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>
#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, INT32_MAX);
	costs[0] = 0;
	priority_queue<Edge> queue;
	for (Edge edge : lists[0])
		queue.push(edge);

	while (!queue.empty())
	{
		Edge edge = queue.top(); queue.pop();
		int dest = edge.second;
		int cost = edge.first;
		if (costs[dest] < cost)continue;
		int new_cost = costs[edge.second] = edge.first;

		for (Edge next : lists[dest])
		{
			next.first += new_cost;
			if(costs[next.second]== INT32_MAX)
				queue.push(next);
		}
	}
	for (int i = 0; i < n; i++)
		cout << i << " " << costs[i] << endl;

	char c;
	cin >> c;

	return 0;
}

C++: #include<iostream>
#include<algorithm>
#include<queue>
#define INF 1<<21
#include<vector>
static const int N = 10000;
using namespace std;
vector<pair<int,int> > A[N];
int n;
void dajkstra(void){
    priority_queue<pair<int, int> > PQ;
    int d[N],color[N];
    for(int i=0;i<n;i++){
        d[i] = INF;
        color[i] = 0;
    }
    d[0] = 0;
    PQ.push(make_pair(0,0));
    while(!PQ.empty()){
        pair<int, int> f = PQ.top(); PQ.pop();
        int u = f.second;
        color[u] = 1;
        if(d[u]<f.first*(-1)){
                continue;
        }
        for(int j=0;j<A[u].size();j++){
            int v = A[u][j].first;
            if(color[v]==1){
                continue;
            }
            if(d[u] + A[u][v].second < d[v]){
                d[v] = d[u] + A[u][v].second;
                PQ.push(make_pair(d[v]*(-1),v));
            }
        }
    }
    for(int i=0;i<n;i++){
        cout << i << ' ' << d[i] << endl;
    }
}
int main(void){
    int u,v,adj,key;
    cin >> n;
    for(int i=0;i<n;i++){
        cin >> u >> adj;
        for(int j=0;j<adj;j++){
            cin >> v >> key;
            A[u].push_back(make_pair(v,key));
        }
    }
    dajkstra();
    return 0;
}

C++: #include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstring>
#include <vector>
#include <string>
#include <queue>
using namespace std;
const int INF = 1 << 30;
const int NIL = -1;
const int MAXN = 10005;
int vis[MAXN];
int d[MAXN];
int head[500005];
int n;
int cnt;
struct Edge {
	int to, next, w;
	Edge() {}
} edge[500005];

void add(int u, int v, int w)
{
	edge[cnt].to = v;
	edge[cnt].w = w;
	edge[cnt].next = head[u];
	head[u] = cnt++;
}

struct Node {
	int u, w;
	Node (int _u, int _w) :u(_u), w(_w) {}
	friend bool operator<(const Node& a, const Node& b)
	{
		return a.w > b.w;
	}
};

void dijkstra(int s)
{
	priority_queue<Node> q;
	for (int i = 0; i < n; ++i)
		d[i] = INF, vis[i] = false;
	d[s] = 0;
	
	Node t(s, 0);
	q.push(t);
	int u, v, w;
	int count = 0;
	while (!q.empty() && count < n - 1)
	{
		t = q.top();
		q.pop();
		u = t.u;
		if (d[u] < t.w)
			continue;
		vis[u] = true;
		++count;
		for (int i = head[u]; i != NIL; i = edge[i].next)
		{
			v = edge[i].to;
			w = edge[i].w;
			if (!vis[v] && d[v] > d[u] + w)
			{
				d[v] = d[u] + w;
				q.push(Node(v, d[v]));
			}
		}
	}
	if (count == n - 1)
		for (int i = 0; i < n; ++i)
			printf("%d %d\n", i, d[i]);

}

int main(void)
{
	int k, s, e, w;
	scanf("%d", &n);
	memset(head, NIL, sizeof(-1));
	cnt = 0;
	for (int i = 0; i < n; ++i)
	{
		scanf("%d%d", &s, &k);
		while (k--)
		{
			scanf("%d %d", &e, &w);
			add(s, e, w);
		}
	}
	dijkstra(0);

	return 0;
}

C++: #include <cstdio>
#include <algorithm>
#include <queue>
#include <utility>
#include <unordered_map>
#include <vector>

using edge = std::pair<int, int>;
#define N 10000

int main(){
    int n;
    std::scanf("%d", &n);
    std::vector<edge> a[N];
    for(int i = 0; i < n; ++i){
        int id;
        int num;
        std::scanf("%d", &id);
        std::scanf("%d", &num);
        for(int j = 0; j < num; ++j){
            edge e;
            std::scanf("%d", &e.second);//id                                                                                                                                                                                        
            std::scanf("%d", &e.first);//weight                                                                                                                                                                                     
            a[id].emplace_back(e);
        }
    }
    std::priority_queue<edge, std::vector<edge>, std::greater<edge> > que;
    std::unordered_map<int, int> checked;
    checked.emplace(std::make_pair(0, 0));
    for(auto &x: a[0]){
        que.emplace(x);
    }
    while(checked.size() != n){
        while(checked.find(que.top().second) != checked.end()){
            que.pop();
        }
        edge e = que.top();
        que.pop();
        checked.emplace(std::make_pair(e.second, e.first));
        for(auto &x: a[e.second]){
            if(checked.find(x.second) == checked.end()){
                x.first += e.first;
                que.emplace(x);
            }
        }
    }

    for(int i = 0; i < n; ++i){
        auto x = checked.find(i);
        std::printf("%d %d\n", x->first, x->second);
    }

    return 0;
}