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 <functional>
#include <string.h>

using namespace std;
static const int INF = 2e9;
static const int SIZE = 10001;
typedef pair<int, int> P;
struct edge
{
	int to;
	int cost;
};

int d[SIZE];
vector<edge> G[SIZE];

void solve()
{
	int n;
	cin >> n;
	for (int i = 0; i < n; ++i)
	{
		int u, k;
		cin >> u >> k;
		for (int j = 0; j < k; ++j)
		{
			int to, cost;
			scanf("%d %d", &to, &cost);
//			cin >> to >> cost;
			edge e1;
			e1.to = to;
			e1.cost = cost;
			G[u].push_back(e1);
		}
	}
	for (int i = 0; i < SIZE; ++i)
	{
		d[i] = INF;
	}
	d[0] = 0;
	priority_queue<P, vector<P>, greater<P> > pque;
	pque.push(P(0, 0));
	while (!pque.empty())
	{
		P p = pque.top();
		pque.pop();
		int v = p.second;
		for (int i = 0; i < G[v].size(); ++i)
		{
			edge e = G[v][i];
			if (d[e.to] > d[v] + e.cost)
			{
				d[e.to] = d[v] + e.cost;
				pque.push(P(d[e.to], e.to));
			}
		}
	}
	for (int i = 0; i < n; ++i)
	{
		printf("%d %d\n", i, d[i]);
//		cout << i << " " << d[i] << endl;
	}
}

int main()
{
	solve();
	return(0);
}

C++: #include <stdio.h>
#include <iostream>
#include <queue>
using namespace std;

#define NIL -1
#define INF 100000000
#define WHITE 1
#define GREY 2
#define BLACK 3
#define N_MAX 100

int G[N_MAX][N_MAX];
int V[N_MAX];
int V_value[N_MAX];

void init(){
    for(int i = 0; i < N_MAX; i++){
        V[i] = WHITE;
        V_value[i] = INF;
    }

    for(int i = 0; i < N_MAX; i++){
        for(int j = 0; j < N_MAX; j++){
            G[i][j] = NIL;
        }
    }
}

int main(void){
    init();
    int n;
    scanf("%d\n", &n);

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

    priority_queue<pair<int, int>> PQ;

    V[0] = BLACK;
    V_value[0] = 0;
    int new_node = 0;
    
    while(1){
        for(int i = 0; i < n; i++){
            if(G[new_node][i] != NIL && V[i] == WHITE){
                V_value[i] = min(V_value[i], V_value[new_node] + G[new_node][i]);
                PQ.push(make_pair(V_value[i] * (-1), i));
            }
        }

        int min_value;
        int min_index = NIL;
        while(!PQ.empty()){
            pair<int, int> p = PQ.top(); PQ.pop();
            if(p.first * (-1) == V_value[p.second])
                min_value = p.first * (-1);
                min_index = p.second;
                break;
        }

        if(min_index == NIL)
            break;

        new_node = min_index;
        V[new_node] = BLACK;
        V_value[new_node] = min_value;
    }
    
    for(int i = 0; i < n; i++){
        printf("%d %d\n", i, V_value[i]);
    }

    return 0;
}

C++: #include <iostream>
#include <utility>
#include <queue>
#include <limits>

using namespace std;

static const int MAX=10000;
static const int INF=numeric_limits<int>::max();

int n,d[MAX];
vector<pair<int,int> > list[MAX];

void dijkstra(){
  //initialize as min-Heap
  priority_queue<pair<int,int>,vector<pair<int,int> >,greater<pair<int,int> > > PQ;
  bool visited[n];
  for(int i=0;i<n;i++){
    visited[i]=false;
    d[i]=INF;
  }
  d[0]=0;
  PQ.push(make_pair(0,0));
  while(!PQ.empty()){
    pair<int,int> f=PQ.top(); PQ.pop();
    int u=f.second;
    visited[u]=true;

    //if(d[u]>f.first) continue;

    for(int i=0;i<list[u].size();i++){
      int v=list[u][i].first;
      if(visited[v]==false && d[v]>d[u]+list[u][i].second){
        d[v]=d[u]+list[u][i].second;
        PQ.push(make_pair(d[v],v));
      }
    }
  }
}

int main(){
  cin >> n;
  for(int i=0;i<n;i++){
    int u,k; cin >> u >> k;
    for(int j=0;j<k;j++){
      int v,c; cin >> v >> c;
      list[u].push_back(make_pair(v,c));
    }
  }
  dijkstra();
  for(int i=0;i<n;i++)
    cout << i << " " << d[i] << endl;
}

C++: #include <bits/stdc++.h>
using namespace std;
typedef long long ll;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
const ll INF = 1LL << 60;
const int MAX = 1000000010;
const ll MOD = 1000000007;

int main() {
    int N; cin >> N;
    vector<vector<pair<int, int>>> G(N);
    for (int i = 0; i < N; i++) {
        int u, k; cin >> u >> k;
        for (int j = 0; j < k; j++) {
            int v, c; cin >> v >> c;
            G[u].push_back(make_pair(v, c));
        }
    }
    vector<int> d(N, MAX);
    vector<bool> checked(N, false);
    priority_queue<pair<int, int>> pq;
    d[0] = 0;
    pq.push(make_pair(0, 0));

    while (!pq.empty()) {
        auto p = pq.top();
        pq.pop();
        int v = p.second;
        
        if (d[v] < p.first * (-1)) continue;
        checked[v] = true;


        for (auto np : G[v]) {
            int nv = np.first;
            if (checked[nv]) continue;

            if (chmin(d[nv], d[v] + np.second)) pq.push(make_pair(d[nv] * (-1), nv));
        }
    }

    for (int v = 0; v < N; v++) {
        cout << v << " " << d[v] << "\n";
    }
    return 0;
}