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<vector>
#include<queue>
#include<tuple>
#include<climits>
using namespace std;

int main(){
  priority_queue <tuple<int,int>,vector<tuple<int,int> >,greater<tuple<int,int> > > checkpoint;
  vector<vector<int> > path;
  vector<int> min_distance;
  int n;

  cin >> n;
  path.resize(n);
  for(int i=0;i<n;i++){
    path[i].resize(n);
    for(int j=0;j<n;j++){
      path[i][j]=INT_MAX;
    }
  }
  min_distance.resize(n);
  for(int i=0;i<n;i++){
    min_distance[i]=INT_MAX;
  }

  for(int i=0,from,to,cost,m;i<n;i++){
    cin >> from >> m;
    for(int j=0;j<m;j++){
      cin >> to >> cost;
      path[i][to]=cost;
    }
  }

  checkpoint.push(make_tuple(0,0));
  while(!checkpoint.empty()){
    int from=get<1>(checkpoint.top());
    int distance=get<0>(checkpoint.top());

    if(distance<min_distance[from]){
      min_distance[from]=distance;
      for(int i=0;i<n;i++){
        if(path[from][i]!=INT_MAX){
          checkpoint.push(make_tuple(path[from][i]+distance,i));
	}
      }
    }
    checkpoint.pop();
  }

  for(int i=0;i<n;i++){
    cout << i << " " << min_distance[i] << endl;
  }
}

C++: // ALDS1_12_B.cpp
// Graph II - Single Source Shortest Path I
#include <iostream>
#include <vector>
#include <algorithm>
#include <cstdio>
using namespace std;

struct Node {
    int v;
    int c;
    Node(int v, int c): v(v), c(c) {}
};

const int maxN = 100;
static const int WHITE = 0;
static const int GRAY = 1;
static const int BLACK = 2;
static const int INF = (1<<21);
vector<Node> G[maxN];
vector<int> dist(maxN, INF);
vector<int> p(maxN);
vector<int> color(maxN, WHITE);
int n;
int cnt = 0;
void dijkstra(int x)
{
    dist[x] = 0;
    p[x] = -1;
    while(++cnt != n) {
        int u = 0;
        int mindist = INF;
        for (int i = 0; i < n; i++) {
            if (color[i] != BLACK && dist[i] < mindist) {
                mindist = dist[i];
                u = i;
            }
        }

        for (int i = 0; i < G[u].size(); i++) {
            if (color[u] == BLACK) continue;
            int v = G[u][i].v;
            int c = G[u][i].c;
            if (dist[u] + c < dist[v]) {
                dist[v] = dist[u] + c;
                p[v] = u;
                color[v] = GRAY;
            }
        }
        color[u] = BLACK;
    }
}

int main()
{
    cin >> n;
    int u, k;
    int v, c;
    for (int i = 0; i < n; i++) {
        cin >> u >> k;
        for (int j = 0; j < k; j++) {
            cin >> v >> c;
            G[i].push_back(Node(v, c));
        }
    }
    dijkstra(0);
    for (int i = 0; i < n; i++) {
        printf("%d %d\n", i, dist[i]);
    }
    return 0;
}

C++: #include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
//#define ll long long
template<class T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T> bool chmin(T &a, const T &b) { if (a>b) { a=b; return 1; } return 0; }
#define rep(i, n) REP(i, 0, n)
#define rep_rev(i, n) for (int (i) = (int)(n) - 1 ; (i) >= 0 ; --(i))
#define ALL(v) v.begin(), v.end()
#define MSG(a) cout << #a << " " << a << endl;
#define REP(i, x, n) for(int i = x; i < n; i++)
#define all(x) (x).begin(),(x).end()
ll t1,t2,t3;
const ll mod = 1000000007;
const int INF = 1e9;
const ll INFLONG = 1e18;

int main(){
  ll n;
  cin >> n;
  vector<ll> ans(n,INFLONG);
  vector<pair<ll,ll>> vec[n];
  ll u;
  ll k;
  rep(_,n){
    cin >> u >> k;
    rep(i,k){
      cin >> t1 >> t2;
      vec[u].emplace_back(make_pair(t2,t1)); //cost , node_num
    }
  }
  priority_queue<pair<ll,ll>> pq;
  ans[0] = 0;
  for(auto itr:vec[0]){
    pq.push(make_pair(-itr.first,itr.second)); //-cost
  }
  pair<ll,ll> pa;
  while(!pq.empty()){
    pa = pq.top();
    pq.pop();
    t1 = -pa.first; //cost
    t2 = pa.second;
    //cout << t1 << " " << t2 << endl;
    if(t1 < ans[t2]){
      ans[t2] = t1;
      for(auto itr:vec[t2]){
        pq.push(make_pair(-t1 - itr.first,itr.second));
      }
    }
  }
  rep(i,n){
    cout << i << " " << ans[i] << endl;
  }
}