data_structure/test/LC_birary_heap.test.cpp

#define PROBLEM "https://judge.yosupo.jp/problem/shortest_path"
#include "../binary_heap.hpp"
#include "../../util/template.hpp"

int main(){
	lint n,m,s,t;
	cin>>n>>m>>s>>t;
	vector<vector<pair<lint,lint>>>g(n);
	rep(i,m){
		lint a,b,c;
		cin>>a>>b>>c;
		g[a].emplace_back(b,c);
	}
	binary_heap<pair<lint,lint>>que;
	vector<binary_heap<pair<lint,lint>>::np>v(n);
	rep(i,n)v[i]=que.insert(make_pair(INF,i));
	que.modify(v[s],make_pair(0,s));
	vector<lint>from(n,-1);
	vector<lint>dif(n,INF);
	dif[s]=0;
	while(!que.empty()){
		auto [cost,now]=que.top();
		que.pop();
		for(auto [e,c]:g[now]){
			if(chmin(dif[e],dif[now]+c)){
				from[e]=now;
				que.modify(v[e],make_pair(dif[e],e));
			}
		}
	}
	if(dif[t]==INF){
		cout<<-1<<endl;
		return 0;
	}
	lint now=t;
	vector<pair<lint,lint>>ans;
	while(1){
		if(now==s)break;
		ans.emplace_back(from[now],now);
		now=from[now];
	}
	cout<<dif[t]<<" "<<ans.size()<<endl;
	reverse(all(ans));
	for(auto e:ans){
		cout<<e.first<<" "<<e.second<<endl;
	}
}

#line 1 "data_structure/test/LC_birary_heap.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/shortest_path"
#line 2 "data_structure/binary_heap.hpp"
#include<vector>
#include<algorithm>
#include<functional>

/**
 * @brief BinaryHeap
 */

template<typename T,typename F=std::less<T>>
struct binary_heap{
	int idx=1;
	struct node{
		int idx;
		T val;
		node(int idx,T val):idx(idx),val(val){}
	};
	using np=node*;
	std::vector<np>v;
	F comp;
	binary_heap(F comp):v(2,0),comp(comp){}
	binary_heap():v(2,0),comp(F()){}
	void __swap(np& s,np& t){
		std::swap(s,t);
		std::swap(s->idx,t->idx);
	}
	void up(int k){
		while(k>1&&comp(v[k]->val,v[k/2]->val)){
			__swap(v[k],v[k/2]);
			k/=2;
		}
	}
	void down(int k){
		while(1){
			if(k*2+1<idx&&(comp(v[k*2]->val,v[k]->val)||comp(v[k*2+1]->val,v[k]->val))){
				if(comp(v[k*2]->val,v[k*2+1]->val)){
					__swap(v[k],v[k*2]);
					k=k*2;
				}else{
					__swap(v[k],v[k*2+1]);
					k=k*2+1;
				}
			}else if(k*2<idx&&comp(v[k*2]->val,v[k]->val)){
				__swap(v[k],v[k*2]);
				k=k*2;
			}else{
				break;
			}
		}
	}
	np insert(T val){
		if((int)v.size()<=idx+1)v.resize(v.size()*2,0);
		np res=new node(idx,val);
		v[idx]=res;
		up(idx++);
		return res;
	}
	T top(){
		return v[1]->val;
	}
	void pop(){
		__swap(v[1],v[--idx]);
		down(1);
	}
	int size(){
		return idx-1;
	}
	bool empty(){
		return idx==1;
	}
	void modify(np t,T val){
		t->val=val;
		up(t->idx);
		down(t->idx);
	}
};
#line 2 "util/template.hpp"
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("avx2")
#include<bits/stdc++.h>
using namespace std;
struct __INIT__{__INIT__(){cin.tie(0);ios::sync_with_stdio(false);cout<<fixed<<setprecision(15);}}__INIT__;
typedef long long lint;
#define INF (1LL<<60)
#define IINF (1<<30)
#define EPS (1e-10)
#define endl ('\n')
typedef vector<lint> vec;
typedef vector<vector<lint>> mat;
typedef vector<vector<vector<lint>>> mat3;
typedef vector<string> svec;
typedef vector<vector<string>> smat;
template<typename T>using V=vector<T>;
template<typename T>using VV=V<V<T>>;
template<typename T>inline void output(T t){bool f=0;for(auto i:t){cout<<(f?" ":"")<<i;f=1;}cout<<endl;}
template<typename T>inline void output2(T t){for(auto i:t)output(i);}
template<typename T>inline void debug(T t){bool f=0;for(auto i:t){cerr<<(f?" ":"")<<i;f=1;}cerr<<endl;}
template<typename T>inline void debug2(T t){for(auto i:t)output(i);}
#define loop(n) for(long long _=0;_<(long long)(n);++_)
#define _overload4(_1,_2,_3,_4,name,...) name
#define __rep(i,a) repi(i,0,a,1)
#define _rep(i,a,b) repi(i,a,b,1)
#define repi(i,a,b,c) for(long long i=(long long)(a);i<(long long)(b);i+=c)
#define rep(...) _overload4(__VA_ARGS__,repi,_rep,__rep)(__VA_ARGS__)
#define _overload3_rev(_1,_2,_3,name,...) name
#define _rep_rev(i,a) repi_rev(i,0,a)
#define repi_rev(i,a,b) for(long long i=(long long)(b)-1;i>=(long long)(a);--i)
#define rrep(...) _overload3_rev(__VA_ARGS__,repi_rev,_rep_rev)(__VA_ARGS__)

// #define rep(i,...) for(auto i:range(__VA_ARGS__)) 
// #define rrep(i,...) for(auto i:reversed(range(__VA_ARGS__)))
// #define repi(i,a,b) for(lint i=lint(a);i<(lint)(b);++i)
// #define rrepi(i,a,b) for(lint i=lint(b)-1;i>=lint(a);--i)
// #define irep(i) for(lint i=0;;++i)
// inline vector<long long> range(long long n){if(n<=0)return vector<long long>();vector<long long>v(n);iota(v.begin(),v.end(),0LL);return v;}
// inline vector<long long> range(long long a,long long b){if(b<=a)return vector<long long>();vector<long long>v(b-a);iota(v.begin(),v.end(),a);return v;}
// inline vector<long long> range(long long a,long long b,long long c){if((b-a+c-1)/c<=0)return vector<long long>();vector<long long>v((b-a+c-1)/c);for(int i=0;i<(int)v.size();++i)v[i]=i?v[i-1]+c:a;return v;}
// template<typename T>inline T reversed(T v){reverse(v.begin(),v.end());return v;}
#define all(n) begin(n),end(n)
template<typename T,typename E>bool chmin(T& s,const E& t){bool res=s>t;s=min<T>(s,t);return res;}
template<typename T,typename E>bool chmax(T& s,const E& t){bool res=s<t;s=max<T>(s,t);return res;}
const vector<lint> dx={1,0,-1,0,1,1,-1,-1};
const vector<lint> dy={0,1,0,-1,1,-1,1,-1};
#define SUM(v) accumulate(all(v),0LL)
template<typename T,typename ...Args>auto make_vector(T x,int arg,Args ...args){if constexpr(sizeof...(args)==0)return vector<T>(arg,x);else return vector(arg,make_vector<T>(x,args...));}
#define extrep(v,...) for(auto v:__MAKE_MAT__({__VA_ARGS__}))
#define bit(n,a) ((n>>a)&1)
vector<vector<long long>> __MAKE_MAT__(vector<long long> v){if(v.empty())return vector<vector<long long>>(1,vector<long long>());long long n=v.back();v.pop_back();vector<vector<long long>> ret;vector<vector<long long>> tmp=__MAKE_MAT__(v);for(auto e:tmp)for(long long i=0;i<n;++i){ret.push_back(e);ret.back().push_back(i);}return ret;}
using graph=vector<vector<int>>;
template<typename T>using graph_w=vector<vector<pair<int,T>>>;
template<typename T,typename E>ostream& operator<<(ostream& out,pair<T,E>v){out<<"("<<v.first<<","<<v.second<<")";return out;}
constexpr inline long long powll(long long a,long long b){long long res=1;while(b--)res*=a;return res;}
#line 4 "data_structure/test/LC_birary_heap.test.cpp"

int main(){
	lint n,m,s,t;
	cin>>n>>m>>s>>t;
	vector<vector<pair<lint,lint>>>g(n);
	rep(i,m){
		lint a,b,c;
		cin>>a>>b>>c;
		g[a].emplace_back(b,c);
	}
	binary_heap<pair<lint,lint>>que;
	vector<binary_heap<pair<lint,lint>>::np>v(n);
	rep(i,n)v[i]=que.insert(make_pair(INF,i));
	que.modify(v[s],make_pair(0,s));
	vector<lint>from(n,-1);
	vector<lint>dif(n,INF);
	dif[s]=0;
	while(!que.empty()){
		auto [cost,now]=que.top();
		que.pop();
		for(auto [e,c]:g[now]){
			if(chmin(dif[e],dif[now]+c)){
				from[e]=now;
				que.modify(v[e],make_pair(dif[e],e));
			}
		}
	}
	if(dif[t]==INF){
		cout<<-1<<endl;
		return 0;
	}
	lint now=t;
	vector<pair<lint,lint>>ans;
	while(1){
		if(now==s)break;
		ans.emplace_back(from[now],now);
		now=from[now];
	}
	cout<<dif[t]<<" "<<ans.size()<<endl;
	reverse(all(ans));
	for(auto e:ans){
		cout<<e.first<<" "<<e.second<<endl;
	}
}