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;

using ll = long long;
using ld = long double;
using P = pair<int, int>;
constexpr ld EPS = 1e-12;
constexpr int INF = numeric_limits<int>::max() / 2;
constexpr int MOD = 1e9 + 7;

template <typename T>
void printv(const vector<T> &v)
{
    int sz = v.size();
    for (int i = 0; i < sz; i++)
    {
        cout << v[i] << " \n"[i == sz - 1];
    }
}

struct UnionFind
{
    vector<int> data;
    UnionFind(int size) : data(size, -1) {}
    bool unite(int x, int y)
    {
        x = root(x);
        y = root(y);
        if (x != y)
        {
            if (data[y] < data[x])
                swap(x, y);
            data[x] += data[y];
            data[y] = x;
        }
        return x != y;
    }
    bool find(int x, int y)
    {
        return root(x) == root(y);
    }
    int root(int x)
    {
        return data[x] < 0 ? x : data[x] = root(data[x]);
    }
    int size(int x)
    {
        return -data[root(x)];
    }
};

struct Edge
{
    int from, to, cost;
    Edge(int from, int to, int cost) : from(from), to(to), cost(cost) {}
};

typedef vector<Edge> Edges;
typedef vector<Edges> Graph;

bool operator<(const Edge &e, const Edge &f)
{
    return e.cost > f.cost;
}

vector<int> dijkstra(const Graph &g, int s)
{
    vector<int> d(g.size(), INF);
    d[s] = 0;
    priority_queue<P, vector<P>, greater<P>> que;
    que.push(P(0, s)); // P(dis, pos)
    while (!que.empty())
    {
        int dist = que.top().first;
        int v = que.top().second;
        que.pop();
        if (d[v] < dist)
            continue;
        for (const auto &e : g[v])
        {
            if (d[e.to] <= d[v] + e.cost)
                continue;
            d[e.to] = d[v] + e.cost;
            que.push(P(d[e.to], e.to));
        }
    }
    return d;
}
int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);

    int n;
    cin >> n;
    Graph 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(Edge{u, v, c});
        }
    }
    vector<int> res = dijkstra(g, 0);
    for (int i = 0; i < n; i++)
        cout << i << " " << res[i] << endl;
}

C++: #include <iostream>
#include <algorithm>
#include <queue>
 using namespace std;
 static const int WHITE = 0;
 static const int GRAY = 1;
 static const int BLACK =2;
 static const int MAX = 10000;
 static const int INFTY = (1<<20);
 
 int n;
 vector<pair<int,int> >adj[MAX];
 
 void dij(){
 	priority_queue<pair<int,int> >PQ;
 	int color[MAX];
 	int d[MAX];
 	for(int i=0;i<n;i++){
 		color[i] = WHITE;
 		d[i] = INFTY;
 	}
 	
 	d[0] = 0;
 	PQ.push(make_pair(0,0));
 	color[0] = GRAY;
 	while(!PQ.empty()){
 		pair<int ,int> f =PQ.top();
 		PQ.pop();
 		int u= f.second;
 		
 		color[u] = GRAY;
 		
 		if(d[u]<f.first*(-1)) continue;
 		
 		for(int j=0;j<adj[u].size();j++){
 			int v = adj[u][j].first;
 			if(color[v]==BLACK) continue;
 			if(d[v]>d[u]+adj[u][v].second){
 				d[v] = d[u]+adj[u][v].second;
 				PQ.push(make_pair(d[v]*(-1),v));
 				color[v] = GRAY;
 			}
 			
 		}
 	}
 	
 	for(int i=0;i<n;i++){
 		cout<<i<<" "<<(d[i]==INFTY?-1:d[i])<<endl; 
 	}
 }
 
 int main(){
 		cin>>n;
 	
 	int k,u,c,v;
 	for(int i=0;i<n;i++){
 		cin>>u>>k;
 		for(int j=0;j<k;j++){
 			cin>>c>>v;
 		adj[u].push_back(make_pair(c,v));
 		}
 	}
 	dij();
 	return 0;
 }

C++: #include <bits/stdc++.h>
using namespace std;
struct Graph{
  using seen_t=size_t; using ver_t=size_t; using edge_t=pair<ver_t,seen_t>;
  const seen_t NO=1e9;
  vector<seen_t> seen;
  vector<vector<edge_t>> edge;
  Graph(size_t n): seen(n,NO), edge(n) {}

  void search(ver_t v0){
    seen[v0]=0;
    priority_queue<pair<seen_t,ver_t>,vector<pair<seen_t,ver_t>>,greater<pair<seen_t,ver_t>>> que; que.push(make_pair(0,v0)); // dijkstra
    ver_t curv; seen_t alt;
    while(!que.empty()){
      curv=que.top().second; que.pop(); // dijkstra
      for(const auto& nextv:edge[curv]){
        alt=seen[curv]+nextv.second;
        if(seen[nextv.first]>alt && alt<NO){
          seen[nextv.first]=alt;
          que.push(make_pair(alt,nextv.first)); // dijkstra
        }
      }
    }
  }
};
ostream& operator<<(ostream& os, const Graph& x){
  for(size_t i=0; i<x.edge.size(); ++i){
    cout<<(i)<<' '<<x.seen[i]<<'\n';
  }
  return os;
}
int32_t main(){
  ios::sync_with_stdio(false); cin.tie(0);
  size_t n; cin>>n;
  Graph graph(n);
  size_t u,k,v,c;
  for(size_t i=0; i<n; ++i){
    cin>>u>>k;
    graph.edge[u].resize(k);
    for(size_t j=0; j<k; ++j){
      cin>>v>>c; graph.edge[u][j]=make_pair(v,c);
    }
  }
  graph.search(0);
  cout<<graph;
}