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 <utility>
#include <queue>
#define INF 10000000
#define MAX 10000
using namespace std;

// ====== Implement of Heap ======
int heap[2000000]={INF};
int eoh=1;

void minHeapify(int* A, int i){
  int h = eoh-1;
  int l = 2*i;
  int r = 2*i+1;
  int smallest;
  if ( l <= h && A[l] < A[i] )
    smallest = l;
  else
    smallest = i;

  if ( r<= h && A[r] < A[smallest])
    smallest = r;

  if (smallest != i){
    swap(A[i], A[smallest]);
    minHeapify(A, smallest);
  }
}

void insert(int v, int p=-1){
  if (p == -1){
    p = eoh++;
    heap[p] = v;
    insert(v, p);
    return;
  }
  if (p == 1)
    return;
  int parent = heap[p/2];
  if (parent < v)
    return;
  swap(heap[p/2], heap[p]);
  insert(v, p/2);
}

int del(void){
  if (eoh == 1)
    return -1;
  int res = heap[1];
  heap[1] = heap[eoh-1];
  eoh--;
  minHeapify(heap, 1);
  return res;
}
// ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 

// ====== Implement of List Structure ======
struct Node {
    int to, cost;
    struct Node * next;
};

typedef struct Node * NodePointer;

NodePointer NIL;

NodePointer makeNode(int to, int cost){
    NodePointer newNode = (NodePointer)malloc(sizeof(struct Node));
    newNode->to = to;
    newNode->cost = cost;
    newNode->next = NIL;
    return newNode;
}

NodePointer insert(NodePointer head, int to, int cost){
    NodePointer ite, newNode;
    for (ite=head;ite->next!=NIL;ite=ite->next);
    newNode = makeNode(to, cost);
    ite->next = newNode;
    return newNode;
}


// decl vals
int dist[MAX];

void dijkstraAlgorithm(NodePointer vertex[], int n){
  auto compare = [=](int i, int j){return dist[i] >= dist[j];};
  priority_queue<int, vector<int>,  decltype(compare)> searchQueue {compare}; 

  // Initialize of distance, previous and Push all of vectex to queue 
  dist[0] = 0;
  for (int i=0;i<n;i++){
    if (i!=0) dist[i] = INF;
    searchQueue.push(i);
  }

  while(!searchQueue.empty()){
    int current = searchQueue.top();
    NodePointer ite;
    searchQueue.pop();
    for (ite=vertex[current]->next;ite!=NIL;ite=ite->next){
      int alt = dist[current]+ite->cost;
      if ( dist[ite->to] > alt ){
        dist[ite->to] = alt;
        searchQueue.push(ite->to);
      }
    }
  }
}

int main(){
  NodePointer vertex[MAX];
  int i, n;
  cin >> n;
  NIL = makeNode(0, 0);
  for(i=0;i<n;++i) vertex[i] = makeNode(-1,INF);
  
  for (int i=0;i<n;++i){
    int id, k;
    scanf("%d%d", &id, &k);
    for (int j=0;j<k;++j){
      int node, cost;
      scanf("%d%d", &node, &cost);
      insert(vertex[id], node, cost);
    }
  }

  dijkstraAlgorithm(vertex, n);

  for (int i=0;i<n;++i){
    cout << i << " " << dist[i] << endl;
  }

  return 0;
}

C++: #include <stdio.h>
#include <cmath>
#include <algorithm>
#include <stack>
#include <queue>
#include <vector>
typedef long long int ll;

#define BIG_NUM 2000000000

using namespace std;

struct Node{

	Node(int arg_to,int arg_cost){
		to = arg_to;
		cost = arg_cost;
	}
	bool operator<(const struct Node &arg) const{
			return cost > arg.cost;
	};

	int to,cost;
};

int main(){

	int N;
	scanf("%d",&N);

	vector<Node> V[N];

	int node,num,to,cost,D[N];;

	for(int loop = 0; loop < N; loop++){
		scanf("%d",&node);
		scanf("%d",&num);
		for(int i = 0; i < num; i++){
			scanf("%d %d",&to,&cost);
			V[node].push_back(Node(to,cost));
		}
		D[loop] = BIG_NUM;
	}

	D[0] = 0;

	bool visited[N];
	for(int i = 1; i < N; i++)visited[i] = false;
	visited[0] = true;

	priority_queue<Node> Q;

	for(int i = 0; i < V[0].size(); i++){
		D[V[0][i].to] = V[0][i].cost;
		Q.push(Node(V[0][i].to,V[0][i].cost));
	}

	int min_index;

	while(!Q.empty()){
		if(Q.top().cost == D[Q.top().to]){
			min_index = Q.top().to;
			Q.pop();
		}else{
			Q.pop();
			continue;
		}

		for(int k = 0; k < V[min_index].size(); k++){ //min_index?????????????????´?????§????????¨??´??°??§??????????????§???min_index?????????????????¨?????????????????¢???
			if(D[V[min_index][k].to] > D[min_index] + V[min_index][k].cost){
				D[V[min_index][k].to] = D[min_index] + V[min_index][k].cost;
				Q.push(Node(V[min_index][k].to,D[V[min_index][k].to]));
			}
		}
	}

	for(int i = 0; i < N; i++)printf("%d %d\n",i,D[i]);

    return 0;
}