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;

#ifdef DEBUG_MODE
	#define DBG(n) n;
#else
	#define DBG(n) ;
#endif
#define REP(i,n) for(ll (i) = (0);(i) < (n);++i)
#define rep(i,s,g) for(ll (i) = (s);(i) < (g);++i)
#define rrep(i,s,g) for(ll (i) = (s);i >= (g);--(i))
#define PB push_back
#define MP make_pair
#define FI first
#define SE second
#define SHOW1d(v,n) {for(int W = 0;W < (n);W++)cerr << v[W] << ' ';cerr << endl << endl;}
#define SHOW2d(v,i,j) {for(int aaa = 0;aaa < i;aaa++){for(int bbb = 0;bbb < j;bbb++)cerr << v[aaa][bbb] << ' ';cerr << endl;}cerr << endl;}
#define ALL(v) v.begin(),v.end()
#define Decimal fixed<<setprecision(20)
#define INF 1000000000
#define MOD 1000000007

typedef long long ll;
typedef pair<ll,ll> P;
#define NODE 100001
#define INF 1000000000
vector<vector<pair<ll,ll> > > v(NODE);
int dist[NODE];
int dijkstra(int start){
	for(int i = 0;i < NODE;i++)dist[i] = INF;
	dist[start] = 0;
	priority_queue<P,vector<P>,greater<P> > pq;
	pq.push(make_pair(0,start));
	while(!pq.empty()){
		P now = pq.top();pq.pop();
		ll d = now.first;
		ll node = now.second;
		if(dist[node] < d)continue;
		for(int i = 0;i < v[node].size();i++){
			ll opp_n = v[node][i].first;
			ll opp_d = v[node][i].second;
			if(dist[opp_n] > d + opp_d){
				dist[opp_n] = d + opp_d;
				pq.push(make_pair(dist[opp_n],opp_n));
			}
		}
	}
}

int main(){
	int n;cin >> n;
	REP(i,n){
		int a,b;cin >> a >> b;
		REP(j,b){
			int x,y;cin >> x >> y;
			v[a].PB(MP(x,y));
		}
	}
	dijkstra(0);
	
	REP(i,n){
		cout << i << ' ' << dist[i] << endl;
	}
	
	return 0;
}

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

/* 大文字を小文字に変換 */
char tolower(char c) {return (c + 0x20);}
/* 小文字を大文字に変換 */
char toupr(char c) {return (c - 0x20);}

// if('A'<=s[i] && s[i]<='Z') s[i] += 'a'-'A';

/*
string s = "abcdefg"
s.substr(4) "efg"
s.substr(0,3) "abc"
s.substr(2,4) "cdef"
*/

static const int MAX = 10000;
static const int INFTY = (1<<20);   // pow(10,19);
static const int WHITE = 0;
static const int GRAY = 1;
static const int BLACK = 2;

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

void dijkstra(){
    priority_queue<pair<int, int> > PQ;
    int color[MAX], d[MAX];
    rep(i, n){
        d[i] = INFTY;
        color[i] = WHITE;
    }
    d[0] = 0; color[0] = GRAY;
    PQ.push(make_pair(0, 0));

    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;

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

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

    dijkstra();

    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];   // 重み付き有向グラフの隣接リスト表現

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;

        // 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;
                PQ.push(make_pair(d[v] * (-1), v));  // priority_queue はデフォルトで大きい値を優先するため -1 を掛ける
                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;
    int i, j;

    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;
}