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 <algorithm>
#include <queue>
using namespace std;

static const int MAX = 10000;
static const int INFTY = (1<<21);
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<n; j++){
            cin >> v >> c;
            adj[u].push_back(make_pair(v, c));
        }
    }
    
    dijkstra();
    
    return 0;
}

C++: #include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)

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];

// int prim() {
//    int u, minv;
//    int d[MAX], p[MAX], color[MAX];

//    // 初期化
//    rep(i, n) {
//       d[i] = INFTY;
//       p[i] = -1;
//       color[i] = WHITE;
//    }

//    d[0] = 0;

//    while(1) {
//       minv = INFTY;
//       u = -1;

//       rep(i, n){
//          if (minv > d[i] && color[i] != BLACK) {
//             u = i;
//             minv = d[i];
//          }
//       }
//       if(u == -1) break;
//       // uの決定
//       color[u] = BLACK;

//       rep(v, n) {
//          if(color[v] != BLACK && M[u][v] != INFTY) {
//             if(d[v] > M[u][v]) {
//                d[v] = M[u][v];
//                p[v] = u;
//                color[v] = GRAY;
//             }
//          }
//       }
//    }
//    int sum = 0;
//    rep(i, n) {
//       if(p[i] != -1) sum += M[i][p[i]];
//    }
//    return sum;
// }

// void dijkstra() {
//    int minv;
//    int d[MAX], color[MAX];

//    // 初期化
//    rep(i, n) {
//       d[i] = INFTY;
//       color[i] = WHITE;
//    }

//    d[0] = 0;
//    color[0] = GRAY;

//    while(true) {
//       minv = INFTY;
//       int u = -1;
//       rep(i, n) {
//          if(minv > d[i] && color[i] != BLACK) {
//             u = i;
//             minv = d[i];
//          }
//       }
//       if (u == -1) break;

//       // 最も小さいコストのuが決まる 初回は必ず0になる
//       color[u] = BLACK;

//       rep(v, n) {
//          // 0 ~ n-1の頂点が未訪問かつuとの経路がある場合
//          if(color[v] != BLACK && M[u][v] != INFTY) {
//             // 頂点uを通った方が目的地に近い場合
//             if (d[v] > d[u] + M[u][v]) {
//                d[v] = d[u] + M[u][v];
//                color[v] = GRAY;
//             }
//          }
//       }
//    }

//    rep(i, n) {
//       cout << i << " " << (d[i] == INFTY ? -1 : d[i]) << endl;
//    }
// }

void dijkstra() {
   priority_queue< pair<int, int> > PQ;
   int color[MAX];
   int d[MAX];

   rep(i, n) {
      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;

      rep(j, adj[u].size()) {
         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;
         }
      }
   }
   rep(i, n) {
      cout << i << " " << (d[i] == INFTY ? -1 : d[i]) << endl;
   }
}


int main(){
   cin >> n;
   int k, c, u, v;
   rep(i, n) {
      cin >> u >> k;
      rep(j, k){
         // v は頂点 cはコスト
         cin >> v >> c;
         adj[u].push_back(make_pair(v, c));
      }
   }

   dijkstra();

   return 0;
}