結果

問題 No.1600 Many Shortest Path Problems
コンテスト
ユーザー Nachia
提出日時 2021-07-22 22:46:45
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 428 ms / 4,000 ms
コード長 5,172 bytes
コンパイル時間 1,627 ms
コンパイル使用メモリ 104,064 KB
最終ジャッジ日時 2025-01-23 07:09:35
ジャッジサーバーID
（参考情報） 		judge3 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 51
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <atcoder/modint>
#include <iostream>
#include <vector>
#include <algorithm>
#include <set>
using namespace atcoder;
using namespace std;
using ll = long long;
using ull = unsigned long long;
const ull MOD = 1000000007;
using mll = static_modint<1000000007>;
#define rep(i,n) for(int i=0; i<(n); i++)

struct DSU{
  vector<int> V;
  DSU(int n){
    V.resize(n);
    rep(i,n) V[i] = i;
  }
  int leader(int a){ if(V[a] == a) return a; return V[a] = leader(V[a]); }
  void merge(int r,int c){ V[leader(c)] = leader(r); }
};

struct HLD{

  int N;
  vector<int> P;
  vector<int> PP;
  vector<int> PD;
  vector<int> D;

  vector<int> rangeL;
  vector<int> rangeR;

  HLD(const vector<vector<int>>& E = {{}}){
    N = E.size();
    P.assign(N, -1);
    vector<int> I = {0};
    rep(i,I.size()){
      int p = I[i];
      for(int e : E[p]) if(P[p] != e){
        I.push_back(e);
        P[e] = p;
      }
    }
    vector<int> Z(N, 1);
    for(int i=N-1; i>=1; i--) Z[P[I[i]]] += Z[I[i]];
    PP.resize(N);
    for(int i=0; i<N; i++) PP[i] = i;
    vector<int> nx(N, -1);
    for(int p : I) if(p != 0){
      if(nx[P[p]] == -1) nx[P[p]] = p;
      if(Z[nx[P[p]]] < Z[p]) nx[P[p]] = p;
    }
    rep(i,N) if(nx[i] != -1) PP[nx[i]] = i;
    for(int p : I) if(p != 0) PP[p] = PP[PP[p]];

    PD.assign(N,N);
    PD[0] = 0;
    for(int p : I) if(p != 0) PD[p] = min(PD[PP[p]], PD[P[p]]+1);
    D.assign(N,0);
    for(int p : I) D[p] = ((PP[p] == p) ? 0 : D[P[p]]+1);
    
    rangeL.assign(N,-1);
    rangeR.assign(N,-1);
    vector<int> dfs;
    int ir = 0;
    dfs.push_back(0);
    while(dfs.size()){
      int p = dfs.back();
      dfs.pop_back();
      if(p < 0){ rangeR[-1-p] = ir; continue; }
      dfs.push_back(-1-p);
      for(int e : E[p]) if(P[p] != e) if(e != nx[p]) dfs.push_back(e);
      if(nx[p] != -1) dfs.push_back(nx[p]);
      rangeL[p] = ir++;
    }
  }

  int lca(int u, int v){
    if(PD[u] < PD[v]) swap(u, v);
    while(PD[u] > PD[v]) u = P[PP[u]];
    while(PP[u] != PP[v]){ u = P[PP[u]]; v = P[PP[v]]; }
    return (D[u] > D[v]) ? v : u;
  }

  vector<pair<int,int>> getpath(int r, int c){
    vector<pair<int,int>> res;
    while(PD[r] < PD[c]){
      res.push_back({ rangeL[PP[c]], rangeL[c]+1 });
      c = P[PP[c]];
    }
    if(PP[r] != PP[c]) return {};
    if(D[r] > D[c]) return {};
    res.push_back({ rangeL[r], rangeL[c]+1 });
    reverse(res.begin(), res.end());
    return move(res);
  }
};


struct Edge{ int u,v,i; };

int N, M;
vector<Edge> J;
vector<vector<Edge>> E;
vector<Edge> flows;
vector<mll> cost;

vector<int> P;
HLD hld;
vector<int> Eidx;
vector<int> depi;
vector<mll> dep;

vector<int> iEidx;
vector<int> flowIdx;



void read_graph(){
  cin >> N >> M;
  vector<vector<int>> E2(N);
  E.resize(N);
  cost.resize(M);
  cost[0] = 2;
  for(int i=1; i<M; i++) cost[i] = cost[i-1] * 2;
  DSU G1(N);
  rep(i,M){
    int u,v; cin >> u >> v; u--; v--;
    J.push_back({u,v,i});
    if(G1.leader(u) == G1.leader(v)){
      flows.push_back({u,v,i});
    }
    else{
      G1.merge(u,v);
      E[u].push_back({u,v,i});
      E[v].push_back({v,u,i});
      E2[u].push_back(v);
      E2[v].push_back(u);
    }
  }
  hld = HLD(E2);
}

void initLCA(){
  vector<int> I;
  P.assign(N,-1);
  I.push_back(0);
  depi.assign(N,0);
  dep.assign(N,0);
  Eidx.assign(N,-1);
  rep(i,I.size()){
    int p = I[i];
    for(Edge e : E[p]) if(P[p] != e.v){
      P[e.v] = p;
      dep[e.v] = dep[p] + cost[e.i];
      depi[e.v] = depi[p] + 1;
      Eidx[e.v] = e.i;
      I.push_back(e.v);
    }
  }
}

int LCA(int u,int v){
  return hld.lca(u,v);
}

int dist0(int u,int v){
  int g = LCA(u,v);
  return depi[u] + depi[v] - depi[g] * 2;
}
mll dist1(int u,int v){
  int g = LCA(u,v);
  return dep[u] + dep[v] - dep[g] * 2;
}

void build_flows(){

  iEidx.assign(M,-1);
  rep(i,N) if(Eidx[i] != -1) iEidx[Eidx[i]] = i;

  flowIdx.assign(N,-1);
  
  DSU G2(N);
  for(Edge e : flows){
    int g = G2.leader(LCA(e.u,e.v));
    for(int s : {e.u,e.v}){
      int p = G2.leader(s);
      while(p != g){
        flowIdx[p] = e.i;
        G2.merge(P[p],p);
        p = G2.leader(p);
      }
    }
  }
}

int path_includes(int u,int v,int z){
  if(iEidx[z] == -1) return -1;
  if((LCA(u,v)^LCA(u,J[z].u)^LCA(v,J[z].u)) != J[z].u) return -1;
  if((LCA(u,v)^LCA(u,J[z].v)^LCA(v,J[z].v)) != J[z].v) return -1;
  int res = flowIdx[iEidx[z]];
  if(res == -1) return -2;
  return res;
}

mll shortest_using(int u,int v,int z){
  mll ans = cost[z];
  if(dist0(u,J[z].u) + dist0(v,J[z].v) < dist0(u,J[z].v) + dist0(v,J[z].u))
    ans += dist1(u,J[z].u) + dist1(v,J[z].v);
  else
    ans += dist1(u,J[z].v) + dist1(v,J[z].u);
  return ans;
}


int main(){
  read_graph();
  initLCA();
  build_flows();

  int Q; cin >> Q;
  rep(q,Q){
    int u,v,z; cin >> u >> v >> z; u--; v--; z--;
    int inc = path_includes(u,v,z);
    if(inc == -2){ cout << "-1\n"; continue; }
    if(inc == -1){ cout << dist1(u,v).val() << "\n"; continue; }
    auto e = J[inc];
    mll ans = shortest_using(u,v,e.i);
    cout << ans.val() << "\n";
  }
  return 0;
}

struct ios_do_not_sync{
  ios_do_not_sync(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
  }
} ios_do_not_sync_inst;
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