Go: package main

import (
	"bufio"
	"container/heap"
	"fmt"
	"os"
)

type Item struct {
	value    int // The value of the item; arbitrary.
	priority int // The priority of the item in the queue.
	// The index is needed by update and is maintained by the heap.Interface methods.
	index int // The index of the item in the heap.
}
type PriorityQueue []*Item

func (pq PriorityQueue) Len() int { return len(pq) }
func (pq PriorityQueue) Less(i, j int) bool {
	return pq[i].priority < pq[j].priority
}
func (pq PriorityQueue) Swap(i, j int) {
	pq[i], pq[j] = pq[j], pq[i]
	pq[i].index = i
	pq[j].index = j
}
func (pq *PriorityQueue) Push(x interface{}) {
	n := len(*pq)
	item := x.(*Item)
	item.index = n
	*pq = append(*pq, item)
}
func (pq *PriorityQueue) Pop() interface{} {
	old := *pq
	n := len(old)
	item := old[n-1]
	item.index = -1 // for safety
	*pq = old[0 : n-1]
	return item
}

type Q struct {
	pq *PriorityQueue
	ds map[int]int // It has always same value as pq. For random access.
}

func newQ() *Q {
	pq := new(PriorityQueue)
	heap.Init(pq)
	return &Q{
		pq: pq,
		ds: make(map[int]int),
	}
}
func (q *Q) pop() (u, d int) {
	item := heap.Pop(q.pq).(*Item)
	delete(q.ds, item.value)
	return item.value, item.priority
}
func (q *Q) get(u int) (int, bool) { // returns d
	d, ok := q.ds[u]
	return d, ok
}
func (q *Q) set(u, d int) {
	q.ds[u] = d
	for _, item := range *q.pq {
		if item.value != u {
			continue
		}

		item.priority = d
		heap.Fix(q.pq, item.index)
		return
	}
	heap.Push(q.pq, &Item{
		priority: d,
		value:    u,
	})
}
func (q *Q) len() int {
	return len(q.ds)
}

func main() {
	r := bufio.NewReader(os.Stdin)

	var n int
	fmt.Fscan(r, &n)
	cs := make([]map[int]int, n) // []v_i -> c_i
	for h := 0; h < n; h++ {
		var u, k int
		fmt.Fscan(r, &u, &k)
		m := make(map[int]int)
		for i := 0; i < k; i++ {
			var v, c int
			fmt.Fscan(r, &v, &c)
			m[v] = c
		}

		cs[u] = m
	}

	q := newQ()
	q.set(0, 0)
	visited := make(map[int]struct{})
	out := make([]int, n)

	for q.len() > 0 {
		u, d := q.pop()
		for uu, c := range cs[u] {
			// Consider the connection between u and uu.
			if _, ok := visited[uu]; ok {
				continue
			}
			dd := d + c
			if d, ok := q.get(uu); !ok || d > dd {
				q.set(uu, dd)
			}
		}

		out[u] = d
		visited[u] = struct{}{}
	}

	for u, d := range out {
		fmt.Println(u, d)
	}
}

C++: #include<iostream>
#include<queue>
using namespace std;

struct Edge {
  /*
    dst -> destination
    weight -> weight
   */
  int dst,weight;
};

struct Data {

  int place,min;

  bool operator < (const Data& data)const{
    //if( min < data.min ) => true;
    if(data.min != min)return min > data.min;
    return data.place > place;
  }

};

//int cost[100001][100001];
vector<Edge> cost[10001];
int n;
int mindist[10001];
bool used[10001];

void dijkstra(){

  for(int i=0 ; i < 10001 ; i++){
    mindist[i]=1e9;
  }
  
  mindist[0]=0;

  priority_queue<Data> PQ;

  PQ.push((Data){0,0});

  while(!PQ.empty()){
    Data a=PQ.top();
    PQ.pop();
    if( mindist[a.place] < a.min ) continue;
    for(int i=0 ; i < (int)cost[a.place].size() ; i++){
      if(mindist[cost[a.place][i].dst] > cost[a.place][i].weight+mindist[a.place]){
	mindist[cost[a.place][i].dst] = cost[a.place][i].weight+mindist[a.place];
	PQ.push((Data){cost[a.place][i].dst,mindist[cost[a.place][i].dst]});
      }
      //cost[a.place].pop_back();
    } 
  }
  
  for(int i=0 ; i < n ; i++){
    cout <<i<<" "<<mindist[i]<<endl;
  }
  
}
int main(){
  
  int u,k,v,c;
  
  // 0 -> 1 weight : 3
  /*  
      cost[0].push_back((Edge){1,3});
      cost[0].push_back((Edge){0,4});
      cost[2].push_back((Edge){0,3});
  */
  
  cin >>n;
  
  for(int i=0 ; i < n ; i++){
    cin >>u>>k;
    for(int j=0 ; j < k ; j++){
      cin >>v>>c;
      cost[u].push_back((Edge){v,c});
    }
  }

  dijkstra();

  return 0;
}


/*
1sec => 10^8


 */

C++: #include <algorithm>
#include <iostream>
#include <vector>
using namespace std;
const long long INF = 1LL << 60;    // 1.15x10^18
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }

using edge = pair<int, long long>;
using Graph = vector<vector<edge>>;

vector<long long> dijkstra(const Graph &g, int s) {
    int n = g.size();
    vector<long long> dist(n, INF);
    vector<bool> fixed(n);
    dist[s] = 0;
    while (true) {
        int u = -1;
        for (int i = 0; i < n; i++) if (!fixed[i]) {
            if (u == -1 || dist[i] < dist[u]) u = i;
        }
        if (u == -1) break;
        fixed[u] = true;
        for (auto &e: g[u]) chmin(dist[e.first], dist[u] + e.second);
    }
    return dist;
}

int main() {
    int V; cin >> V;
    Graph g(V);
    for (int i = 0; i < V; i++) {
        int u, k; cin >> u >> k;
        while (k--) {
            int v, c; cin >> v >> c;
            g[u].emplace_back(v, c);
        }
    }
    auto dist = dijkstra(g, 0);
    for (int u = 0; u < V; u++) cout << u << " " << dist[u] << endl;
    return 0;
}

C++: #include<iostream>
#include<algorithm>
#include<queue>
#include<vector>
#include<stdio.h>
using namespace std;

static const int INFTY = (1<<21);
enum Color{
    WHITE,
    GRAY,
    BLACK
};
int n;

//int M[100][100];
vector<pair<int,int> > adj[10000];   //隣接リスト
priority_queue<pair<int, int> > PQ; 
Color color[10000];
int d[10000];

void dijkstra(){
    for(int i=0; i<n; i++){
        color[i] = WHITE;
        d[i] = INFTY;
    }
    d[0] = 0;
    PQ.push(make_pair(0,0));
    color[0] = GRAY;
    
    while(!PQ.empty()){
        pair<int,int> f = PQ.top(); 
        PQ.pop();
        int u = f.second;
        color[u] = BLACK;

        if(d[u] < f.first*(-1)) continue;

        for(int j=0, size = adj[u].size(); j<size;  j++){
            int v = adj[u][j].first;
            if(color[v]==BLACK) continue;
            if(d[v] > d[u] + adj[u][j].second){
                d[v] = d[u] + adj[u][j].second;
                PQ.push(make_pair(d[v]*(-1), v));
                color[v] = GRAY;
            }
        }
    }

    for(int i=0; i<n; i++){
        cout << i << " " << ((d[i]==INFTY)? -1:d[i]) << endl;
    }
}

int main(){

    cin >> n;
    for(int i=0; i<n; i++){
        int u, k;
        cin >> u >> k;
        for(int j=0; j<k; j++){
        int v, g;
        cin >> v >> g;
        adj[u].push_back(make_pair(v, g));
        }
    }

    dijkstra();
    return 0;
}

C++: #include<iostream>
#include<algorithm>
#include<queue>
#include<utility>
#include<vector>


using namespace std;



int main() {
	int n,tmp1,tmp2,size;
	int cnt_arrived=0;
	pair<int, int> ptmp;
	priority_queue<pair<int, int>,vector<pair<int,int>>,greater<pair<int,int>>> pq;
	cin >> n;
	int** mat = new int* [n];
	vector<pair<int, int>>* list_adjacent = new vector<pair<int, int>>[n];
	int* dist = new int[n];
	for (int i = 0;i < n;i++) {
		cin >> tmp1 >> size;
		for (int j = 0;j < size;j++) {
			cin >> tmp1 >> tmp2;
			list_adjacent[i].push_back(make_pair(tmp1, tmp2));
		}
		dist[i] = -1;
	}
	pq.push(make_pair(0, 0));
	while (cnt_arrived < n) {
		ptmp = pq.top();
		pq.pop();
		if (dist[ptmp.second] == -1) {
			cnt_arrived++;
			dist[ptmp.second] = ptmp.first;
			for (int i = 0;i < list_adjacent[ptmp.second].size();i++) {
				pq.push(make_pair(ptmp.first + list_adjacent[ptmp.second][i].second, list_adjacent[ptmp.second][i].first));
			}
		}
	}
	for (int i = 0;i < n;i++) {
		cout << i << " " << dist[i] << endl;
	}
}