#676404 (C++17) No.1600 Many Shortest Path Problems

提出ソース

結果

問題	No.1600 Many Shortest Path Problems
ユーザー	👑 Nachia
提出日時	2021-07-09 22:57:17
言語	C++17 (gcc 13.2.0 + boost 1.83.0)
結果	AC
実行時間	774 ms / 4,000 ms
コード長	3,766 bytes
コンパイル時間	1,992 ms
コンパイル使用メモリ	101,812 KB
実行使用メモリ	41,436 KB
最終ジャッジ日時	2023-09-14 10:30:54
合計ジャッジ時間	22,639 ms
ジャッジサーバーID （参考情報）	judge11 / judge15

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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	1 ms 4,380 KB
testcase_01	AC	1 ms 4,380 KB
testcase_02	AC	1 ms 4,376 KB
testcase_03	AC	2 ms 4,380 KB
testcase_04	AC	767 ms 40,376 KB
testcase_05	AC	766 ms 40,416 KB
testcase_06	AC	1 ms 4,376 KB
testcase_07	AC	2 ms 4,376 KB
testcase_08	AC	1 ms 4,376 KB
testcase_09	AC	1 ms 4,380 KB
testcase_10	AC	150 ms 9,748 KB
testcase_11	AC	216 ms 10,928 KB
testcase_12	AC	410 ms 19,612 KB
testcase_13	AC	693 ms 30,960 KB
testcase_14	AC	774 ms 40,532 KB
testcase_15	AC	2 ms 4,380 KB
testcase_16	AC	2 ms 4,376 KB
testcase_17	AC	558 ms 25,688 KB
testcase_18	AC	760 ms 40,328 KB
testcase_19	AC	1 ms 4,376 KB
testcase_20	AC	2 ms 4,380 KB
testcase_21	AC	543 ms 25,504 KB
testcase_22	AC	1 ms 4,380 KB
testcase_23	AC	2 ms 4,380 KB
testcase_24	AC	761 ms 40,280 KB
testcase_25	AC	1 ms 4,380 KB
testcase_26	AC	2 ms 4,376 KB
testcase_27	AC	2 ms 4,380 KB
testcase_28	AC	2 ms 4,380 KB
testcase_29	AC	603 ms 25,060 KB
testcase_30	AC	561 ms 25,588 KB
testcase_31	AC	494 ms 25,496 KB
testcase_32	AC	455 ms 25,468 KB
testcase_33	AC	2 ms 4,376 KB
testcase_34	AC	2 ms 4,376 KB
testcase_35	AC	441 ms 41,436 KB
testcase_36	AC	392 ms 40,876 KB
testcase_37	AC	2 ms 4,380 KB
testcase_38	AC	518 ms 25,232 KB
testcase_39	AC	1 ms 4,380 KB
testcase_40	AC	596 ms 25,612 KB
testcase_41	AC	232 ms 24,840 KB
testcase_42	AC	244 ms 25,640 KB
testcase_43	AC	235 ms 25,360 KB
testcase_44	AC	257 ms 25,580 KB
testcase_45	AC	593 ms 24,724 KB
testcase_46	AC	489 ms 25,560 KB
testcase_47	AC	653 ms 25,776 KB
testcase_48	AC	496 ms 25,700 KB
testcase_49	AC	2 ms 4,380 KB
testcase_50	AC	2 ms 4,380 KB
testcase_51	AC	1 ms 4,376 KB
testcase_52	AC	1 ms 4,380 KB
testcase_53	AC	2 ms 4,376 KB

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ソースコード

raw source code

#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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結果

テストケース

ソースコード