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<cstdio>
#include<iostream>
#include<queue>
#include<algorithm>
#define Lens 10005
#define Inf 1<<22

using namespace std;
vector<pair<int, int> > adj[Lens];
int N;
char c[Lens];
int d[Lens];

void dijkstra()
{
	d[0] = 0;
	priority_queue<pair<int, int> > PQ;
	PQ.push(make_pair(0, 0));
	while (!PQ.empty())
	{
		pair<int, int> t = PQ.top();
		PQ.pop();
		int u = t.second;
		c[u] = 'b';
		if (d[u] < -t.first) continue;
		for (int i = 0; i < adj[u].size(); i++)
		{
			int tmp = adj[u][i].first;
			if (c[tmp] == 'w'&&d[tmp] > d[u] + adj[u][i].second)
			{
				d[tmp] = d[u] + adj[u][i].second;
				PQ.push(make_pair(-d[tmp],tmp));
				cout << tmp << "  " << d[tmp] << endl;
			}
		}

	}
}

int main()
{

	cin >> N;
	for (int i = 0; i < N; i++)
	{
		int k, n;
		cin >> k >> n;
		c[k] = 'w';
		d[k] = Inf;
		for (int j = 0; j < n; j++)
		{
			int v, tw;
			cin >> v >> tw;
			adj[k].push_back(make_pair(v, tw));
		}

	}
	dijkstra();
	for (int i = 0; i < N; i++)
	{
		cout << i << ' ' << d[i] << endl;;
	}
	return 0;
}

C++: #include<iostream>
#include<algorithm>
#include<queue>
#include<vector>
#include<utility>
#include<limits>
using namespace std;
typedef pair<int, int> Edge;
int main()
{
	int n; cin >> n;
	vector< vector< Edge > > lists;

	for (int i = 0; i < n; i++)
	{
		vector<Edge> list;
		int u, k;
		cin >> u >> k;
		for (int j = 0; j < k; j++)
		{
			Edge edge;
			cin >> edge.second >> edge.first;
			list.push_back(edge);
		}
		lists.push_back(list);
	}

	vector<int> costs(n, -1);
	costs[0] = 0;
	priority_queue<Edge> queue;
	queue.push(Edge(0, 0));

	while (!queue.empty())
	{
		Edge edge = queue.top(); queue.pop();
		int dest = edge.second;
		int cost = edge.first;
		if (costs[dest]<cost)continue;
		for (Edge next : lists[dest])
		{
			next.first += cost;
			if (costs[next.second] > next.first||costs[next.second]==-1)
			{
				costs[next.second] = next.first;
				queue.push(next);
			}
		}
	}
	for (int i = 0; i < n; i++)
		cout << i << " " << costs[i] << endl;

	char c;
	cin >> c;

	return 0;
}

C++: #include <bits/stdc++.h>
using namespace std;

#define rep(i, a, b) for (int i = (a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (a); i >= (int)(b); i--)
#define all(x) (x).begin(), (x).end()
using i32 = int32_t;
using i64 = int64_t;
using f32 = float;
using f64 = double;
using P   = pair<int, int>;

template <class T>
bool chmin(T& a, T b) {
    if (a > b) {
        a = b;
        return true;
    } else {
        return false;
    }
}
template <class T>
bool chmax(T& a, T b) {
    if (a < b) {
        a = b;
        return true;
    } else {
        return false;
    }
}

template <class T>
void dump_vec(const vector<T>& v) {
    auto len = v.size();
    rep(i, 0, len) {
        cout << v[i] << (i == (int)len - 1 ? "\n" : " ");
    }
}

struct FastIO {
    FastIO() {
        cin.tie(0);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(20);
    }
} FASTIO;

//---------------------------------------------------------------------------------------------------

struct Edge {
    int from, to;
    i64 cost;
    Edge() {}
    Edge(int t, i64 c) : from(-1), to(t), cost(c) {}
    Edge(int f, int t, i64 c) : from(f), to(t), cost(c) {}

    bool operator<(const Edge& r) const {
        return cost < r.cost;
    }
    bool operator>(const Edge& r) const {
        return cost > r.cost;
    }
};

using Vertex = vector<Edge>;
using Graph  = vector<Vertex>;

// 無向
void link(Graph& g, int from, int to, int cost = 1) {
    g[from].push_back(Edge(from, to, cost));
    g[to].push_back(Edge(to, from, cost));
    return;
}

// 有向
void connect(Graph& g, int from, int to, int cost = 1) {
    g[from].push_back(Edge(from, to, cost));
    return;
}

vector<i64> dijkstra(const Graph& g, int start) {
    const auto inf = numeric_limits<i64>::max();
    vector<i64> dist(g.size(), inf);

    using Pi = pair<i64, int>;
    priority_queue<Pi, vector<Pi>, greater<Pi>> que;
    dist[start] = 0;
    que.push(make_pair(0, 0));
    while (!que.empty()) {
        const auto e    = que.top();
        const auto cost = e.first;
        const auto from = e.second;
        que.pop();
        if (dist[from] < cost) continue;

        for (const auto& e : g[from]) {
            const auto next_cost = e.cost + cost;
            if (chmin(dist[e.to], next_cost)) {
                que.push(make_pair(next_cost, e.to));
            }
        }
    }

    return dist;
}

//---------------------------------------------------------------------------------------------------

signed main() {
    int N;
    cin >> N;
    Graph G(N);
    rep(i, 0, N) {
        int u, k;
        cin >> u >> k;
        rep(j, 0, k) {
            int v, c;
            cin >> v >> c;
            connect(G, u, v, c);
        }
    }
    auto dist = dijkstra(G, 0);
    rep(i, 0, N) {
        cout << i << " " << dist[i] << "\n";
    }
}