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 <bits/stdc++.h>
#define rep(i,n) for(int i=0;i<n;i++)
#define all(x) (x).begin(),(x).end()
using namespace std;
const int INF=1145141919,MOD=1e9+7;
const long long LINF=8931145141919364364,LMOD=998244353;
// const int dx[]={1,0,-1,0,1,1,-1,-1},dy[]={0,-1,0,1,1,-1,-1,1};

const int VMAX=100010;
int V,E,start,goal;
vector<pair<long long,int>> edge[VMAX];
long long dist[VMAX];
bool used[VMAX];

void dijkstra(){
    // 距離をLINFで初期化
    rep(to,VMAX) dist[to]=LINF;
    // 始点は0
    dist[start]=0;
    // フラグを下げる
    rep(v,VMAX) used[v]=false;
    // 優先度付きキュー:[距離,頂点]←距離の昇順
    priority_queue<pair<long long,int>,vector<pair<long long,int>>,greater<pair<long long,int>>> q;
    // 距離0,始点
    q.push({0,start});
    // dijkstra
    while(q.size()){
        // 取り出してd=距離,v=頂点
        pair<long long,int> p=q.top(); q.pop();
        long long d=p.first;
        int from=p.second;
        if(used[from]) continue;
        used[from]=true;
        // 頂点から出る辺すべてについて
        for(auto e:edge[from]){
            long long cost=e.first,to=e.second;
            // 短縮できるとき
            if(d+cost<dist[to]){
                dist[to]=d+cost;
                q.push({dist[to],to});
            }
        }
    }
}

int main(){
    cin>>V;
    rep(i,V){
        int u,k; cin>>u>>k;
        rep(j,k){
            int to,distance;
            cin>>to>>distance;
            edge[u].push_back({distance,to});
        }
    }
    start=0;
    dijkstra();
    rep(i,V){
        cout<<i<<" "<<dist[i]<<endl;
    }
    return 0;
}