結果

問題 No.1600 Many Shortest Path Problems
ユーザー NachiaNachia
提出日時 2021-07-09 22:57:17
言語 C++17
(gcc 11.1.0 + boost 1.77.0)
結果
AC  
実行時間 743 ms / 4,000 ms
コード長 3,766 Byte
コンパイル時間 1,508 ms
使用メモリ 41,524 KB
最終ジャッジ日時 2021-09-19 14:52:39
合計ジャッジ時間 21,477 ms
ジャッジサーバーID
(参考情報)
judge13 / judge11
このコードへのチャレンジ(β)

テストケース

テストケース表示
入力 結果 実行時間
使用メモリ
testcase_00 AC 1 ms
3,492 KB
testcase_01 AC 1 ms
3,468 KB
testcase_02 AC 1 ms
3,432 KB
testcase_03 AC 2 ms
3,540 KB
testcase_04 AC 703 ms
40,404 KB
testcase_05 AC 726 ms
40,340 KB
testcase_06 AC 2 ms
3,548 KB
testcase_07 AC 2 ms
3,384 KB
testcase_08 AC 2 ms
3,532 KB
testcase_09 AC 2 ms
3,524 KB
testcase_10 AC 144 ms
9,360 KB
testcase_11 AC 204 ms
10,928 KB
testcase_12 AC 392 ms
18,792 KB
testcase_13 AC 658 ms
30,964 KB
testcase_14 AC 721 ms
40,424 KB
testcase_15 AC 1 ms
3,492 KB
testcase_16 AC 2 ms
3,536 KB
testcase_17 AC 529 ms
25,484 KB
testcase_18 AC 743 ms
40,420 KB
testcase_19 AC 2 ms
3,396 KB
testcase_20 AC 1 ms
3,532 KB
testcase_21 AC 547 ms
25,556 KB
testcase_22 AC 2 ms
3,536 KB
testcase_23 AC 2 ms
3,556 KB
testcase_24 AC 732 ms
40,328 KB
testcase_25 AC 1 ms
3,552 KB
testcase_26 AC 1 ms
3,536 KB
testcase_27 AC 1 ms
3,532 KB
testcase_28 AC 2 ms
3,536 KB
testcase_29 AC 552 ms
25,108 KB
testcase_30 AC 543 ms
25,548 KB
testcase_31 AC 477 ms
25,516 KB
testcase_32 AC 429 ms
25,460 KB
testcase_33 AC 2 ms
3,484 KB
testcase_34 AC 2 ms
3,480 KB
testcase_35 AC 422 ms
41,524 KB
testcase_36 AC 375 ms
40,640 KB
testcase_37 AC 1 ms
3,460 KB
testcase_38 AC 499 ms
25,364 KB
testcase_39 AC 2 ms
3,404 KB
testcase_40 AC 564 ms
25,636 KB
testcase_41 AC 217 ms
24,868 KB
testcase_42 AC 231 ms
25,636 KB
testcase_43 AC 221 ms
25,300 KB
testcase_44 AC 259 ms
25,572 KB
testcase_45 AC 589 ms
24,788 KB
testcase_46 AC 489 ms
25,632 KB
testcase_47 AC 632 ms
25,492 KB
testcase_48 AC 481 ms
25,636 KB
testcase_49 AC 1 ms
3,440 KB
testcase_50 AC 1 ms
3,480 KB
testcase_51 AC 2 ms
3,468 KB
testcase_52 AC 2 ms
3,400 KB
testcase_53 AC 2 ms
3,532 KB
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 Edge{ int u,v,i; };

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

vector<int> P;
vector<vector<int>> P2;
vector<int> Eidx;
vector<int> depi;
vector<mll> dep;

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



void read_graph(){
  cin >> N >> M;
  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});
    }
  }
}

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);
    }
  }
  P2.assign(20,vector<int>(N));
  rep(i,N) P2[0][i] = P[i];
  P2[0][0] = 0;
  rep(d,19) rep(i,N) P2[d+1][i] = P2[d][P2[d][i]];
}

int LCA(int u,int v){
  if(depi[u] < depi[v]) swap(u,v);
  for(int i=19; i>=0; i--) if(depi[u]-depi[v] >= (1<<i)) u = P2[i][u];
  if(u == v) return u;
  for(int i=19; i>=0; i--) if(P2[i][u] != P2[i][v]){ u = P2[i][u]; v = P2[i][v]; }
  return P2[0][u];
}

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];
  //cout << "u = " << u << ", v = " << v << ", z = " << z << endl;
  //cout << "e = " << J[z].u << ", " << J[z].v << endl;
  //cout << "d1 = " << (dist0(u,J[z].u) + dist0(v,J[z].v)) << ", d2 = " << (dist0(u,J[z].v) + dist0(v,J[z].u)) << endl;
  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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