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>
#include <list>
using namespace std;

class Node
{
private:
	list<int> next_node_list;
	list<int> next_weight_list;
public:
	Node();
	void AddNextNode(int id, int weight);
	void SetWeight(int weight);
	void DistributeWeight();
	int weight_from_0;
	bool check;
	int id;
};

Node::Node()
{
	weight_from_0 = -1;
	check = false;
}

Node *Node_list;

struct GreatNode
{
	bool operator()(const Node n1, const Node n2) const;
};
bool GreatNode::operator()(const Node n1, const Node n2) const
{
	return n1.weight_from_0 > n2.weight_from_0;
}
priority_queue<Node, vector<Node>, GreatNode > Q;

void Node::AddNextNode(int id, int weight)
{
	next_node_list.push_back(id);
	next_weight_list.push_back(weight);
}

void Node::SetWeight(int weight)
{
	if (weight_from_0 == -1 || weight < weight_from_0) {
		weight_from_0 = weight;
	}
}

void Node::DistributeWeight()
{
	check = true;
	list<int>::iterator itr2 = next_weight_list.begin();
	for(list<int>::iterator itr = next_node_list.begin(); itr != next_node_list.end(); itr++){	
		if (Node_list[*itr].check == false) {
			Node_list[*itr].SetWeight(weight_from_0 + *itr2);
			Q.push(Node_list[*itr]);
		}
		itr2++;
	}
	next_node_list.clear();
	next_weight_list.clear();
}

int main(void)
{
	//input
	int n;
	cin >> n;
	Node_list = new Node[n]();
	for (int i = 0; i < n; i++) {
		Node_list[i].id = i;
		int u, k;
		cin >> u >> k;
		for (int j = 0; j < k; j++) {
			int v, c;
			cin >> v >> c;
			Node_list[u].AddNextNode(v, c);
		}
	}

	//weight from 0 ?
	Node_list[0].weight_from_0 = 0;
	Node_list[0].DistributeWeight();
	while (!Q.empty()) {
		Node node = Q.top();
		Q.pop();
		Node_list[node.id].DistributeWeight();
	}

	//output
	for (int i = 0; i < n; i++) {
		cout << i << " " << Node_list[i].weight_from_0 << endl;
	}
	
	return 0;
}

C++: #include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for(int i=0; i<(n); i++)

#define NIL -1
#define WHITE 0
#define GRAY 1
#define BLACK 2
#define INF 1 << 21

//ダイクストラ法 優先度付きキューを用いた高速化
void dijkstra(vector<vector<pair<int, int> > > &graph, int n){

    priority_queue<pair<int, int> > PQ;
    vector<int> color(n, WHITE);
    vector<int> cost(n, INF);

    PQ.push(make_pair(0, 0));
    cost[0] = 0;
    color[0] = GRAY;

    while(!PQ.empty()){
        pair<int, int> f = PQ.top(); PQ.pop();
        int u = f.second;    //現在地

        color[u] = BLACK;

        if(cost[u] < f.first * (-1)) continue;

        rep(i, graph[u].size()){
            int v = graph[u][i].first;
            
            if(color[v] == BLACK) continue;

            if(cost[v] > cost[u] + graph[u][i].second){
                cost[v] = cost[u] + graph[u][i].second;
                PQ.push(make_pair(cost[v]*(-1), v));
                color[v] = GRAY;
            }
        }
    }

    rep(i, n){
        cout << i << " " << cost[i] << endl;
    }
}

int main() {

    int n;
    cin >> n;
    vector<vector<pair<int, int> > > graph(n);
    int k, c, u , v;
    rep(i, n){
        cin >> u >> k; //u 頂点  k 隣接リストの個数
        rep(j, k){
            cin >> v >> c;      //隣接リストの番号 //隣接リストの重み
            graph[i].push_back(make_pair(v, c));
        }
    }

    dijkstra(graph, n);

    return 0;
}

C++: #include <iostream>
#include <cstring>
#include <algorithm>
#include <vector>
#include <queue>
using namespace std;
#define fi first
#define se second
#define mkp make_pair
#define rep(i,n) for(int i=0; i<(n); ++i)
#define reps(i,f,n) for(int i=(f); i<=(n); ++i)
#define outl(x) cout << (x) << '\n'
#define FAST() cin.tie(0), ios::sync_with_stdio(false)
typedef pair<int,int> pii;
template<class A, class B>inline bool chmax(A &a, B b){return b>a ? a=b,1 : 0;}
template<class A, class B>inline bool chmin(A &a, B b){return b<a ? a=b,1 : 0;}
#define INF 0x3f3f3f3f

int N;
vector <pii> G[100005];
int mcos[100005];

void dijkstra(int s)
{
   priority_queue< pii, vector<pii>, greater<pii> > pq;
   pq.emplace( mkp(0,s) );
   memset( mcos, INF, sizeof(mcos) );
   mcos[s] = 0;

   while( !pq.empty() ){
      const pii tmp = pq.top(); pq.pop();
      if( mcos[tmp.se] < tmp.fi )continue;
      for( const auto& v: G[tmp.se] ){
         const int nc = v.fi + tmp.fi;
         if( chmin( mcos[v.se], nc ) )
            pq.emplace( mkp(nc, v.se) );
      }
   }
   return;
}

signed main()
{
   FAST();
   cin >> N;
   rep(i, N){
      int u, k, c, to;
      cin >> u >> k;
      while(k--){
         cin >> to >> c;
         G[i].emplace_back( mkp(c, to) );
      }
   }
   dijkstra(0);

   rep(i, N){
      cout << i << ' ' << mcos[i] << '\n';
   }
}