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 <vector>
#include <algorithm>
#include <queue>

using namespace std;

using Weight=int;
using DArray=vector<Weight>;
using DMatrix=vector<DArray>;

static const Weight INF=1<<29;

struct Edge {
    size_t src, dst;
    Weight weight;
    Edge() {}
    Edge(size_t src, size_t dst, Weight weight=1):
        src(src), dst(dst), weight(weight)
    {}
};

bool operator<(const Edge &e, const Edge &f) {
    if (e.weight != f.weight) {
        return e.weight > f.weight;
    } else {
        return e.src!=f.src? e.src<f.src : e.dst<f.dst;
    }
}

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

void join(Graph &g, size_t s, size_t d, Weight w=1) {
    // non-directed
    g[s].push_back(Edge(s, d, w));
    g[d].push_back(Edge(d, s, w));
}

void connect(Graph &g, size_t s, size_t d, Weight w=1) {
    // directed
    g[s].push_back(Edge(s, d, w));
}

template <class T>
using lp_queue=priority_queue<T, deque<T>, greater<T>>;

vector<Weight> shortest_distance(const Graph &g, size_t s) {
    /* Dijkstra */
    size_t V=g.size();
    vector<Weight> d(V, INF); d[s]=0;

    lp_queue<pair<Weight, size_t>> q; q.push(make_pair(0, s));
    while (!q.empty()) {
        pair<Weight, size_t> p=q.top(); q.pop();
        size_t v=p.second;
        if (d[v] < p.first) continue;

        for (const Edge &e: g[v])
            if (d[e.dst] > d[v] + e.weight) {
                d[e.dst] = d[v] + e.weight;
                q.push(make_pair(d[e.dst], e.dst));
            }
    }
    return d;
}

int main() {
    size_t n;
    scanf("%zu", &n);

    Graph g(n);
    for (size_t i=0; i<n; ++i) {
        size_t u, k;
        scanf("%zu %zu", &u, &k);

        for (size_t j=0; j<k; ++j) {
            size_t c;
            Weight v;
            scanf("%zu %d", &c, &v);

            connect(g, u, c, v);
        }
    }

    vector<Weight> d=shortest_distance(g, 0);
    for (size_t i=0; i<n; ++i)
        printf("%zu %d\n", i, d[i]);

    return 0;
}

C++: #include <iostream>
#include <vector>
#include <algorithm>
#include <queue>
using namespace std;
static const int MAX = 10000, INFTY = (1 << 20), WHITE = 0, GRAY = 1, BLACK = 2;

int N;
vector<pair<int, int> > adj[MAX];

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

	for (int i = 0; i < N; i++) {
		D[i] = INFTY;
		C[i] = WHITE;
	}

	D[0] = 0;
	PQ.push(make_pair(0, 0));
	C[0] = GRAY;
	while (!PQ.empty()) {
		pair<int, int> F = PQ.top(); PQ.pop();
		int u = F.second;
		C[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 (C[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));
				C[v] = GRAY;
			}
		}
	}
	for (int i = 0; i < N; i++) {
		cout << i << ' ' << (D[i] == INFTY ? -1 : D[i]) << endl;
	}
}

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

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

    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> f = PQ.top();PQ.pop();

        int u = f.second;

        color[u] = BLACK;

        if(d[u] < f.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 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;

}