test/yukicoder/yuki_1326.test.cpp

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• Last update: 2022-07-20 02:04:32+09:00
• Problem: https://yukicoder.me/problems/no/1326

Depends on

• 重軽分解 (data_structure/tree/heavy_light_decomposition.hpp)
• 二重頂点連結成分分解 (graph/biconnected_components.hpp)
• Block Cut Tree (graph/block_cut_tree.hpp)

Code

#define PROBLEM "https://yukicoder.me/problems/no/1326"
#include <bits/stdc++.h>
using namespace std;
#include "../../graph/block_cut_tree.hpp"
#include "../../data_structure/tree/heavy_light_decomposition.hpp"
int main(){
  int N, M;
  cin >> N >> M;
  vector<vector<int>> E(N);
  for (int i = 0; i < M; i++){
    int a, b;
    cin >> a >> b;
    a--;
    b--;
    E[a].push_back(b);
    E[b].push_back(a);
  }
  block_cut_tree G(E);
  vector<int> id(N, -1);
  for (int i = 0; i < G.V; i++){
    for (int j : G.node[i]){
      if (id[j] == -1){
        id[j] = i;
      }
    }
  }
  vector<int> p(G.V, -1);
  vector<vector<int>> c(G.V);
  vector<int> d(G.V, 0);
  if (G.cut[0]){
    d[0]++;
  }
  queue<int> q;
  q.push(0);
  while (!q.empty()){
    int v = q.front();
    q.pop();
    for (int w : G.G[v]){
      if (w != p[v]){
        p[w] = v;
        c[v].push_back(w);
        d[w] = d[v];
        if (G.cut[w]){
          d[w]++;
        }
        q.push(w);
      }
    }
  }
  heavy_light_decomposition T(p, c);
  int Q;
  cin >> Q;
  for (int i = 0; i < Q; i++){
    int x, y;
    cin >> x >> y;
    x--;
    y--;
    x = id[x];
    y = id[y];
    if (x == y){
      cout << 0 << endl;
    } else {
      int z = T.lca(x, y);
      int ans = d[x] + d[y] - d[z] * 2;
      if (G.cut[z]){
        ans++;
      }
      if (G.cut[x]){
        ans--;
      }
      if (G.cut[y]){
        ans--;
      }
      cout << ans << endl;
    }
  }
}

#line 1 "test/yukicoder/yuki_1326.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1326"
#include <bits/stdc++.h>
using namespace std;
#line 2 "graph/block_cut_tree.hpp"
/**
 * @brief Block Cut Tree
*/
#line 2 "graph/biconnected_components.hpp"
/**
 * @brief 二重頂点連結成分分解
*/
struct biconnected_components{
  vector<int> bcc;
  int cnt = 0;
  biconnected_components(vector<vector<pair<int, int>>> &E){
    int N = E.size();
    vector<int> next(N, -1);
    vector<int> d(N, -1);
    vector<int> imos(N, 0);
    for (int i = 0; i < N; i++){
      if (d[i] == -1){
        d[i] = 0;
        dfs1(E, next, d, imos, i);
      }
    }
    int M = 0;
    for (int i = 0; i < N; i++){
      M += E[i].size();
    }
    M /= 2;
    bcc = vector<int>(M, -1);
    for (int i = 0; i < N; i++){
      if (d[i] == 0){
        dfs2(E, d, imos, cnt, i);
      }
    }
  }
  void dfs1(vector<vector<pair<int, int>>> &E, vector<int> &next, vector<int> &d, vector<int> &imos, int v){
    for (auto P : E[v]){
      int w = P.second;
      if (d[w] == -1){
        d[w] = d[v] + 1;
        next[v] = w;
        dfs1(E, next, d, imos, w);
        imos[v] += imos[w];
      } else if (d[w] < d[v] - 1){
        imos[v]++;
        imos[next[w]]--;
      }
    }
  }
  void dfs2(vector<vector<pair<int, int>>> &E, vector<int> &d, vector<int> &imos, int b, int v){
    for (auto P : E[v]){
      int x = P.first;
      int w = P.second;
      if (d[w] < d[v]){
        bcc[x] = b;
      } else if (d[w] == d[v] + 1 && bcc[x] == -1){
        if (imos[w] > 0){
          bcc[x] = b;
        } else {
          bcc[x] = cnt;
          cnt++;
        }
        dfs2(E, d, imos, bcc[x], w);
      }
    }
  }
  int operator [](int k){
    return bcc[k];
  }
};
#line 6 "graph/block_cut_tree.hpp"
struct block_cut_tree{
  int V;
  vector<bool> art;
  vector<bool> cut;
  vector<vector<int>> G;
  vector<vector<int>> node;
  block_cut_tree(vector<vector<int>> &E){
    int N = E.size();
    int M = 0;
    vector<vector<pair<int, int>>> E2(N);
    for (int i = 0; i < N; i++){
      for (int j : E[i]){
        if (j > i){
          E2[i].push_back(make_pair(M, j));
          E2[j].push_back(make_pair(M, i));
          M++;
        }
      }
    }
    biconnected_components B(E2);
    art = vector<bool>(N, false);
    int cnt = 0;
    for (int i = 0; i < N; i++){
      for (auto P : E2[i]){
        if (B[P.first] != B[E2[i][0].first]){
          art[i] = true;
        }
      }
      if (art[i]){
        cnt++;
      }
      if (E[i].empty()){
        cnt++;
      }
    }
    V = cnt + B.cnt;
    cut = vector<bool>(V, false);
    G.resize(V);
    node.resize(V);
    int cnt2 = 0;
    vector<bool> used(B.cnt, false);
    for (int i = 0; i < N; i++){
      if (art[i]){
        cut[cnt2] = true;
        node[cnt2].push_back(i);
        for (auto P : E2[i]){
          int b = B[P.first];
          if (!used[b]){
            used[b] = true;
            G[cnt + b].push_back(cnt2);
            G[cnt2].push_back(cnt + b);
            node[cnt + b].push_back(i);
          }
        }
        for (auto P : E2[i]){
          int b = B[P.first];
          used[b] = false;
        }
        cnt2++;
      } else if (!E2[i].empty()){
        int b = B[E2[i][0].first];
        node[cnt + b].push_back(i);
      } else {
        node[cnt2].push_back(i);
        cnt2++;
      }
    }
  }
};
#line 2 "data_structure/tree/heavy_light_decomposition.hpp"
/**
 * @brief 重軽分解
*/
struct heavy_light_decomposition{
  vector<int> p, sz, in, next;
  void dfs1(vector<vector<int>> &c, int v){
    sz[v] = 1;
    for (int &w : c[v]){
      dfs1(c, w);
      sz[v] += sz[w];
      if (sz[w] > sz[c[v][0]]){
        swap(w, c[v][0]);
      }
    }
  }
  void dfs2(vector<vector<int>> &c, int &t, int v){
    in[v] = t;
    t++;
    for (int w : c[v]){
      if (w == c[v][0]){
        next[w] = next[v];
      } else {
        next[w] = w;
      }
      dfs2(c, t, w);
    }
  }
  heavy_light_decomposition(vector<int> &p, vector<vector<int>> &c, int r = 0): p(p){
    int N = p.size();
    sz = vector<int>(N);
    dfs1(c, r);
    in = vector<int>(N);
    next = vector<int>(N, r);
    int t = 0;
    dfs2(c, t, r);
  }
  int lca(int u, int v){
    while (true){
      if (in[u] > in[v]){
        swap(u, v);
      }
      if (next[u] == next[v]){
        return u;
      }
      v = p[next[v]];
    }
  }
  int dist(int u, int v){
    int ans = 0;
    while (true){
      if (in[u] > in[v]){
        swap(u, v);
      }
      if (next[u] == next[v]){
        ans += in[v] - in[u];
        return ans;
      }
      ans += in[v] - in[next[v]] + 1;
      v = p[next[v]];
    }
  }
};
#line 6 "test/yukicoder/yuki_1326.test.cpp"
int main(){
  int N, M;
  cin >> N >> M;
  vector<vector<int>> E(N);
  for (int i = 0; i < M; i++){
    int a, b;
    cin >> a >> b;
    a--;
    b--;
    E[a].push_back(b);
    E[b].push_back(a);
  }
  block_cut_tree G(E);
  vector<int> id(N, -1);
  for (int i = 0; i < G.V; i++){
    for (int j : G.node[i]){
      if (id[j] == -1){
        id[j] = i;
      }
    }
  }
  vector<int> p(G.V, -1);
  vector<vector<int>> c(G.V);
  vector<int> d(G.V, 0);
  if (G.cut[0]){
    d[0]++;
  }
  queue<int> q;
  q.push(0);
  while (!q.empty()){
    int v = q.front();
    q.pop();
    for (int w : G.G[v]){
      if (w != p[v]){
        p[w] = v;
        c[v].push_back(w);
        d[w] = d[v];
        if (G.cut[w]){
          d[w]++;
        }
        q.push(w);
      }
    }
  }
  heavy_light_decomposition T(p, c);
  int Q;
  cin >> Q;
  for (int i = 0; i < Q; i++){
    int x, y;
    cin >> x >> y;
    x--;
    y--;
    x = id[x];
    y = id[y];
    if (x == y){
      cout << 0 << endl;
    } else {
      int z = T.lca(x, y);
      int ans = d[x] + d[y] - d[z] * 2;
      if (G.cut[z]){
        ans++;
      }
      if (G.cut[x]){
        ans--;
      }
      if (G.cut[y]){
        ans--;
      }
      cout << ans << endl;
    }
  }
}

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