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 <vector>
#include <queue>
#include <climits>

struct Node {
	int id;
	std::vector<int> edge_to;
	std::vector<int> edge_cost;
	bool done;
	int cost;
};

bool operator>(const Node& u, const Node& v) { return u.cost > v.cost; }
bool operator<(const Node& u, const Node& v) { return u.cost < v.cost; }
bool operator>=(const Node& u, const Node& v) { return u.cost >= v.cost; }
bool operator<=(const Node& u, const Node& v) { return u.cost <= v.cost; }
bool operator==(const Node& u, const Node& v) { return u.id == v.id; }
bool operator!=(const Node& u, const Node& v) { return u.id != v.id; }

void swap(int& x, int& y)
{
	int tmp = x;
	x = y;
	y = tmp;
}

int min(int x, int y)
{
	return x>y ? y : x;
}

int main()
{
	int n; std::cin >> n;
	
	Node* nodes = new Node[n];
	
	for (int i=0; i<n; i++) {
		nodes[i].done = false;
		nodes[i].cost = INT_MAX;
	}
	
	for (int i=0; i<n; i++) {
		int id, deg;
		std::cin >> id >> deg;
		nodes[i].id = id;
		for (int j=0; j<deg; j++) {
			int t, cost;
			std::cin >> t >> cost;
			nodes[i].edge_to.push_back(t);
			nodes[i].edge_cost.push_back(cost);
		}
	}
	
	std::priority_queue<Node, std::vector<Node>, std::greater<std::vector<Node>::value_type>> que;
	que.push(nodes[0]);
	nodes[0].cost = 0;
	
	while (!que.empty()) {
		Node v = que.top(); que.pop();
		int s = v.id;
		// std::cout << s << " " << nodes[s].cost << std::endl;
		nodes[s].done = true;
		for (int k=0; k<nodes[s].edge_to.size(); k++) {
			int t = nodes[s].edge_to[k];
			int cost = nodes[s].edge_cost[k];
			if (nodes[t].done) continue;
			if ( nodes[t].cost > nodes[s].cost + cost) {
				nodes[t].cost = nodes[s].cost + cost;
				que.push(nodes[t]);
			}
		}
	}
	
	for (int i=0; i<n; i++) {
		std::cout << nodes[i].id << " " << nodes[i].cost << std::endl;
	}
	
	delete[] nodes;
	
	return 0;
}

C++: #include<iostream>
#include<vector>
#include<queue>
#include<utility>
#include<climits>
#include<algorithm>
using namespace std;
typedef int Cost;
typedef int Node;

void dijkstra(int start,   vector<vector< pair<Node,Cost> > > m){
  vector<Cost> costs(m.size());
  bool visited[m.size()];

  fill(costs.begin(),costs.end(),INT_MAX);
  fill(visited,visited+m.size(),false);
  
  priority_queue<pair<Cost,Node> ,vector<pair<Cost,Node> >, greater<pair<Cost,Node> > > q;
  q.push(make_pair(0,start));
  while(!q.empty()){
    Cost c = q.top().first;
    Node n = q.top().second;
    q.pop();
    if(!visited[n]){
      costs[n] = c;
      for(auto &x:m[n]){
        int node = x.first;
        int cost = x.second;
        q.push(make_pair(cost+c,node));
      }
      visited[n] = true;
    }
  }
  for(int i = 0;i < costs.size();i++){
    cout << i << ' ' << costs[i] << endl;
  }
}

int main(){
  int n;
  cin >> n;
  vector<vector< pair<Node,Cost> > > m(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;
      m[u].push_back(make_pair(v,c));
    }
  }
  dijkstra(0,m);
}

C++: #include<iostream>
#include<algorithm>
#include<queue>
using namespace std;
static const int MAX=10000;
static const int INF=1<<20;
static const int WHITE=0;
static const int GRAY=1;
static const int BLACK=2;

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

void dijkstra(){
	int color[n];
	int d[n];
	for(int i=0;i<n;i++){
		color[i]=WHITE;
		d[i]=INF;
	}

	d[0]=0;
	priority_queue<pair<int,int> > pq;
	pq.push(make_pair(0,0));
	
	while(!pq.empty()){
		pair<int,int> f=pq.top();pq.pop();
		int u=f.second;
		color[u]=BLACK;
		
		int size=adj[u].size();
		for(int j=0;j<size;j++){
			int v=adj[u][j].first;
			if(color[v]==BLACK) continue;
			int w=adj[u][j].second;
			if(d[v]>d[u]+w){
				d[v]=d[u]+w;
				pq.push(make_pair(d[v]*-1,v));
			}
		}
	}

	for(int i=0;i<n;i++){
		cout << i << " ";
		cout << (d[i]==INF?-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,c;
			cin >> v >> c;
			pair<int,int> p;
			p=make_pair(v,c);
			adj[u].push_back(p);
		}
	}
	dijkstra();
    return 0;
}