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 <vector>
#include <queue>
#include <utility>
using namespace std;

struct Edge {
    int from, to, cost;
    Edge(int f, int t, int c) : from(f), to(t), cost(c) { }
    bool operator <(const Edge& e) const {
        return cost < e.cost;
    }
};

const int INF = (int)1e9;
typedef pair<int, int> P;

vector<int> dijkstra(const vector<vector<Edge> >& g, int s) {
    vector<int> res(g.size(), INF);
    priority_queue<P, vector<P>, greater<P> > Q;
    Q.push(P(0, s));
    res[s] = 0;
    while(!Q.empty()) {
        P p = Q.top(); Q.pop();
        if(p.first > res[p.second]) continue;
        for(int i = 0; i < (int)g[p.second].size(); i++) {
            Edge e = g[p.second][i];
            if(res[e.to] > p.first + e.cost) {
                res[e.to] = p.first + e.cost;
                Q.push(P(res[e.to], e.to));
            }
        }
    }
    return res;
}

int main() {
    int N; cin >> N;
    vector<vector<Edge> > es(N);
    for(int i = 0; i < N; i++) {
        int u, k; cin >> u >> k;
        while(k--) {
            int v, c; cin >> v >> c;
            es[u].push_back(Edge(u, v, c));
        }
    }
    vector<int> res = dijkstra(es, 0);
    for(int i = 0; i < N; i++) {
        cout << i << ' ' << res[i] << endl;
    }
}

C++: #include <cstdio>
#include <vector>
#include <queue>
using namespace std;
const int MAXN = 1e4 + 7, INF = 5e5 + 7;
int d[MAXN];
struct node {
	int id, dist;
	node(int id, int dist) :id(id), dist(dist) {}
	bool operator < (const node &rhs) const {
		return dist > rhs.dist;
	}
};
vector<pair<int, int> > G[MAXN];
priority_queue<node> nodes;
int main() {
    int n;
    scanf("%d", &n);
    for (int i = 1; i < n; i++) {
    	d[i] = INF;
	}
    for (int i = 0; i < n; i++) {
    	int u, k;
    	scanf("%d%d", &u, &k);
    	for (int j = 0; j < k; j++) {
    		int v, c;
    		scanf("%d%d", &v, &c);
    		G[u].push_back(make_pair(v, c));
		}
	}
	nodes.push(node(0, 0));
	while (!nodes.empty()) {
		node tmp = nodes.top();
		nodes.pop();
		if (tmp.dist > d[tmp.id]) continue;
		int cnt = G[tmp.id].size();
		for (int i = 0; i < cnt; i++) {
			if (d[G[tmp.id][i].first] > d[tmp.id] + G[tmp.id][i].second) {
				d[G[tmp.id][i].first] = d[tmp.id] + G[tmp.id][i].second;
				nodes.push(node(G[tmp.id][i].first, d[G[tmp.id][i].first]));
			}
		}
	}
	for (int i = 0; i < n; i++) {
		printf("%d %d\n", i, d[i]);
	}
	return 0;
}

C++: #include <iostream>
#include <stdio.h>
#include <vector>

using namespace std;

struct Wside{
	int vertex;
	int weight;
	Wside(int a, int b){
		vertex=a; weight=b;
	}
};

vector<Wside>* info;
vector<int> scanned;
int* result, *candidates;
int n;

bool isScanned(int v){
	for(int i=0,sz=scanned.size(); i<sz; ++i){
		if(v==scanned[i]) return 1;
	}
	return 0;
}

int scan(){
	int nextvtx;
	for(int j=0, scn=scanned[scanned.size()-1], sz=info[scn].size(); j<sz; ++j){
		int vtx = info[scn][j].vertex;
		if(isScanned(vtx)) continue;
		int wgh = info[scn][j].weight;

		result[vtx] = result[vtx] > result[scn] + wgh ? (result[scn] + wgh) : result[vtx];
		candidates[vtx] = result[vtx];
	}

	int minimum=0xfffffff;
	for(int i=0; i<n; ++i){
		if(candidates[i]==-1) continue;
		nextvtx = minimum<candidates[i]? nextvtx : i;
		minimum = result[nextvtx];
	}
	candidates[nextvtx]=-1;
	scanned.push_back(nextvtx);
	return 0;
}

int main()
{
	scanf("%d",&n);
	scanned.reserve(n);
	info = new vector<Wside> [n];
	result = new int [n];
	candidates = new int [n];
	for(int i=0; i<n; ++i){
		result[i] = 0xfffffff;
		candidates[i] = -1;
	}

	int org,k,v,c;
	for(int i=0; i<n; ++i){
		scanf("%d %d",&org,&k);
		info[org].reserve(k);
		for(int j=0; j<k; ++j){
			scanf("%d %d",&v,&c);
			info[org].push_back(Wside(v,c));
		}
	}

	scanned.push_back(0);
	result[0] = 0;
	while(scanned.size()!=n){
		scan();
	}

	for(int i=0; i<n; ++i){
		cout << i << " " << result[i] << endl;
	}

	delete[] info;
	delete[] result;
	delete[] candidates;

	return 0;
}