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 <cstdio>
#include <vector>
#include <queue>
#include <utility>
#include <limits.h>

#define DIRECTED true //有向か無向か
#define ull unsigned long long
#define mp(X , Y) make_pair(X , Y)

using namespace std;

bool operator>(const pair<ull,int> a, const pair<ull,int> b){
    return a.first > b.first;
}

class dijkstra{
public:
    int num;
    vector<ull> dist;
    vector<int> prev;

    vector<vector<pair<int,ull>>> side; 

    dijkstra(){
    }

    dijkstra(int n){

        num = n;
        //0オリジンとの混合を避けるため+1する
        for(int i = 0; i < n + 1; i++){
            dist.push_back(ULONG_LONG_MAX);
            prev.push_back(-1);
            vector<pair<int,ull>> v;
            side.push_back(v);
        }
    }

    void reset(){
        dist.clear();
        prev.clear();

        for(int i = 0; i < num + 1; i++){
            dist.push_back(ULONG_LONG_MAX);
            prev.push_back(-1);

        }
    }

    void input(int f, int t,ull d){

        side[f].push_back(mp(t, d));
        if(!DIRECTED) side[t].push_back(mp(f,d));
    }

    void search(int start){
        
        dist[start] = 0;
        prev[start] = 0;

        priority_queue<pair<ull,int>, vector<pair<ull,int>>, greater<pair<ull,int>>> pq;
        pq.push(mp(0,start));

        while(!pq.empty()){
            
            ull d = pq.top().first;
            int s = pq.top().second;

            for(auto itr = side[s].begin(); itr != side[s].end(); itr++){

                ull tmp_d = (*itr).second;
                int to = (*itr).first; 

                if(dist[to] > d + tmp_d){
                    dist[to] = d + tmp_d;
                    prev[to] = s;
                    pq.push(mp(d + tmp_d,to));
                }
            }

            pq.pop();
        }
    }

    ull min_distance(int to){
        return dist[to];
    }

};

int main(){

    int n,u,k;

    cin >> n;

    dijkstra dijk;
    dijk = dijkstra(n);

    for(int i = 0; i < n; i++){
        scanf(" %d %d",&u,&k);
        for(int j = 0; j < k; j++){
            int v;
            ull c;

            scanf(" %d %llu",&v,&c);

            dijk.input(u,v,c);

        }
    }

    dijk.search(0);
    for(int i = 0; i < n; i++){
        cout << i << " " << dijk.min_distance(i) << endl;
    }
}