add rerooting

Author: atcoder-live

README.md

@@ -27,6 +27,7 @@ AtCoder解説放送ライブラリ集
 |名前|コード|説明|
 |:--|:--|:--|
 |LCA|[lca.cpp](lca.cpp)|最小共通祖先|
+|全方位木DP|[rerooting.cpp](rerooting.cpp)|全方位木DP|
 
 ### 文字列
 |名前|コード|説明|

rerooting.cpp

@@ -0,0 +1,58 @@
+// Rerooting
+// https://youtu.be/zG1L4vYuGrg?t=7092
+// TODO: vertex info, edge info
+struct Rerooting {
+  struct DP {
+    DP() {}
+    DP operator+(const DP& a) const {
+      // edit here
+    }
+    DP addRoot() const {
+      // edit here
+    }
+  };
+  
+  int n;
+  vector<vector<int>> to;
+  vector<vector<DP>> dp;
+  vector<DP> ans;
+  Rerooting(int n=0):n(n),to(n),dp(n),ans(n) {}
+  void addEdge(int a, int b) {
+    to[a].push_back(b);
+    to[b].push_back(a);
+  }
+  void init() {
+    dfs(0);
+    bfs(0);
+  }
+
+  DP dfs(int v, int p=-1) {
+    DP dpSum;
+    dp[v] = vector<DP>(to[v].size());
+    rep(i,to[v].size()) {
+      int u = to[v][i];
+      if (u == p) continue;
+      dp[v][i] = dfs(u,v);
+      dpSum = dpSum + dp[v][i];
+    }
+    return dpSum.addRoot();
+  }
+  void bfs(int v, const DP& dpP=DP(), int p=-1) {
+    int deg = to[v].size();
+    rep(i,deg) if (to[v][i] == p) dp[v][i] = dpP;
+
+    vector<DP> dpSumL(deg+1);
+    rep(i,deg) dpSumL[i+1] = dpSumL[i] + dp[v][i];
+    vector<DP> dpSumR(deg+1);
+    for (int i = deg-1; i >= 0; --i)
+      dpSumR[i] = dpSumR[i+1] + dp[v][i];
+    ans[v] = dpSumL[deg].addRoot();
+
+    rep(i,deg) {
+      int u = to[v][i];
+      if (u == p) continue;
+      DP d = dpSumL[i] + dpSumR[i+1];
+      bfs(u, d.addRoot(), v);
+    }
+  }
+};