + \ { return Children(); }\nSubtree add_vertex(Children x, int v_id) { return Subtree();\ + \ }\n\nvector>> to;\nrerooting tree(to);\n*/\n" dependsOn: [] isVerificationFile: false path: tree/rerooting.hpp requiredBy: [] - timestamp: '2023-04-25 08:57:43+09:00' + timestamp: '2024-05-05 15:10:50+09:00' verificationStatus: LIBRARY_ALL_AC verifiedWith: - tree/test/rerooting.yuki1718.test.cpp @@ -118,12 +130,12 @@ title: "Rerooting \uFF08\u5168\u65B9\u4F4D\u6728 DP\uFF09" - 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） @@ -134,29 +146,29 @@ 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>>> to; -rerooting, Subtree, Child, merge, f, g, e> tree(to); +rerooting, Subtree, Children, rake, add_edge, add_vertex, e> tree(to); tree.run(); for (auto x : tree.dpall) cout << x.oneway << '\n'; ``` diff --git a/tree/test/rerooting.aoj1595.test.cpp.md b/tree/test/rerooting.aoj1595.test.cpp.md index 53b7894c..241c157f 100644 --- a/tree/test/rerooting.aoj1595.test.cpp.md +++ b/tree/test/rerooting.aoj1595.test.cpp.md @@ -19,77 +19,84 @@ data: \ \"tree/rerooting.hpp\"\n#include \n#include \n#include \n\ #include \n\n// Rerooting\n// Reference:\n// - https://atcoder.jp/contests/abc222/editorial/2749\n\ // - https://null-mn.hatenablog.com/entry/2020/04/14/124151\ntemplate \nstruct rerooting {\n int n_;\n std::vector\ - \ par, visited;\n std::vector>> to;\n std::vector\ - \ dp_subtree;\n std::vector dp_par;\n std::vector dpall;\n rerooting(const\ + \ class Subtree, class Children, Children (*rake)(Children, Children),\n \ + \ Children (*add_edge)(Subtree, int, Edge), Subtree (*add_vertex)(Children,\ + \ int),\n Children (*e)()>\nstruct rerooting {\n int n_;\n std::vector\ + \ par, visited;\n std::vector>> to;\n\n \ + \ // dp_subtree[i] = DP(root=i, edge (i, par[i]) is removed).\n std::vector\ + \ dp_subtree;\n\n // dp_par[i] = DP(root=par[i], edge (i, par[i]) is removed).\ + \ dp_par[root] is meaningless.\n std::vector dp_par;\n\n // dpall[i]\ + \ = DP(root=i, all edges exist).\n std::vector dpall;\n\n rerooting(const\ \ std::vector>> &to_)\n : n_(to_.size()),\ \ par(n_, -1), visited(n_, 0), to(to_) {\n for (int i = 0; i < n_; ++i)\ - \ dp_subtree.push_back(g(e(), i));\n dp_par = dpall = dp_subtree;\n \ - \ }\n\n void run_connected(int root) {\n if (visited[root]) return;\n\ - \ visited[root] = 1;\n std::vector visorder{root};\n\n \ - \ for (int t = 0; t < int(visorder.size()); ++t) {\n int now = visorder[t];\n\ - \ for (const auto &edge : to[now]) {\n int nxt = edge.first;\n\ - \ if (visited[nxt]) continue;\n visorder.push_back(nxt);\n\ - \ visited[nxt] = 1;\n par[nxt] = now;\n \ - \ }\n }\n\n for (int t = int(visorder.size()) - 1; t >= 0; --t)\ - \ {\n int now = visorder[t];\n Ch ch = e();\n \ - \ for (const auto &edge : to[now]) {\n int nxt = edge.first;\n\ - \ if (nxt == par[now]) continue;\n ch = merge(ch,\ - \ f(dp_subtree[nxt], nxt, edge.second));\n }\n dp_subtree[now]\ - \ = g(ch, now);\n }\n\n std::vector left;\n for (int\ - \ now : visorder) {\n int m = int(to[now].size());\n left.assign(m\ - \ + 1, e());\n for (int j = 0; j < m; j++) {\n int nxt\ - \ = to[now][j].first;\n const St &st = (nxt == par[now] ? dp_par[now]\ - \ : dp_subtree[nxt]);\n left[j + 1] = merge(left[j], f(st, nxt,\ - \ to[now][j].second));\n }\n dpall[now] = g(left.back(),\ - \ now);\n\n Ch rprod = e();\n for (int j = m - 1; j >= 0;\ - \ --j) {\n int nxt = to[now][j].first;\n if (nxt\ - \ != par[now]) dp_par[nxt] = g(merge(left[j], rprod), now);\n\n \ - \ const St &st = (nxt == par[now] ? dp_par[now] : dp_subtree[nxt]);\n \ - \ rprod = merge(f(st, nxt, to[now][j].second), rprod);\n }\n\ + \ dp_subtree.push_back(add_vertex(e(), i));\n dp_par = dpall = dp_subtree;\n\ + \ }\n\n void run_connected(int root) {\n if (visited.at(root)) return;\n\ + \ visited.at(root) = 1;\n std::vector visorder{root};\n\n \ + \ for (int t = 0; t < int(visorder.size()); ++t) {\n int now\ + \ = visorder.at(t);\n for (const auto &[nxt, _] : to[now]) {\n \ + \ if (visited.at(nxt)) continue;\n visorder.push_back(nxt);\n\ + \ visited.at(nxt) = 1;\n par.at(nxt) = now;\n \ + \ }\n }\n\n for (int t = int(visorder.size()) - 1; t >=\ + \ 0; --t) {\n const int now = visorder.at(t);\n Children\ + \ ch = e();\n for (const auto &[nxt, edge] : to.at(now)) {\n \ + \ if (nxt != par.at(now)) ch = rake(ch, add_edge(dp_subtree.at(nxt),\ + \ nxt, edge));\n }\n dp_subtree.at(now) = add_vertex(ch,\ + \ now);\n }\n\n std::vector left;\n for (int now\ + \ : visorder) {\n const int m = to.at(now).size();\n left.assign(m\ + \ + 1, e());\n for (int j = 0; j < m; j++) {\n const\ + \ auto &[nxt, edge] = to.at(now).at(j);\n const Subtree &st = (nxt\ + \ == par.at(now) ? dp_par.at(now) : dp_subtree.at(nxt));\n left.at(j\ + \ + 1) = rake(left.at(j), add_edge(st, nxt, edge));\n }\n \ + \ dpall.at(now) = add_vertex(left.back(), now);\n\n Children rprod\ + \ = e();\n for (int j = m - 1; j >= 0; --j) {\n const\ + \ auto &[nxt, edge] = to.at(now).at(j);\n\n if (nxt != par.at(now))\ + \ dp_par.at(nxt) = add_vertex(rake(left.at(j), rprod), now);\n\n \ + \ const Subtree &st = (nxt == par.at(now) ? dp_par.at(now) : dp_subtree.at(nxt));\n\ + \ rprod = rake(add_edge(st, nxt, edge), rprod);\n }\n\ \ }\n }\n\n void run() {\n for (int i = 0; i < n_; ++i) {\n\ - \ if (!visited[i]) run_connected(i);\n }\n }\n\n const\ - \ St &get_subtree(int root_, int par_) const {\n if (par_ < 0) return dpall.at(root_);\n\ - \ if (par.at(root_) == par_) return dp_subtree.at(root_);\n if (par.at(par_)\ - \ == root_) return dp_par.at(par_);\n std::exit(1);\n }\n};\n/* Template:\n\ - struct Subtree {};\nstruct Child {};\nstruct Edge {};\nChild e() { return Child();\ - \ }\nChild merge(Child x, Child y) { return Child(); }\nChild f(Subtree x, int\ - \ ch_id, Edge edge) { return Child(); }\nSubtree g(Child x, int v_id) { return\ - \ Subtree(); }\n\nvector>> to;\nrerooting tree(to);\n*/\n#line 3 \"tree/test/rerooting.aoj1595.test.cpp\"\ + \ if (!visited.at(i)) run_connected(i);\n }\n }\n\n const\ + \ Subtree &get_subtree(int root_, int par_) const {\n if (par_ < 0) return\ + \ dpall.at(root_);\n if (par.at(root_) == par_) return dp_subtree.at(root_);\n\ + \ if (par.at(par_) == root_) return dp_par.at(par_);\n std::exit(1);\n\ + \ }\n};\n/* Template:\nstruct Subtree {};\nstruct Children {};\nstruct Edge\ + \ {};\nChildren e() { return Children(); }\nChildren rake(Children x, Children\ + \ y) { return Children(); }\nChildren add_edge(Subtree x, int ch_id, Edge edge)\ + \ { return Children(); }\nSubtree add_vertex(Children x, int v_id) { return Subtree();\ + \ }\n\nvector>> to;\nrerooting tree(to);\n*/\n#line 3 \"tree/test/rerooting.aoj1595.test.cpp\"\ \n#include \n#include \n#line 7 \"tree/test/rerooting.aoj1595.test.cpp\"\ \nusing namespace std;\n\nstruct Subtree {\n int oneway, round;\n};\nstruct\ - \ Child {\n int oneway, round;\n};\n\nChild merge(Child x, Child y) {\n \ - \ return Child{min(x.oneway + y.round, y.oneway + x.round), x.round + y.round};\n\ - }\n\nChild f(Subtree x, int, tuple<>) { return {x.oneway + 1, x.round + 2}; }\n\ - \nSubtree g(Child x, int) { return {x.oneway, x.round}; }\n\nChild e() { return\ - \ {0, 0}; }\n\nint main() {\n cin.tie(nullptr), ios::sync_with_stdio(false);\n\ - \ int N;\n cin >> N;\n vector>>> to(N);\n \ - \ for (int i = 0; i < N - 1; ++i) {\n int u, v;\n cin >> u >> v;\n\ - \ --u, --v;\n to[u].push_back({v, {}}), to[v].push_back({u, {}});\n\ - \ }\n rerooting, Subtree, Child, merge, f, g, e> tree(to);\n \ - \ tree.run();\n for (auto x : tree.dpall) cout << x.oneway << '\\n';\n}\n" - code: "#define PROBLEM \"https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=1595\"\ - \n#include \"../rerooting.hpp\"\n#include \n#include \n#include\ - \ \n#include \nusing namespace std;\n\nstruct Subtree {\n \ - \ int oneway, round;\n};\nstruct Child {\n int oneway, round;\n};\n\nChild\ - \ merge(Child x, Child y) {\n return Child{min(x.oneway + y.round, y.oneway\ - \ + x.round), x.round + y.round};\n}\n\nChild f(Subtree x, int, tuple<>) { return\ - \ {x.oneway + 1, x.round + 2}; }\n\nSubtree g(Child x, int) { return {x.oneway,\ - \ x.round}; }\n\nChild e() { return {0, 0}; }\n\nint main() {\n cin.tie(nullptr),\ + \ Children {\n int oneway, round;\n};\n\nChildren merge(Children x, Children\ + \ y) {\n return Children{min(x.oneway + y.round, y.oneway + x.round), x.round\ + \ + y.round};\n}\n\nChildren add_edge(Subtree x, int, tuple<>) { return {x.oneway\ + \ + 1, x.round + 2}; }\n\nSubtree add_vertex(Children x, int) { return {x.oneway,\ + \ x.round}; }\n\nChildren e() { return {0, 0}; }\n\nint main() {\n cin.tie(nullptr),\ \ ios::sync_with_stdio(false);\n int N;\n cin >> N;\n vector>>> to(N);\n for (int i = 0; i < N - 1; ++i) {\n int u, v;\n\ \ cin >> u >> v;\n --u, --v;\n to[u].push_back({v, {}}),\ - \ to[v].push_back({u, {}});\n }\n rerooting, Subtree, Child, merge,\ - \ f, g, e> tree(to);\n tree.run();\n for (auto x : tree.dpall) cout << x.oneway\ - \ << '\\n';\n}\n" + \ to[v].push_back({u, {}});\n }\n rerooting, Subtree, Children,\ + \ merge, add_edge, add_vertex, e> tree(to);\n tree.run();\n for (auto x\ + \ : tree.dpall) cout << x.oneway << '\\n';\n}\n" + code: "#define PROBLEM \"https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=1595\"\ + \n#include \"../rerooting.hpp\"\n#include \n#include \n#include\ + \ \n#include \nusing namespace std;\n\nstruct Subtree {\n \ + \ int oneway, round;\n};\nstruct Children {\n int oneway, round;\n};\n\nChildren\ + \ merge(Children x, Children y) {\n return Children{min(x.oneway + y.round,\ + \ y.oneway + x.round), x.round + y.round};\n}\n\nChildren add_edge(Subtree x,\ + \ int, tuple<>) { return {x.oneway + 1, x.round + 2}; }\n\nSubtree add_vertex(Children\ + \ x, int) { return {x.oneway, x.round}; }\n\nChildren e() { return {0, 0}; }\n\ + \nint main() {\n cin.tie(nullptr), ios::sync_with_stdio(false);\n int N;\n\ + \ cin >> N;\n vector>>> to(N);\n for (int i\ + \ = 0; i < N - 1; ++i) {\n int u, v;\n cin >> u >> v;\n --u,\ + \ --v;\n to[u].push_back({v, {}}), to[v].push_back({u, {}});\n }\n \ + \ rerooting, Subtree, Children, merge, add_edge, add_vertex, e> tree(to);\n\ + \ tree.run();\n for (auto x : tree.dpall) cout << x.oneway << '\\n';\n}\n" dependsOn: - tree/rerooting.hpp isVerificationFile: true path: tree/test/rerooting.aoj1595.test.cpp requiredBy: [] - timestamp: '2023-04-25 08:57:43+09:00' + timestamp: '2024-05-05 15:10:50+09:00' verificationStatus: TEST_ACCEPTED verifiedWith: [] documentation_of: tree/test/rerooting.aoj1595.test.cpp diff --git a/tree/test/rerooting.yuki1718.test.cpp.md b/tree/test/rerooting.yuki1718.test.cpp.md index 663f73e0..1647ce4b 100644 --- a/tree/test/rerooting.yuki1718.test.cpp.md +++ b/tree/test/rerooting.yuki1718.test.cpp.md @@ -19,85 +19,92 @@ data: #include \n#include \n#include \n#include \n\ \n// Rerooting\n// Reference:\n// - https://atcoder.jp/contests/abc222/editorial/2749\n\ // - https://null-mn.hatenablog.com/entry/2020/04/14/124151\ntemplate \nstruct rerooting {\n int n_;\n std::vector\ - \ par, visited;\n std::vector>> to;\n std::vector\ - \ dp_subtree;\n std::vector dp_par;\n std::vector dpall;\n rerooting(const\ + \ class Subtree, class Children, Children (*rake)(Children, Children),\n \ + \ Children (*add_edge)(Subtree, int, Edge), Subtree (*add_vertex)(Children,\ + \ int),\n Children (*e)()>\nstruct rerooting {\n int n_;\n std::vector\ + \ par, visited;\n std::vector>> to;\n\n \ + \ // dp_subtree[i] = DP(root=i, edge (i, par[i]) is removed).\n std::vector\ + \ dp_subtree;\n\n // dp_par[i] = DP(root=par[i], edge (i, par[i]) is removed).\ + \ dp_par[root] is meaningless.\n std::vector dp_par;\n\n // dpall[i]\ + \ = DP(root=i, all edges exist).\n std::vector dpall;\n\n rerooting(const\ \ std::vector>> &to_)\n : n_(to_.size()),\ \ par(n_, -1), visited(n_, 0), to(to_) {\n for (int i = 0; i < n_; ++i)\ - \ dp_subtree.push_back(g(e(), i));\n dp_par = dpall = dp_subtree;\n \ - \ }\n\n void run_connected(int root) {\n if (visited[root]) return;\n\ - \ visited[root] = 1;\n std::vector visorder{root};\n\n \ - \ for (int t = 0; t < int(visorder.size()); ++t) {\n int now = visorder[t];\n\ - \ for (const auto &edge : to[now]) {\n int nxt = edge.first;\n\ - \ if (visited[nxt]) continue;\n visorder.push_back(nxt);\n\ - \ visited[nxt] = 1;\n par[nxt] = now;\n \ - \ }\n }\n\n for (int t = int(visorder.size()) - 1; t >= 0; --t)\ - \ {\n int now = visorder[t];\n Ch ch = e();\n \ - \ for (const auto &edge : to[now]) {\n int nxt = edge.first;\n\ - \ if (nxt == par[now]) continue;\n ch = merge(ch,\ - \ f(dp_subtree[nxt], nxt, edge.second));\n }\n dp_subtree[now]\ - \ = g(ch, now);\n }\n\n std::vector left;\n for (int\ - \ now : visorder) {\n int m = int(to[now].size());\n left.assign(m\ - \ + 1, e());\n for (int j = 0; j < m; j++) {\n int nxt\ - \ = to[now][j].first;\n const St &st = (nxt == par[now] ? dp_par[now]\ - \ : dp_subtree[nxt]);\n left[j + 1] = merge(left[j], f(st, nxt,\ - \ to[now][j].second));\n }\n dpall[now] = g(left.back(),\ - \ now);\n\n Ch rprod = e();\n for (int j = m - 1; j >= 0;\ - \ --j) {\n int nxt = to[now][j].first;\n if (nxt\ - \ != par[now]) dp_par[nxt] = g(merge(left[j], rprod), now);\n\n \ - \ const St &st = (nxt == par[now] ? dp_par[now] : dp_subtree[nxt]);\n \ - \ rprod = merge(f(st, nxt, to[now][j].second), rprod);\n }\n\ + \ dp_subtree.push_back(add_vertex(e(), i));\n dp_par = dpall = dp_subtree;\n\ + \ }\n\n void run_connected(int root) {\n if (visited.at(root)) return;\n\ + \ visited.at(root) = 1;\n std::vector visorder{root};\n\n \ + \ for (int t = 0; t < int(visorder.size()); ++t) {\n int now\ + \ = visorder.at(t);\n for (const auto &[nxt, _] : to[now]) {\n \ + \ if (visited.at(nxt)) continue;\n visorder.push_back(nxt);\n\ + \ visited.at(nxt) = 1;\n par.at(nxt) = now;\n \ + \ }\n }\n\n for (int t = int(visorder.size()) - 1; t >=\ + \ 0; --t) {\n const int now = visorder.at(t);\n Children\ + \ ch = e();\n for (const auto &[nxt, edge] : to.at(now)) {\n \ + \ if (nxt != par.at(now)) ch = rake(ch, add_edge(dp_subtree.at(nxt),\ + \ nxt, edge));\n }\n dp_subtree.at(now) = add_vertex(ch,\ + \ now);\n }\n\n std::vector left;\n for (int now\ + \ : visorder) {\n const int m = to.at(now).size();\n left.assign(m\ + \ + 1, e());\n for (int j = 0; j < m; j++) {\n const\ + \ auto &[nxt, edge] = to.at(now).at(j);\n const Subtree &st = (nxt\ + \ == par.at(now) ? dp_par.at(now) : dp_subtree.at(nxt));\n left.at(j\ + \ + 1) = rake(left.at(j), add_edge(st, nxt, edge));\n }\n \ + \ dpall.at(now) = add_vertex(left.back(), now);\n\n Children rprod\ + \ = e();\n for (int j = m - 1; j >= 0; --j) {\n const\ + \ auto &[nxt, edge] = to.at(now).at(j);\n\n if (nxt != par.at(now))\ + \ dp_par.at(nxt) = add_vertex(rake(left.at(j), rprod), now);\n\n \ + \ const Subtree &st = (nxt == par.at(now) ? dp_par.at(now) : dp_subtree.at(nxt));\n\ + \ rprod = rake(add_edge(st, nxt, edge), rprod);\n }\n\ \ }\n }\n\n void run() {\n for (int i = 0; i < n_; ++i) {\n\ - \ if (!visited[i]) run_connected(i);\n }\n }\n\n const\ - \ St &get_subtree(int root_, int par_) const {\n if (par_ < 0) return dpall.at(root_);\n\ - \ if (par.at(root_) == par_) return dp_subtree.at(root_);\n if (par.at(par_)\ - \ == root_) return dp_par.at(par_);\n std::exit(1);\n }\n};\n/* Template:\n\ - struct Subtree {};\nstruct Child {};\nstruct Edge {};\nChild e() { return Child();\ - \ }\nChild merge(Child x, Child y) { return Child(); }\nChild f(Subtree x, int\ - \ ch_id, Edge edge) { return Child(); }\nSubtree g(Child x, int v_id) { return\ - \ Subtree(); }\n\nvector>> to;\nrerooting tree(to);\n*/\n#line 3 \"tree/test/rerooting.yuki1718.test.cpp\"\ + \ if (!visited.at(i)) run_connected(i);\n }\n }\n\n const\ + \ Subtree &get_subtree(int root_, int par_) const {\n if (par_ < 0) return\ + \ dpall.at(root_);\n if (par.at(root_) == par_) return dp_subtree.at(root_);\n\ + \ if (par.at(par_) == root_) return dp_par.at(par_);\n std::exit(1);\n\ + \ }\n};\n/* Template:\nstruct Subtree {};\nstruct Children {};\nstruct Edge\ + \ {};\nChildren e() { return Children(); }\nChildren rake(Children x, Children\ + \ y) { return Children(); }\nChildren add_edge(Subtree x, int ch_id, Edge edge)\ + \ { return Children(); }\nSubtree add_vertex(Children x, int v_id) { return Subtree();\ + \ }\n\nvector>> to;\nrerooting tree(to);\n*/\n#line 3 \"tree/test/rerooting.yuki1718.test.cpp\"\ \n#include \n#include \n#line 6 \"tree/test/rerooting.yuki1718.test.cpp\"\ \nusing namespace std;\n\nvector inD;\n\nstruct Subtree {\n bool exist;\n\ - \ int oneway, round;\n};\nstruct Child {\n bool exist;\n int oneway,\ - \ round;\n};\nChild e() { return {false, 0, 0}; }\n\nChild merge(Child x, Child\ - \ y) {\n if (!x.exist) return y;\n if (!y.exist) return x;\n return Child{true,\ - \ min(x.oneway + y.round, y.oneway + x.round), x.round + y.round};\n}\n\nChild\ - \ f(Subtree x, int, tuple<>) {\n if (!x.exist) return e();\n return {true,\ - \ x.oneway + 1, x.round + 2};\n}\n\nSubtree g(Child x, int v) {\n if (x.exist\ - \ or inD[v]) return {true, x.oneway, x.round};\n return {false, 0, 0};\n}\n\ - \nint main() {\n cin.tie(nullptr);\n ios::sync_with_stdio(false);\n int\ - \ N, K;\n cin >> N >> K;\n vector>>> to(N);\n \ - \ for (int e = 0; e < N - 1; e++) {\n int u, v;\n cin >> u >>\ + \ int oneway, round;\n};\nstruct Children {\n bool exist;\n int oneway,\ + \ round;\n};\nChildren e() { return {false, 0, 0}; }\n\nChildren merge(Children\ + \ x, Children y) {\n if (!x.exist) return y;\n if (!y.exist) return x;\n\ + \ return Children{true, min(x.oneway + y.round, y.oneway + x.round), x.round\ + \ + y.round};\n}\n\nChildren add_edge(Subtree x, int, tuple<>) {\n if (!x.exist)\ + \ return e();\n return {true, x.oneway + 1, x.round + 2};\n}\n\nSubtree add_vertex(Children\ + \ x, int v) {\n if (x.exist or inD[v]) return {true, x.oneway, x.round};\n\ + \ return {false, 0, 0};\n}\n\nint main() {\n cin.tie(nullptr);\n ios::sync_with_stdio(false);\n\ + \ int N, K;\n cin >> N >> K;\n vector>>> to(N);\n\ + \ for (int e = 0; e < N - 1; e++) {\n int u, v;\n cin >> u >>\ \ v;\n u--, v--;\n to[u].emplace_back(v, make_tuple());\n \ \ to[v].emplace_back(u, make_tuple());\n }\n inD.assign(N, 0);\n while\ \ (K--) {\n int d;\n cin >> d;\n inD[d - 1] = 1;\n }\n\ - \ rerooting, Subtree, Child, merge, f, g, e> tree(to);\n tree.run();\n\ - \ for (auto x : tree.dpall) cout << x.oneway << '\\n';\n}\n" + \ rerooting, Subtree, Children, merge, add_edge, add_vertex, e> tree(to);\n\ + \ tree.run();\n for (auto x : tree.dpall) cout << x.oneway << '\\n';\n}\n" code: "#define PROBLEM \"https://yukicoder.me/problems/no/1718\"\n#include \"../rerooting.hpp\"\ \n#include \n#include \n#include \nusing namespace std;\n\ \nvector inD;\n\nstruct Subtree {\n bool exist;\n int oneway, round;\n\ - };\nstruct Child {\n bool exist;\n int oneway, round;\n};\nChild e() { return\ - \ {false, 0, 0}; }\n\nChild merge(Child x, Child y) {\n if (!x.exist) return\ - \ y;\n if (!y.exist) return x;\n return Child{true, min(x.oneway + y.round,\ - \ y.oneway + x.round), x.round + y.round};\n}\n\nChild f(Subtree x, int, tuple<>)\ - \ {\n if (!x.exist) return e();\n return {true, x.oneway + 1, x.round +\ - \ 2};\n}\n\nSubtree g(Child x, int v) {\n if (x.exist or inD[v]) return {true,\ - \ x.oneway, x.round};\n return {false, 0, 0};\n}\n\nint main() {\n cin.tie(nullptr);\n\ - \ ios::sync_with_stdio(false);\n int N, K;\n cin >> N >> K;\n vector>>> to(N);\n for (int e = 0; e < N - 1; e++) {\n int u, v;\n\ - \ cin >> u >> v;\n u--, v--;\n to[u].emplace_back(v, make_tuple());\n\ - \ to[v].emplace_back(u, make_tuple());\n }\n inD.assign(N, 0);\n\ - \ while (K--) {\n int d;\n cin >> d;\n inD[d - 1] = 1;\n\ - \ }\n rerooting, Subtree, Child, merge, f, g, e> tree(to);\n \ - \ tree.run();\n for (auto x : tree.dpall) cout << x.oneway << '\\n';\n}\n" + };\nstruct Children {\n bool exist;\n int oneway, round;\n};\nChildren e()\ + \ { return {false, 0, 0}; }\n\nChildren merge(Children x, Children y) {\n if\ + \ (!x.exist) return y;\n if (!y.exist) return x;\n return Children{true,\ + \ min(x.oneway + y.round, y.oneway + x.round), x.round + y.round};\n}\n\nChildren\ + \ add_edge(Subtree x, int, tuple<>) {\n if (!x.exist) return e();\n return\ + \ {true, x.oneway + 1, x.round + 2};\n}\n\nSubtree add_vertex(Children x, int\ + \ v) {\n if (x.exist or inD[v]) return {true, x.oneway, x.round};\n return\ + \ {false, 0, 0};\n}\n\nint main() {\n cin.tie(nullptr);\n ios::sync_with_stdio(false);\n\ + \ int N, K;\n cin >> N >> K;\n vector>>> to(N);\n\ + \ for (int e = 0; e < N - 1; e++) {\n int u, v;\n cin >> u >>\ + \ v;\n u--, v--;\n to[u].emplace_back(v, make_tuple());\n \ + \ to[v].emplace_back(u, make_tuple());\n }\n inD.assign(N, 0);\n while\ + \ (K--) {\n int d;\n cin >> d;\n inD[d - 1] = 1;\n }\n\ + \ rerooting, Subtree, Children, merge, add_edge, add_vertex, e> tree(to);\n\ + \ tree.run();\n for (auto x : tree.dpall) cout << x.oneway << '\\n';\n}\n" dependsOn: - tree/rerooting.hpp isVerificationFile: true path: tree/test/rerooting.yuki1718.test.cpp requiredBy: [] - timestamp: '2023-04-25 08:57:43+09:00' + timestamp: '2024-05-05 15:10:50+09:00' verificationStatus: TEST_ACCEPTED verifiedWith: [] documentation_of: tree/test/rerooting.yuki1718.test.cpp