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 rep(i,n) for(int i=0;i<(n);i++)

const long long INFF = 1e18;

const int MAX_N = 11000;
using TYPE = long long; // ?????¢???????????\??????
vector<pair<int, TYPE> > G[MAX_N];

vector<TYPE> A_star(int start){
	vector<TYPE> dist(MAX_N, INFF);
	dist[start] = 0;//dist[i] :=???start->i?????§??????????????¢
	priority_queue<pair<TYPE, int>, vector<pair<TYPE, int> >, greater<pair<TYPE, int> > >  que;
	que.push(make_pair(1, start));
	while(!que.empty()){
		TYPE cost; int u;//????????§???????????£????????? ?????¨?????????
		cost = que.top().first, u = que.top().second;
		que.pop();
		// if(dist[u] < cost) continue;
		for (auto tmp : G[u]){
			int v = tmp.first; TYPE time = tmp.second;//??£??\???????????? ?????????????????§????????????
			if(dist[v] > dist[u] + time){//u->v
				dist[v] = dist[u] + time;
				TYPE h = 1; // ??´???????????§?????¨??????
				// printf("%f\n", h);
				que.push(make_pair(dist[v] + h, v));
			}
		}
	}
	return dist;
}

int main(void) {
	int n; cin >> n;
	rep(q, n) {
		int u, k; cin >> u >> k;
		vector<int> v(k); vector<long long> c(k);
		rep(i, k) cin >> v[i] >> c[i];
		rep(i, k) G[u].push_back(make_pair(v[i], c[i]));
	}
	auto dist = A_star(0);
	rep(i, n) printf("%d %d\n", i, dist[i]);
	return 0;
}

C++: #include <stdio.h>
#include <cmath>
#include <algorithm>
#include <stack>
#include <queue>
#include <vector>
typedef long long int ll;

#define BIG_NUM 2000000000

using namespace std;

struct Node{

	Node(int arg_to,int arg_cost){
		to = arg_to;
		cost = arg_cost;
	}
	bool operator<(const struct Node &arg) const{
			return cost > arg.cost;
	};

	int to,cost;
};

int main(){

	int N;
	scanf("%d",&N);

	int** distance = new int*[N];

	for(int i = 0; i < N; i++){
		distance[i] = new int[N];
		for(int k = 0; k < N; k++)distance[i][k] = BIG_NUM;
	}

	int node,num,to,cost,D[N];;

	for(int loop = 0; loop < N; loop++){
		scanf("%d",&node);
		scanf("%d",&num);
		for(int i = 0; i < num; i++){
			scanf("%d %d",&to,&cost);
			distance[node][to] = cost;
			distance[to][node] = cost;
		}
		D[loop] = BIG_NUM;
	}

	D[0] = 0;
	distance[0][0] = 0;

	bool visited[N];
	for(int i = 1; i < N; i++)visited[i] = false;
	visited[0] = true;

	priority_queue<Node> Q;

	for(int i = 1; i < N; i++){
		if(distance[0][i] != BIG_NUM){
			D[i] = distance[0][i];
			Q.push(Node(i,distance[0][i]));
		}
	}

	int min_index;

	while(!Q.empty()){
		if(visited[Q.top().to] == false){ //Q???BIG_NUM????????£?????????????????¨??????????????§???BIG_NUM??¨??????????????????
			min_index = Q.top().to;
			Q.pop();
		}else{
			Q.pop();
			continue;
		}

		visited[min_index] = true;

		for(int i = 1; i < N; i++){
			if(distance[min_index][i] != BIG_NUM && D[i] > D[min_index]+distance[min_index][i]){
				D[i] = D[min_index]+distance[min_index][i];
				Q.push(Node(i,D[i]));
			}
		}
	}

	for(int i = 0; i < N; i++)printf("%d %d\n",i,D[i]);

    return 0;
}

C++: #include<iostream>
#include<vector>
#include<queue>
#include<algorithm>
using namespace std;

int INF=1000000001;

typedef struct edge{
  int to;
  int cost;
}edge;

int N,E;
vector< edge > G[100000];
long long mincost[100000];

void dijkstra(){
  typedef pair<int,int> P;
  priority_queue<P,vector<P>,greater<P> > Q;
  for(int i=0;i<N;i++){
    mincost[i]=INF;
  }
  mincost[0]=0;
  Q.push(P(0,0));
  while(!Q.empty()){
    int pos=Q.top().second;
    int pos_cost=Q.top().first;
    Q.pop();
    if( mincost[pos] < pos_cost )continue;
    
    for(int i=0;i<(int)G[pos].size();i++){
      edge e=G[pos][i];
      if(mincost[e.to]>pos_cost+e.cost){
	mincost[e.to]=pos_cost+e.cost;
	Q.push(P(mincost[e.to],e.to));
      }
    }
  }
  for(int i=0;i<N;i++){
    cout<<i<<" "<<mincost[i]<<endl;
  }
}

int main(){
  cin>>N;
  for(int i=0;i<N;i++){
    int id,k;
    cin>>id>>k;
    for(int j=0;j<k;j++){
      edge e;
      cin>>e.to>>e.cost;
      G[id].push_back(e);
    }
  }

  dijkstra();
  
  return 0;
}