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>
using namespace std;
#define M 1000000007
#define ff first.first
#define fs first.second
#define sf second.first
#define ss second.second
typedef pair<int,int> P;
typedef pair<P,P> PP;
int main(void)
{
	int i,j,k,u,n,flg[10001],v,c,sum,ky[10001],t,min,g;
	PP ke[10001];
	scanf("%d",&n);
	sum=0;
	for(i=0;i<n;i++) ky[i]=M,flg[i]=0;
	ky[0]=0;
	for(i=0;i<n;i++){
		scanf("%d%d",&u,&k);
		for(j=sum;j<k+sum;j++){
			scanf("%d%d",&v,&c);
			ke[j].ff=u , ke[j].fs=v , ke[j].sf=c;
		}
		sum+=k;
	}
	sort(ke,ke+sum);
	//for(i=0;i<sum;i++) printf("ke[%d].ff=%d ke[%d].fs=%d ke[%d].sf=%d\n",i,ke[i].ff,i,ke[i].fs,i,ke[i].sf);
	for(i=0;i<sum;i++){
		min=M;
		for(j=0;j<sum;j++) if(flg[j]==0&&min>ky[j]) g=j,min=j;
		flg[g]=1;
		if(min==M) break;
		for(j=0;j<sum;j++){
			t=ky[ke[j].ff]+ke[j].sf;
			if(ky[ke[j].fs]>t) g=j,ky[ke[j].fs]=t;
		}
	}
	for(i=0;i<n;i++) printf("%d %d\n",i,ky[i]);
	return 0;
}