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 <algorithm>
#include <iostream>
#include <queue>
#include <vector>
using namespace std;
static const int NMAX = 10000;
#define INF (1 << 30)

int main() {
  int n;
  cin >> n;
  vector<pair<int, int>> adj[NMAX];

  for (int i = 0; i < n; i++) {
    int id, nn;
    cin >> id >> nn;
    for (int j = 0; j < nn; j++) {
      int to, weight;
      cin >> to >> weight;
      // use negative weights for priority_queue
      adj[id].push_back(make_pair(-weight, to));
    }
  }

  bool visited[n];
  int dist[n];
  for (int i = 0; i < n; i++) {
    visited[i] = false;
    dist[i] = -INF;
  }

  priority_queue<pair<int, int>> distQ;

  // add node 0
  for (int i = 0; i < adj[0].size(); i++) {
    distQ.push(adj[0][i]);
    int weight = adj[0][i].first;
    int id = adj[0][i].second;
    dist[id] = weight;
  }
  visited[0] = true;

  while (!distQ.empty()) {
    // find nearest node
    int minnode = distQ.top().second;
    distQ.pop();

    // add node
    visited[minnode] = true;

    // update dist
    for (int i = 0; i < adj[minnode].size(); i++) {
      int weight = adj[minnode][i].first;
      int id = adj[minnode][i].second;

      if (visited[id] == false) {
        int newWeight = dist[minnode] + weight;
        if (-newWeight < -dist[id]) {
          distQ.push(make_pair(newWeight, id));
          dist[id] = newWeight;
        }
      }
    }
  }

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

C++: #include<iostream>
#define INF 1<<30
using std::cin;
using std::cout;
using std::endl;
typedef struct { int vertex, cost; } pair;
pair pqueue[500000], graph[10000][10001];
int mincost[10000], size;
void fswap(pair *x, pair *y) {
  pair tmp;
  tmp = *x;
  *x = *y;
  *y = tmp;
}
void maxheap(int x) {
  int left = 2 * x, right = 2 * x + 1, minimum = x;
  if (left <= size && pqueue[left].cost<pqueue[x].cost) minimum = left;
  if (right <= size && pqueue[right].cost<pqueue[minimum].cost) minimum = right;
  if (minimum != x) {
    fswap(&pqueue[x], &pqueue[minimum]);
    maxheap(minimum);
  }
}
int extract() {
  while (1) {
    pair x = pqueue[1];
    pqueue[1] = pqueue[size--];
    maxheap(1);
    if (mincost[x.vertex] == INF) {
      mincost[x.vertex] = x.cost;
      return x.vertex;
    }
    if (size <= 0) return INF;
  }
}
void insert(pair x) {
  pqueue[++size] = x;
  int cur = size;
  while (cur != 1 && pqueue[cur].cost<pqueue[cur / 2].cost) {
    fswap(&pqueue[cur], &pqueue[cur / 2]);
    cur /= 2;
  }
}
int main() {
  int n; cin >> n;
  for (int i = 0; i < n; ++i) {
    int u, k; cin >> u >> k;
    for (int j = 0; j < k; ++j) cin >> graph[u][j].vertex >> graph[u][j].cost;
    graph[u][k].cost = INF;
  }
  for (int i = 0; i < n; ++i) mincost[i] = INF;
  insert({ 0,0 });
  while (1) {
    int x = extract();
    if (x == INF) break;
    for (int i = 0; graph[x][i].cost != INF; ++i)
      if(mincost[graph[x][i].vertex]==INF) insert({ graph[x][i].vertex,mincost[x] + graph[x][i].cost });
  }
  for (int i = 0; i < n; ++i) cout << i << " " << mincost[i] << endl;
  return 0;
}

C++: #include<bits/stdc++.h>
using namespace std;
#define INF 10000000

// O(ElogE)

// pq<pair> はfirstが大きい順に出てくるのですか？
// s:= 開始ノード  v:= 頂点数  adjlist:= 隣接リスト (first:= コスト   second:= 行先)
vector<int> dijk(int s, int v, vector<vector<pair<int, int> > > adjlist){
    
    priority_queue <pair<int, int> > wait;
    vector<int> result(v, INF);

    //スタート地点を追加
    result[s] = 0;
    wait.push(make_pair(0, s));

    //ダイクストラ本体
    while(!wait.empty()){    //waitが空になるまで

        int nowpoint = wait.top().second;
        int nowcost = -wait.top().first;
        wait.pop();

        if(result[nowpoint] < nowcost) continue;


        //今いる頂点と隣接しているすべての頂点をなめる
        for(int i = 0; i < adjlist[nowpoint].size(); i++){

            int nextpoint = adjlist[nowpoint][i].second;
            int nextcost = nowcost + adjlist[nowpoint][i].first;
            //現時点より安く到達できそうであれば、結果を更新して優先度付きキューに格納
            if(result[nextpoint] > nextcost){
                result[nextpoint] = nextcost;
                wait.push(make_pair(-nextcost, nextpoint));
            }
        }
    }
    
    return result;         //結果列を返す
}

int main(){

    int V; cin >> V;
    vector<vector<pair<int, int> > > adjlist(V);      //first := コスト　second := 行先

    //入力
    for(int i = 0; i < V; i++){
        int gomi; cin >> gomi;
        int k; cin >> k;
        for(int j = 0; j < k; j++){
            int v, c; cin >> v >> c;           // a ,b 間に コスト c の辺がある
            adjlist[i].push_back(make_pair(c, v));
        }     
    }

    vector<int> result(V);
    result = dijk(0, V, adjlist);
    //cout << result[G] << endl;

    for(int i = 0; i < V; i++){
        cout << i << " " << result[i] << endl;
    }
    return 0;
}