lca.cpp

// Lowest Common Ancestor by binary lifting
// https://youtu.be/8uowVvQ_-Mo?t=4306
template<typename T=int> // T: type of cost
struct lca {
  int n, root, l;
  vector<vector<int>> to;
  vector<vector<T>> co;
  vector<int> dep;
  vector<T> costs;
  vector<vector<int>> par;
  lca(int n):n(n),to(n),co(n),dep(n),costs(n) {
    l = 0;
    while ((1<<l) < n) ++l;
    par = vector<vector<int>>(n+1,vector<int>(l,n));
  }
  void addEdge(int a, int b, T c=0) {
    to[a].push_back(b); co[a].push_back(c);
    to[b].push_back(a); co[b].push_back(c);
  }
  void dfs(int v, int d=0, T c=0, int p=-1) {
    if (p != -1) par[v][0] = p;
    dep[v] = d;
    costs[v] = c;
    for (int i = 0; i < to[v].size(); ++i) {
      int u = to[v][i];
      if (u == p) continue;
      dfs(u, d+1, c+co[v][i], v);
    }
  }

  void init(int _root=0) {
    root = _root;
    dfs(root);
    for (int i = 0; i < l-1; ++i) {
      for (int v = 0; v < n; ++v) {
        par[v][i+1] = par[par[v][i]][i];
      }
    }
  }
  // LCA
  int up(int v, int k) {
    for (int i = l-1; i >= 0; --i) {
      int len = 1<<i;
      if (k >= len) k -= len, v = par[v][i];
    }
    return v;
  }
  int operator()(int a, int b) {
    if (dep[a] > dep[b]) swap(a,b);
    b = up(b, dep[b]-dep[a]);
    if (a == b) return a;
    for (int i = l-1; i >= 0; --i) {
      int na = par[a][i], nb = par[b][i];
      if (na != nb) a = na, b = nb;
    }
    return par[a][0];
  }
  int length(int a, int b) {
    int c = (*this)(a,b);
    return dep[a]+dep[b]-dep[c]*2;
  }
  T dist(int a, int b) {
    int c = (*this)(a,b);
    return costs[a]+costs[b]-costs[c]*2;
  }
};