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 NIL -1
#define MAX (1 << 24)

struct Node {
	int dis = MAX;
	bool flag = false;
	vector<pair<int, int>> d;
};


void dijkstra(vector<Node>& u)
{
	priority_queue<pair<int, int>> PQ;
	u[0].dis = 0;
	PQ.push(make_pair(0, 0));

	while (!PQ.empty())
	{
		pair<int, int> f = PQ.top();
		PQ.pop();
		
		int mini = MAX;
		int n = f.second;
		u[n].flag = true;

		if (u[n].dis < f.first * (-1)) continue;		

		for (int i = 0; i < u[n].d.size(); i++)
		{
			int v = u[n].d[i].first;
			int s = u[n].d[i].second;
			if (u[v].flag) continue;
			if (u[n].dis + s < u[v].dis) {
				u[v].dis = u[n].dis + s;

				PQ.push(make_pair(u[v].dis * (-1), v));
			}
		}
	}
}

int main(void)
{
	int i, N, v, k, c, x;
	cin >> N;
	vector<Node> u(N);
	for (i = 0; i < N; i++)
	{
		cin >> v >> k;
		for (int j = 0; j < k; j++)
		{
			cin >> x >> c;
			u[v].d.push_back(make_pair(x, c));
		}
	}

	
	dijkstra(u);

	for (i = 0; i < N; i++) cout << i << " " << u[i].dis << endl;

	return 0;
}

C++: #include <bits/stdc++.h>

using namespace std;

int n;
typedef pair<int, int> P;
const int N = 1e5 + 10;
vector<P> G[N];
int dis[N];
bool vis[N];

void dijkstra() {
    memset(vis, false, sizeof(vis));
    for (int i = 0; i < n; i++) dis[i] = INT_MAX;
    priority_queue<P, vector<P>, greater<P>> heap;
    heap.push({0, 0});
    dis[0] = 0;

    while (!heap.empty()) {
        int u = heap.top().second, cost = heap.top().first;
        heap.pop();
        if (vis[u]) continue;
        vis[u] = true;
        for (int i = 0; i < G[u].size(); i++) {
            int v = G[u][i].second, len = G[u][i].first;
            if (!vis[v] && dis[u] + len < dis[v]) {
                dis[v] = dis[u] + len;
                heap.push({dis[v], v});
            }
        }
    }
}

int main() {
    cin >> n;
    for (int i = 0; i < n; i++) {
        int u, k;
        cin >> u >> k;
        int v, c;
        for (int j = 0; j < k; j++) {
            cin >> v >> c;
            G[u].push_back({c, v});
        }
    }

    dijkstra();

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

    return 0;
}

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

static const int MAX = 10000;
static const int INFTY = (1<<20);
static const int WHITE = 0;
static const int GRAY = 1;
static const int BLACK = 2;

int n;
vector<pair<int, int> >adj[MAX];

void dijkstra(){
  priority_queue<pair<int, int> >PQ;
  int color[MAX];
  int d[MAX];
  for(int i = 0; i < n;i++){
    d[i] = INFTY;
    color[i] = WHITE;
  }

  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] = BLACK;

    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][j].second){
        d[v] = d[u] + adj[u][j].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(){
  int k,u,v,c;

  cin >> n;
  for(int i = 0;i < n;i++){
    cin >> u >> k;
    for(int j = 0;j < k;j++){
      cin >> v >> c;
      adj[u].push_back(make_pair(v,c));
    }
  }

  dijkstra();

  return 0;
}

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

const int MAX = 10000;
const int INFINITY = 2 << 21;
int n;
int G[MAX][MAX];
int distances[MAX];
int states[MAX];

void dijkstra() {
  int id = 0;
  distances[id] = 0;

  while (1) {
    int min = INFINITY;

    for (int i = 0; i < n; i++) {
      if (states[i] == 0 && distances[i] < min) {
        min = distances[i];
        id = i;
      }
    }

    if (min == INFINITY) break;

    for (int i = 0; i < n; i++) {
      if (states[i] != 0 || G[id][i] == -1) continue;
      if (distances[id] + G[id][i] < distances[i]) {
        distances[i] = distances[id]+ G[id][i];
      }
    }

    states[id] = 1;
  }

  for (int i = 0; i < n; i++) {
    cout << i << " " << (distances[i] == INFINITY ? -1 : distances[i]) << endl;
  }
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  cin >> n;

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

  int u, k, v, c;
  for (int i = 0; i < n; i++) {
    distances[i] = INFINITY;
    states[i] = 0;
    cin >> u >> k;
    for (int j = 0; j < k; j++) {
      cin >> v >> c;
      G[i][v] = c;
    }
  }

  dijkstra();

  return 0;
}