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<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 << 21);

int n;
vector<pair<int, int> > adj[MAX]; //重み付き有向グラフの隣接リスト表現

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

    d[s] = 0;
    PQ.push(make_pair(0, s));
    color[s] = GRAY;

    while( !PQ.empty()){
        pair<int, int> f = PQ.top(); PQ.pop();
        int u = f.second;
        color[u] = BLACK;
/*
        //最小値を取り出し、それが最短でなければ無視
        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;
                //priority_queue　はデフォルトで大きい値を優先するため -1 をかける
                PQ.push(make_pair(d[v] * (-1), v)); //pqは一つ目の値でソートされるため、第一項に距離を持ってきている
                color[v] = GRAY;
            }
        }
    }

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

int main(){
    cin >> n;
    int u, k, v, c;

    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(0);

    return 0;
}

C++: #include <vector>
#include <iostream>
#include <algorithm>
#include <limits>
#include <queue>

using namespace std;
using graph = vector<vector<int>>;


struct edge {
    int src;
    int dst;
    int weight;

    edge(int src, int dst, int w) : src(src), dst(dst), weight(w) {}
};

bool operator < (const edge &a, const edge &b) {
  return a.weight > b.weight;
}


int main() {
    int n;
    cin >> n;

    graph G(n, vector<int>(n, -1));
    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][v] = c;
        }
    }

    // Dijkstra's algorithm (with pritority queue)
    vector<int> d(n, -1);
    vector<bool> visited(n, false);
    priority_queue<edge> Q;

    Q.push(edge(-1, 0, 0));
    while (!Q.empty()) {
        auto e = Q.top(); Q.pop();
        if (visited[e.dst])
            continue;
        d[e.dst] = e.weight;
        visited[e.dst] = true;

        int i = e.dst;
        int minw = numeric_limits<int>::max();
        for (int j = 0; j < n; ++j) {
            if (visited[j] || G[i][j] < 0)
                continue;
            int w = G[i][j] + d[i];
            if (w < minw) {
                minw = w;
                Q.push(edge(i, j, w));
            }
        }
    }

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

    return 0;
}

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

using namespace std;

typedef pair<int, int> P;

const int INF = 1 << 29;

int main() {
  int n;
  cin >> n;

  vector<vector<P>> edge(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;
      edge[u].push_back(P(c, v));
    }
  }

  vector<int> dist(n, INF);
  priority_queue<P, vector<P>, greater<P>> que;
  dist[0] = 0;
  que.push(P(0, 0));
  while (!que.empty()) {
    P p = que.top();
    que.pop();

    for (int i = 0; i < edge[p.second].size(); i++) {
      if (dist[edge[p.second][i].second] > p.first + edge[p.second][i].first) {
        dist[edge[p.second][i].second] = p.first + edge[p.second][i].first;
        que.push(
            P(p.first + edge[p.second][i].first, edge[p.second][i].second));
      }
    }
  }

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

  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 i,j;
  int d[MAX],color[MAX];

  for(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>a = PQ.top(); PQ.pop();

    int u = a.second;
    color[u] = BLACK;

    if(d[u] < a.first*(-1)) continue;

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

int main(){
  int i, j, k, u, v, c;

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

  dijkstra();

  return 0;
}