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<bits/stdc++.h>
using namespace std;

#define rep(i,n) for(int i = 0; i < n; i++)
#define Rep(i,n) for(int i = 1; i <= n; i++)
#define sz(x) int(x.size())
#define all(v) v.begin(), v.end()
#define rall(v) v.rbegin(), v.rend()
#define YesorNo(a) printf(a ? "Yes\n" : "No\n")
#define endl '\n'
#define fi first
#define se second
using ll = long long;
using P = pair<int,int>;
using Pl = pair<ll,ll>;
template<class T> using V = vector<T>;
const int dx[] = {0,1,0,-1,1,1,-1,-1};
const int dy[] = {1,0,-1,0,1,-1,-1,1};
const int inf = (1<<30)-1;
const ll infll = (1LL<<62)-1;
ll ceil(const ll &a, const ll &b){return ((a)+(b)-1)/b;}
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }


void Dijkstra(int s, const vector<vector<P>> &g, vector<int> &dis) {
  priority_queue<P, vector<P>, greater<P>> que; // pair = (cost, v);
  dis[s] = 0;
  que.emplace(0,s);
  while(!que.empty()) {
    P p = que.top(); que.pop();
    int now = p.second;
    if(dis[now] < p.first) continue;
    for(P np : g[now]) {
      int next = np.second;
      if(dis[next] > dis[now] + np.first) {
        dis[next] = dis[now] + np.first;
        que.emplace(dis[next], next);
      }
    }
  }
}


int main(){
    
    int n;
    cin >> n;
    V<V<P>> g(n); // pair = (cost, to);
    rep(i,n) {
        int a, k;
        cin >> a >> k;
        rep(j,k) {
            int b, v;
            cin >> b >> v;
            g[a].emplace_back(v,b);
        }
    }

    V<int> d(n, inf);
    Dijkstra(0,g,d);
    rep(i,n) {
        printf("%d %d\n", i, d[i]);
    }
}

C++: #include <iostream>
#include <cstdio>
#include <vector>
#include <climits>
#include <queue>

#define INF INT_MAX

using namespace std;

int main(){
  int n; cin >> n;
  vector<pair<int,int> > G[n];
  for(int i=0;i<n;i++){
    int u,k; cin >> u >> k;
    for(int j=0;j<k;j++){
      int v,c; cin >> v >> c;
      G[u].push_back(make_pair(v,c));
    }
  }
  //dijkstra from 0
  priority_queue<pair<int,int>,vector<pair<int,int> >,greater<pair<int,int> > > PQ;
  int visited[n],d[n];
  for(int i=0;i<n;i++){
    visited[i]=0;
    d[i]=INF;
  }
  d[0]=0;
  PQ.push(make_pair(d[0],0));
  while(PQ.empty()==false){
    int u=PQ.top().second;
    int u_first=PQ.top().first;
    PQ.pop();
    //cout << "u:" << u << endl;
    visited[u]=1;
    if(d[u]<u_first) continue;
    for(int i=0;i<G[u].size();i++){
      int v=G[u][i].first;
      //cout << "v:" << v << endl;
      if(visited[v]==0){
        if(d[u]+G[u][i].second<d[v]){
          d[v]=d[u]+G[u][i].second;
          PQ.push(make_pair(d[v],v));
        }
      }
    }
  }
  for(int i=0;i<n;i++) cout << i << " " << d[i] << endl;
}

C++: #include<iostream>
#include<algorithm>
#include<vector>
#include<queue>
#define MAX 10000
#define INF (1 << 21)
#define WHITE  1
#define GRAY  2
#define BLACK  3
using namespace std;

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

void dijkstra(){
  priority_queue<pair<int, int> > pq;

  vector<int> color(MAX);
  vector<int> d(MAX);
  
  for(int i = 0; i < n; i++){
    d[i] = INF;
    color[i] = WHITE;
  }

  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 i = 0; i < adj[u].size(); i++){
      int v = adj[u][i].first;

      if(color[v] == BLACK) continue;
      if(d[v] > d[u] + adj[u][i].second){
	d[v] = d[u] + adj[u][i].second;
	pq.push(make_pair(d[v] * (-1), v));
	color[v] = GRAY;
      }
    }
  }

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

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

  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;

}