procon
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test/yosupo_KSW.test.cpp
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- Last update: 2024-05-17 14:55:36+09:00
- Problem: https://judge.yosupo.jp/problem/k_shortest_walk
Depends on
Graph2/GraphTemplate.hpp
Code
#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;
}