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 <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <string>
#include <vector>

// Acknowledgement: Special thanks to kyomukyomupurin, who developed this
// template.
template <class T, class U>
std::ostream& operator<<(std::ostream& os, const std::pair<T, U>& p) {
  return os << '(' << p.first << ", " << p.second << ')';
}

template <class T>
std::ostream& operator<<(std::ostream& os, const std::vector<T>& vec) {
  int n = 0;
  for (auto e : vec) os << (n++ ? ", " : "{") << e;
  return os << (n ? "}" : "{}");
}

template <class T>
std::ostream& operator<<(std::ostream& os, const std::set<T>& st) {
  int n = 0;
  for (auto e : st) os << (n++ ? ", " : "{") << e;
  return os << (n ? "}" : "{}");
}

template <class T, class U>
std::ostream& operator<<(std::ostream& os, const std::map<T, U>& mp) {
  int n = 0;
  for (auto e : mp) os << (n++ ? ", " : "{") << e;
  return os << (n ? "}" : "{}");
}

template <class T>
std::istream& operator>>(std::istream& is, std::vector<T>& vec) {
  for (T& e : vec) is >> e;
  return is;
}

#ifdef LOCAL
#define debug(...) \
  std::cerr << "[" << #__VA_ARGS__ << "]: ", debug_out(__VA_ARGS__)
#else
#define debug(...)
#endif

void debug_out() { std::cerr << '\n'; }

template <class Head, class... Tail>
void debug_out(Head&& head, Tail&&... tail) {
  std::cerr << head;
  if (sizeof...(Tail) != 0) std::cerr << ", ";
  debug_out(std::forward<Tail>(tail)...);
}
using namespace std;
using int64 = long long;

const int VERY_LARGE_NUM = 1e6;
vector<pair<int, int>> G[VERY_LARGE_NUM];

void dijkstra(int start_node_id, vector<int>& color, vector<int>& d) {
  d[start_node_id] = 0;
  color[start_node_id] = 1;
  priority_queue<pair<int, int>, vector<pair<int, int>>,
                 greater<pair<int, int>>>
      PQ;
  PQ.push(make_pair(start_node_id, 0));
  while (!PQ.empty()) {
    pair<int, int> min_node = PQ.top();
    PQ.pop();
    int u = min_node.second;
    color[u] = 2;
    if (d[u] < min_node.first) continue;
    for (int i = 0; i < G[u].size(); i++) {
      int node_id = G[u][i].second;
      int weight = G[u][i].first;
      if (color[node_id] != 2) {
        if (d[node_id] > d[u] + weight) {
          d[node_id] = d[u] + weight;
          color[node_id] = 1;
          PQ.push(make_pair(d[node_id], node_id));
        }
      }
    }
  }
}

int main() {
  int n, u, k, c, v;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> u >> k;
    for (int j = 0; j < k; j++) {
      cin >> v >> c;
      G[u].push_back(make_pair(c, v));
    }
  }
  debug(G);
  vector<int> color(n);
  vector<int> d(n, VERY_LARGE_NUM);
  dijkstra(0, color, d);
  for (int i = 0; i < n; i++) {
    cout << i << ' ' << d[i] << endl;
  }
  return 0;
}

C++: //
//  main.cpp
//
//
//  Created by ???????????? on 2017/10/23.
//  Copyright ?? 2017 ????????????. All rights reserved.
//

#include <iostream>
#include <stdio.h>
#include <queue>
#include <algorithm>


#define n_max 100
#define WHITE 0
#define GRAY 1
#define BLACK 2
#define INFTY 1<<21

using namespace std;

int n, M[n_max][n_max], color[n_max], d[n_max], p[n_max];

void init(){
    int i, j, id, num, node;
    scanf("%d", &n);
    for(i = 0; i < n; i++){
        for(j = 0; j < n; j++){
            M[i][j] = INFTY;
        }
    }
    
    
    for(i = 0; i < n; i++){
        scanf("%d %d", &id, &num);
        for(j = 0; j < num; j++){
            scanf("%d", &node);
            scanf("%d", &M[id][node]);
        }
        color[i] = WHITE;
        d[i] = INFTY;
    }
}

void dijkstra(){
    //initializing
    d[0] = 0;
    p[0] = -1;
    
    priority_queue<pair<int, int>> PQ;
    
    PQ.push(make_pair(0, 0));
    
    int u;
    while(!PQ.empty()){
        int mincost = INFTY;
        //first weight, second idx
        pair<int, int> f= PQ.top(); PQ.pop();
        u = f.second;
        color[u] = BLACK;
        
        if(d[u] < f.first*(-1)) continue;
        
        for(int v = 0; v < n; v++){
            if((color[v] != BLACK) && (M[u][v] != INFTY)){
                if((d[u] + M[u][v]) < d[v]){
                    d[v] = M[u][v] + d[u];
//                    p[v] = u;
                    PQ.push(make_pair(d[v]*(-1), v));
                    color[v] = GRAY;
                }
            }
        }
    }
    for(int i = 0; i < n; i++){
        cout<<i<<" "<<d[i]<<endl;
    }
}

int main(int argc, const char * argv[]) {
    init();
    dijkstra();
    //    std::cout << "Hello, World!\n";
    return 0;
}