結果

問題 No.1600 Many Shortest Path Problems
ユーザー 👑 NachiaNachia
提出日時 2021-08-20 00:13:58
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 475 ms / 4,000 ms
コード長 7,465 bytes
コンパイル時間 1,608 ms
コンパイル使用メモリ 105,992 KB
実行使用メモリ 41,012 KB
最終ジャッジ日時 2024-11-15 01:40:50
合計ジャッジ時間 13,051 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge4
このコードへのチャレンジ
（要ログイン）

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
5,248 KB
testcase_01 AC 2 ms
5,248 KB
testcase_02 AC 2 ms
5,248 KB
testcase_03 AC 2 ms
5,248 KB
testcase_04 AC 437 ms
37,984 KB
testcase_05 AC 445 ms
38,004 KB
testcase_06 AC 2 ms
5,248 KB
testcase_07 AC 2 ms
5,248 KB
testcase_08 AC 1 ms
5,248 KB
testcase_09 AC 2 ms
5,248 KB
testcase_10 AC 112 ms
9,576 KB
testcase_11 AC 142 ms
10,648 KB
testcase_12 AC 207 ms
17,756 KB
testcase_13 AC 345 ms
29,312 KB
testcase_14 AC 436 ms
37,948 KB
testcase_15 AC 2 ms
5,248 KB
testcase_16 AC 2 ms
5,248 KB
testcase_17 AC 268 ms
23,728 KB
testcase_18 AC 475 ms
37,956 KB
testcase_19 AC 2 ms
5,248 KB
testcase_20 AC 2 ms
5,248 KB
testcase_21 AC 264 ms
23,724 KB
testcase_22 AC 2 ms
5,248 KB
testcase_23 AC 1 ms
5,248 KB
testcase_24 AC 474 ms
38,104 KB
testcase_25 AC 2 ms
5,248 KB
testcase_26 AC 1 ms
5,248 KB
testcase_27 AC 2 ms
5,248 KB
testcase_28 AC 2 ms
5,248 KB
testcase_29 AC 165 ms
22,700 KB
testcase_30 AC 175 ms
23,480 KB
testcase_31 AC 212 ms
23,644 KB
testcase_32 AC 223 ms
23,672 KB
testcase_33 AC 2 ms
5,248 KB
testcase_34 AC 2 ms
5,248 KB
testcase_35 AC 242 ms
39,212 KB
testcase_36 AC 181 ms
41,012 KB
testcase_37 AC 2 ms
5,248 KB
testcase_38 AC 164 ms
23,472 KB
testcase_39 AC 2 ms
5,248 KB
testcase_40 AC 176 ms
23,348 KB
testcase_41 AC 155 ms
22,572 KB
testcase_42 AC 185 ms
23,340 KB
testcase_43 AC 171 ms
23,480 KB
testcase_44 AC 194 ms
23,488 KB
testcase_45 AC 164 ms
22,564 KB
testcase_46 AC 171 ms
23,348 KB
testcase_47 AC 178 ms
23,356 KB
testcase_48 AC 192 ms
23,332 KB
testcase_49 AC 2 ms
5,248 KB
testcase_50 AC 2 ms
5,248 KB
testcase_51 AC 2 ms
5,248 KB
testcase_52 AC 2 ms
5,248 KB
testcase_53 AC 1 ms
5,248 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 <iostream>
#include <vector>
#include <algorithm>
using namespace std;


struct heavy_light_decomposition{
private:

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

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

public:

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

    for(int p : I) if(nx[p] != -1) PP[nx[p]] = p;

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

    I.resize(N);
    for(int i=0; i<N; i++) I[rangeL[i]] = i;
  }

  int depth(int p) const {
    return D[p];
  }

  int lca(int u, int v) const {
    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;
  }

  int dist(int u, int v) const {
    return depth(u) + depth(v) - depth(lca(u,v)) * 2;
  }

  vector<pair<int,int>> path(int r, int c, bool include_root = true, bool reverse_path = false) const {
    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 });
    if(!include_root){
      res.back().first++;
      if(res.back().first == res.back().second) res.pop_back();
    }
    if(!reverse_path) reverse(res.begin(),res.end());
    return move(res);
  }

  const vector<int>& idxs() const {
    return rangeL;
  }

  int meet(int x, int y, int z) const {
    //return lca(x,y) ^ lca(y,z) ^ lca(x,z);
    if(PD[x] > PD[y]) swap(x,y);
    if(PD[y] > PD[z]) swap(y,z);
    if(PD[x] > PD[y]) swap(x,y);
    while(PD[z] > PD[y]) z = P[PP[z]];
    while(PD[y] > PD[x]){
      if(PP[y] == PP[z]) return (D[y] > D[z]) ? z : y;
      y = P[PP[y]];
      z = P[PP[z]];
    }
    while(true){
      if(PP[x] == PP[y]){
        if(PP[y] == PP[z]){
          if(D[x] > D[y]) swap(x,y);
          if(D[y] > D[z]) swap(y,z);
          if(D[x] > D[y]) swap(x,y);
          return y;
        }
        return (D[x] > D[y]) ? y : x;
      }
      if(PP[x] == PP[z]) return (D[x] > D[z]) ? z : x;
      if(PP[y] == PP[z]) return (D[y] > D[z]) ? z : y;
      x = P[PP[x]];
      y = P[PP[y]];
      z = P[PP[z]];
    }
    return -1;
  }

  int jump(int from, int to, int d) const {
    int g = lca(from,to);
    int dist0 = D[from] - D[g] * 2 + D[to];
    if(dist0 > d) return -1;
    int p = from;
    if(D[from] - D[g] > d){ p = to; d = dist0 - d; }
    while(D[p] - D[PP[p]] > d){
      d -= D[p] - D[PP[p]] + 1;
      p = P[PP[p]];
    }
    return I[rangeL[p] - d];
  }
};



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

struct mll{
  using u32 = uint32_t;
  using u64 = uint64_t;
  u32 v;
  mll(u32 x = 0) : v(x) {}
  u32 val() const { return v; }
  mll& operator+=(const mll& r){ v += r.val(); if(v >= MOD) v -= MOD; return *this; }
  mll& operator-=(const mll& r){ v += MOD - r.val(); if(v >= MOD) v -= MOD; return *this; }
  mll& operator*=(const mll& r) { v = (u64)v * r.val() % MOD; return *this; }
  mll operator+(const mll& r) const { mll res = *this; res += r; return res; }
  mll operator-(const mll& r) const { mll res = *this; res -= r; return res; }
  mll operator*(const mll& r) const { mll res = *this; res *= r; return res; }
  mll operator-() const { return v ? mll(MOD-v) : mll(0); }
};

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<int> Eidx;
vector<mll> dep;

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

heavy_light_decomposition hld;



void read_graph(){
  cin >> N >> M;
  E.resize(N);
  vector<vector<int>> idE(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});
      idE[u].push_back(v);
      idE[v].push_back(u);
    }
  }
  hld = heavy_light_decomposition(idE);
}

void initLCA(){
  vector<int> I;
  P.assign(N,-1);
  I.push_back(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];
      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){
  return hld.dist(u,v);
}
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(hld.meet(u,v,J[z].u) != J[z].u) return -1;
  if(hld.meet(u,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;
0