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<algorithm>
#include<queue>
using namespace std;
static const int MAX = 10000;
static const int INFTY = (1<<20);

int n;
vector<pair<int,int> > G[MAX];

void dij(){
  priority_queue<pair<int,int> > PQ;
  int color[MAX], d[MAX], i, j, u, v;
  for(i = 0; i < n; i++){
    d[i] = INFTY;
    color[i] = 0;
  }
  d[0] = 0;
  PQ.push(make_pair(0,0));
  color[0] = 1;

  while(!PQ.empty()){
    pair<int,int> f = PQ.top();
    PQ.pop();
    u = f.second;
    color[u] = 2;

    if(d[u] < f.first * (-1)) continue;
    for(j = 0; j < G[u].size(); j++){
      v = G[u][j].first;
      if(color[v] == 2) continue;
      if(d[v] > d[u] + G[u][j].second){
        d[v] =  d[u] + G[u][j].second;
        PQ.push(make_pair(d[v] * (-1), v));
        color[v] = 1;
      }
    }
  }

  for(i = 0; i < n; i++){
    cout << i << " " << (d[i] == INFTY ? -1 : d[i]) << endl;
  }
}
int main()
{
  int k, u, v, c, i, j;

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

  dij();
  return 0;
}

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

const int MAX = 10000;
const int INF = 1e9 + 7;

int n;
vector<pair<int, int> > adj[MAX];

void dijkstra()
{
  int d[MAX], color[MAX];
  priority_queue<pair<int, int> > pq;

  fill(d, d + MAX, INF);
  fill(color, color + MAX, 0);

  d[0] = 0;
  pq.push(make_pair(0, 0));
  color[0] = 1;

  while (!pq.empty()) {
    pair<int, int> f = pq.top();
    pq.pop();
    int u = f.second;
    color[u] = 2;

    if (d[u] < f.first * (-1)) continue;
    for (int j = 0; j < adj[u].size(); j++) {
      int v = adj[u][j].first;
      if (color[v] == 2) 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] = 1;
      }
    }
  }
  
  for (int i = 0; i < n; i++) 
    cout << i << " " << (d[i] == INF ? -1 : d[i]) << endl;
  }
}

signed main()
{
  int u, k, c, v;

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

  dijkstra();

  return (0);
}

C++: #include<iostream>
#include<algorithm>
#include<queue>
#define MAX 10000
int INF=(1<<20), WH=0, GR=1, BL=2;
int n;
std::vector<std::pair<int,int> > adj[MAX];
void dij(void);
int main(){
  int k, u, v, c;
  std::cin >> n;
  for(int i=0; i<n; i++){
    std::cin >> u >> k;
    for(int j=0; j<k; j++){
      std::cin >> v >> c;
      adj[u].push_back(std::make_pair(v,c));
    }
  }
  dij();
  return 0;
}
void dij(void){
  std::priority_queue<std::pair<int,int> > PQ;
  int color[MAX], d[MAX];
  for(int i=0; i<n; i++) d[i] = INF, color[i] = WH;
  d[0] = 0;
  PQ.push(std::make_pair(0,0));
  color[0] = GR;
  while(!PQ.empty()){
    std::pair<int,int> f=PQ.top(); PQ.pop();
    int u=f.second;
    color[u] = BL;
    if(d[u] < f.first * (-1)) continue;
    for(int j=0; j<adj[u].size(); j++){
      int v=adj[u][j].first;
      if(color[v] == BL) continue;
      if(d[v] > d[u] + adj[u][j].second){
	d[v] = d[u] + adj[u][j].second;
	PQ.push(std::make_pair(d[v]*(-1),v));
      }
    }
  }
  for(int i=0; i<n; i++) std::cout << i << " " << (d[i] == INF ? -1 : d[i]) << std::endl;
}