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#define PROBLEM "https://judge.yosupo.jp/problem/k_shortest_walk" #include "../template.hpp" #include "../Graph2/Eppstein.hpp" signed main(){ int n,m,s,t,k;cin>>n>>m>>s>>t>>k; Graph<ll> g(n); g.read(m,0,true,true); auto res=Eppstein(g,s,t,k); rep(i,k){ if(i<(int)res.size()) cout<<res[i]<<endl; else cout<<-1<<endl; } return 0; }
#line 1 "test/yosupo_KSW.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/k_shortest_walk" #line 1 "template.hpp" #include<bits/stdc++.h> using namespace std; #define ALL(x) begin(x),end(x) #define rep(i,n) for(int i=0;i<(n);i++) #define debug(v) cout<<#v<<":";for(auto x:v){cout<<x<<' ';}cout<<endl; #define mod 1000000007 using ll=long long; const int INF=1000000000; const ll LINF=1001002003004005006ll; int dx[]={1,0,-1,0},dy[]={0,1,0,-1}; // ll gcd(ll a,ll b){return b?gcd(b,a%b):a;} template<class T>bool chmax(T &a,const T &b){if(a<b){a=b;return true;}return false;} template<class T>bool chmin(T &a,const T &b){if(b<a){a=b;return true;}return false;} struct IOSetup{ IOSetup(){ cin.tie(0); ios::sync_with_stdio(0); cout<<fixed<<setprecision(12); } } iosetup; template<typename T> ostream &operator<<(ostream &os,const vector<T>&v){ for(int i=0;i<(int)v.size();i++) os<<v[i]<<(i+1==(int)v.size()?"":" "); return os; } template<typename T> istream &operator>>(istream &is,vector<T>&v){ for(T &x:v)is>>x; return is; } #line 4 "test/yosupo_KSW.test.cpp" #line 1 "Graph2/GraphTemplate.hpp" // graph template // ref : https://ei1333.github.io/library/graph/graph-template.hpp template<typename T=int> struct Edge{ int from,to; T w; int idx; Edge()=default; Edge(int from,int to,T w=1,int idx=-1):from(from),to(to),w(w),idx(idx){} operator int() const{return to;} }; template<typename T=int> struct Graph{ vector<vector<Edge<T>>> g; int V,E; Graph()=default; Graph(int n):g(n),V(n),E(0){} int size(){ return (int)g.size(); } void resize(int k){ g.resize(k); V=k; } inline const vector<Edge<T>> &operator[](int k)const{ return (g.at(k)); } inline vector<Edge<T>> &operator[](int k){ return (g.at(k)); } void add_directed_edge(int from,int to,T cost=1){ g[from].emplace_back(from,to,cost,E++); } void add_edge(int from,int to,T cost=1){ g[from].emplace_back(from,to,cost,E); g[to].emplace_back(to,from,cost,E++); } void read(int m,int pad=-1,bool weighted=false,bool directed=false){ for(int i=0;i<m;i++){ int u,v;cin>>u>>v; u+=pad,v+=pad; T w=T(1); if(weighted) cin>>w; if(directed) add_directed_edge(u,v,w); else add_edge(u,v,w); } } }; #line 2 "Graph2/Eppstein.hpp" template<typename T> struct PersistentLeftistHeapNode{ PersistentLeftistHeapNode *l,*r; int s; T val; PersistentLeftistHeapNode(T val):l(nullptr),r(nullptr),s(1),val(val){} }; template<typename T,bool less=true> struct PersistentLeftistHeap{ PersistentLeftistHeapNode<T> *root; PersistentLeftistHeap(PersistentLeftistHeapNode<T> *t=nullptr):root(t){} PersistentLeftistHeapNode<T> *meld(PersistentLeftistHeapNode<T> *a,PersistentLeftistHeapNode<T> *b){ if(!a or !b) return (a?a:b); if((a->val>b->val)^(!less)) swap(a,b); a=new PersistentLeftistHeapNode(*a); a->r=meld(a->r,b); if(!a->l or a->l->s<a->r->s) swap(a->l,a->r); a->s=(a->r?a->r->s:0)+1; return a; } PersistentLeftistHeap meld(PersistentLeftistHeap b){ return PersistentLeftistHeap(meld(root,b.root)); } PersistentLeftistHeap push(T x){ return PersistentLeftistHeap(meld(root,new PersistentLeftistHeapNode(x))); } PersistentLeftistHeap pop(){ assert(root!=nullptr); return PersistentLeftistHeap(meld(root->l,root->r)); } bool empty(){ return (root==nullptr); } T top(){ assert(root!=nullptr); return root->val; } }; // ref: https://qiita.com/hotman78/items/42534a01c4bd05ed5e1e // K Shortest Walk template<typename T> vector<T> Eppstein(Graph<T> &G,int s,int t,int k){ int N=G.V,M=G.E; T inf=numeric_limits<T>::max(); Graph<T> rG(N); vector<Edge<T>> edges(M); for(int i=0;i<N;i++)for(auto &e:G[i]) edges[e.idx]=e; for(auto &e:edges) rG.add_directed_edge(e.to,e.from,e.w); // Dijkstra rG, make Tree vector<int> prev_e(N,-1),prev_v(N,-1); vector<T> dis(N,inf); vector<vector<int>> tree(N); vector<bool> tree_edge(M,false); { using P=pair<T,int>; priority_queue<P,vector<P>,greater<P>> que; dis[t]=0; que.emplace(dis[t],t); while(!que.empty()){ auto [d_cur,cur]=que.top();que.pop(); if(dis[cur]<d_cur) continue; for(auto &e:rG[cur])if(chmin(dis[e.to],d_cur+e.w)){ prev_e[e.to]=e.idx; prev_v[e.to]=cur; que.emplace(dis[e.to],e.to); } } if(dis[s]>=inf) return {}; for(auto &i:prev_e)if(i>=0) tree[edges[i].to].push_back(edges[i].from),tree_edge[i]=true; } // make H_G vector<PersistentLeftistHeap<pair<T,int>>> H_G(N);// (potential, edge index) { function<void(int)> dfs=[&](int cur){ if(prev_v[cur]>=0) H_G[cur]=H_G[cur].meld(H_G[prev_v[cur]]); for(auto &e:G[cur]){ if(e.to!=t and prev_v[e.to]<0) continue; // cant reach if(tree_edge[e.idx]) continue; H_G[cur]=H_G[cur].push({e.w-dis[cur]+dis[e.to],e.idx}); } for(auto &to:tree[cur]) dfs(to); }; dfs(t); } // return KSP vector<T> ret; { using P_TN=pair<T,PersistentLeftistHeapNode<pair<T,int>>*>; auto comp=[](const P_TN &x,const P_TN &y){return x.first>y.first;}; priority_queue<P_TN,vector<P_TN>,decltype(comp)> que(comp); ret.push_back(dis[s]); if(H_G[s].root) que.emplace(dis[s]+H_G[s].root->val.first,H_G[s].root); while(!que.empty() and (int)ret.size()<k){ auto [cost,cur]=que.top();que.pop(); ret.emplace_back(cost); int to=edges[cur->val.second].to; if(H_G[to].root) que.emplace(cost+H_G[to].root->val.first,H_G[to].root); if(cur->l) que.emplace(cost+cur->l->val.first-cur->val.first,cur->l); if(cur->r) que.emplace(cost+cur->r->val.first-cur->val.first,cur->r); } } return ret; } #line 6 "test/yosupo_KSW.test.cpp" signed main(){ int n,m,s,t,k;cin>>n>>m>>s>>t>>k; Graph<ll> g(n); g.read(m,0,true,true); auto res=Eppstein(g,s,t,k); rep(i,k){ if(i<(int)res.size()) cout<<res[i]<<endl; else cout<<-1<<endl; } return 0; }