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 <stdio.h>
#include <iostream>
#include <queue>
using namespace std;

class Vertice;
class Edge;

class Vertice{
private:
	int id;
	int edge_num;
	int *vertice_id_list;
	Edge **edges;
	bool flag_fixed;
	int distance_min;
public:
	Vertice(int id, int edge_num_max);
	~Vertice(){ delete[] edges, vertice_id_list; }
	int getDistanceMin() const { return distance_min; }
	void addEdge(int vertice_id, Edge *edge);
	void addVertices(Vertice *vertices[]);
	void setDistance(int d);
	void serveDistance();
	void setFlagFixed(){ flag_fixed = true; }
};

class Edge{
private:
	int distance;
	Vertice *vertice;
public:
	Edge(int distance){ this->distance = distance; }
	void addVertice(Vertice *vertice){ this->vertice = vertice; }
	void setDistance(int distance){ vertice->setDistance(distance + this->distance); }
};

struct verticeComp {
	bool operator()(const Vertice *v1, const Vertice *v2)
	{
		return v1->getDistanceMin() > v2->getDistanceMin();
	}
};

priority_queue<Vertice*, vector<Vertice*>, verticeComp > PQ; 

Vertice::Vertice(int id, int edge_num_max)
{
	this->id = id;
	edge_num = 0;
	vertice_id_list = new int[edge_num_max];
	edges = new Edge*[edge_num_max];
	flag_fixed = false;
	distance_min = INT_MAX;
}

void Vertice::addEdge(int vertice_id, Edge *edge)
{
	edges[edge_num] = edge;
	vertice_id_list[edge_num] = vertice_id;
	edge_num++;
}

void Vertice::addVertices(Vertice *vertices[])
{
	for (int i = 0; i < edge_num; i++) {
		edges[i]->addVertice(vertices[vertice_id_list[i]]);
	}
}

void Vertice::setDistance(int d)
{
	if (flag_fixed) return;
	if (d < distance_min) distance_min = d;
	PQ.push(this);
}

void Vertice::serveDistance()
{
	if (PQ.empty()) return;
	for (int i = 0; i < edge_num; i++) {
		edges[i]->setDistance(distance_min);
	}
	Vertice *fixed_vertice = PQ.top();
	PQ.pop();
	fixed_vertice->setFlagFixed();
	fixed_vertice->serveDistance();
}

int main(void)
{
	Vertice **vertices;

	int n;
	cin >> n;
	vertices = new Vertice*[n];
	for (int i = 0; i < n; i++) {
		int u, k;
		cin >> u >> k;
		vertices[u] = new Vertice(u, k);
		for (int j = 0; j < k; j++) {
			int v, c;
			cin >> v >> c;
			vertices[u]->addEdge(v, new Edge(c));
		}
	}
	
	for (int i = 0; i < n; i++) {
		vertices[i]->addVertices(vertices);
	}

	vertices[0]->setDistance(0);
	vertices[0]->serveDistance();

	for (int i = 0; i < n; i++) {
		cout << i << " ";
		cout << vertices[i]->getDistanceMin() << endl;
	}

	return 0;
}

C++: #include<iostream>
#include<vector>
#include<queue>
using namespace std;
template< typename FirstType, typename SecondType >
struct PairComparator {
  bool operator()( const pair<FirstType, SecondType>& p1, const pair<FirstType, SecondType>& p2 ) const 
    {  
		return p1.first > p2.first;
    }
};
bool inMST(vector< std::pair<int,int> > & MST,int j) {
	for (int k=0;k<(int)MST.size();++k){
		if(j == MST[k].second)
			return true;
	}
	return false;
}
int main(){
	int n;
	cin >> n;
	vector<int> E(n*n,-1);
	vector<int> DPG(n,-1);
	vector< std::pair<int,int> > MST;
	for(int j=0;j<n;++j) {
		int u,k; 
		cin >> u >> k;
		for(int i=0;i<k;++i){
			int v,c;
			cin >> v >> c;
			E[u*n+v] = c;
			E[u+v*n] = c;
		}
	}
	priority_queue<pair<int,pair<int,int> >,vector< pair<int,pair<int,int> > >,
		PairComparator<int,pair<int,int> > > r;

	//put Node 0
	int cost = 0;
	int i=0;
	MST.push_back(pair<int,int>(i,i));
	DPG[i] = 0;
	while((int)MST.size() < n) {
		int ii=i*n;
		for (int j=0;j<n;++j) {
			if (E[ii+j] >= 0) {
				pair<int,int> add = std::make_pair(i,j);
				if (!inMST(MST,add.second)){
					r.push(std::pair<int,std::pair<int,int> >(E[ii+j],add));
				}
			}
		}
		pair<int,pair<int,int> > top;
		while (!r.empty()) {
			top = r.top();
			r.pop();
			if (!inMST(MST,top.second.second)){
				break;
			}
		}
		cost += top.first;
		MST.push_back(top.second);
		i = top.second.second;
		DPG[i] = DPG[top.second.first] + top.first;
		for(int j=0;j<n;++j){
			if (DPG[j] < 0)continue;
			if (E[i*n+j] < 0)continue;
			DPG[j] = std::min(DPG[j],DPG[i] + E[i*n+j]);
		}
	}
	for (int j=0;j<n;++j) {
		cout << j << " " <<  DPG[j] << endl;
	}
}

C++: #include <algorithm>
#include <iostream>
#include <list>
#include <vector>

class TNode
{
	std::list<std::pair<TNode*, int> > FNexts;
	int  FDistance;
public:
	TNode()
	: FDistance(-1)
	{
	}
	
	int GetDistance()const {return FDistance;}
	
	void Push(TNode* New, int Weight)
	{
		FNexts.push_back(std::make_pair(New, Weight));
	}
	
	void Visit(int Distance)
	{
		if(FDistance >= 0 && Distance > FDistance) return;
		FDistance = Distance;
		for(std::list<std::pair<TNode*, int> >::iterator It = FNexts.begin(); It != FNexts.end(); ++It){
			It->first->Visit(Distance + It->second);
		}
	}
};

class TGraph
{
	std::vector<TNode*> FNodes;
public:
	TGraph(int Count)
	: FNodes(Count)
	{
		for(int i = 0; i < Count; ++i){
			FNodes[i] = new TNode();
		}
	}
	
	~TGraph()
	{
		for(unsigned int i = 0; i < FNodes.size(); ++i){
			delete FNodes[i];
		}
	}
	
	void InputNode()
	{
		int Index;
		std::cin >> Index;
		int BranchCount;
		std::cin >> BranchCount;
		for(int i = 0; i < BranchCount; ++i){
			int Target, Weight;
			std::cin >> Target >> Weight;
			FNodes[Index]->Push(FNodes[Target], Weight);
		}
	}
	
	void BreathFirstSearch()
	{
		FNodes[0]->Visit(0);
	}
	
	int Distance(int Target)const
	{
		return FNodes[Target]->GetDistance();
	}
};

int main()
{
	int Count;
	std::cin >> Count;
	TGraph Graph(Count);
	for(int i = 0; i < Count; ++i){
		Graph.InputNode();
	}
	Graph.BreathFirstSearch();
	
	for(int i = 0; i < Count; ++i){
		std::cout << i << " " << Graph.Distance(i) << std::endl;
	}
	return 0;
}