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>

#define NIL -2
#define INF 1000000001

using namespace std;
static const int BLK = 2;
static const int GRY = 1;
static const int WHT = 0;

void dijkstra(const vector<vector<pair<int,int> > > &adj_list, 
                    vector<int> &color, 
                    vector<int> &parent, 
                    vector<int> &minpath,
                    int start_node)
{
    priority_queue<pair<int,int>,vector<pair<int,int> >, greater<pair<int,int> > >  PQ;
    PQ.push(make_pair(start_node,0));

    while(!PQ.empty()){
        pair<int,int> t = PQ.top(); PQ.pop();
        int u = t.second;
        color[u] = BLK;
        if(minpath[u] < t.first) continue;
        for(int i = 0;i < adj_list[u].size();i++){
            int v = adj_list[u][i].first;
            if(color[v] != BLK){
                if(minpath[u] + adj_list[u][i].second < minpath[v]){
                    minpath[v] = minpath[u] + adj_list[u][i].second;
                    parent[v] = u;
                    color[v] = GRY;
                    PQ.push(make_pair(minpath[v],v));
                }  
            }
        }
        
    }

}


int main(){
    int mat_size;
    int node, deg;
    int to,weight;
    int temp;
    int cost = 0;

    scanf("%d",&mat_size);
    vector<vector<pair<int,int> > > adj_list(mat_size);
    vector<int> color(mat_size,WHT);
    vector<int> minpath(mat_size,INF);
    vector<int> parent(mat_size,-1);
    
    for(int i = 0;i < mat_size;i++){
        scanf("%d %d",&node,&deg);
        for(int j = 0;j < deg;j++){
            scanf("%d %d", &to, &weight);
            adj_list[node].push_back(make_pair(to,weight));
        }
    }
    
    minpath[0] = 0;
    dijkstra(adj_list,color,parent,minpath,0);

    for(int i = 0; i < mat_size;i++){
        printf("%d %d\n",i,minpath[i]);
    }

    return 0;   
}

C++: #include<stdio.h>
#include<queue>
#include<string.h>
using namespace std;
#define INF 1 << 30
struct ss{
	int next;
	int to;
	int val;
}e[100050];
int head[100050];
int tot;
void add(int x,int y,int val){
	e[tot].next=head[x];
	e[tot].to=y;
	e[tot].val=val;
	head[x]=tot++;
}
int n;
int vis[100050]={0};
int dis[10005];
void spfa(){
	for(int i=0;i<n;i++){
		dis[i]=INF;
	}
	vis[0]=1;
	dis[0]=0;
	queue<int> st;
	st.push(0);
	while(!st.empty()){
		int t=st.front();
		st.pop();
		vis[t]=0;
		for(int i=head[t];i!=-1;i=e[i].next){
			int to=e[i].to;
			if(dis[to]>dis[t]+e[i].val){
				dis[to]=dis[t]+e[i].val;
				if(!vis[to]){
					st.push(to);
					vis[to]=1;
				}
			}
		}
	}
}
int main(){
	scanf("%d",&n);
	tot=0;
	memset(head,-1,sizeof(head));
	int a,to,val,num;
	for(int i=0;i<n;i++){
		scanf("%d %d",&a,&num);
		for(int j=1;j<=num;j++){
			scanf("%d %d",&to,&val);
			add(a,to,val);
		}
	}
	spfa();
	printf("0 0\n");
	for(int i=1;i<n;i++){
		printf("%d %d\n",i,dis[i]);
	}
	return 0;
}

C++: #include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define repr(i, n) for (int i = (int)(n); i >= 0; i--)
#define REP(i, m, n) for (int i = (int)(m); i <= (int)(n); i++)
#define REPR(i, m, n) for (int i = (int)(m); i >= (int)(n); i--)
#define all(v) v.begin(), v.end()
typedef long long ll;
const int INF = 1001001001;
typedef pair<int,int> pii;

template<class t> inline bool chmax(t& a, t b) { if (a < b) { a = b; return 1; } return 0; }
template<class t> inline bool chmin(t& a, t b) { if (a > b) { a = b; return 1; } return 0; }

using Graph = vector<vector<pii> >;

int n;
vector<bool> seen;
vector<int> dist;
priority_queue<pair<int, int> > pq;

void dijkstra(const Graph &G, int v){
  seen[v] = true;

  for(pii p : G[v]){
    int u = p.first;
    int c = p.second;
    if(seen[u] == true) continue;
    if(chmin(dist[u], dist[v]+c)) pq.push(make_pair((-1)*dist[u], u));
  }

  while(!pq.empty()){
    pair<int, int> tmp;
    tmp = pq.top();
    pq.pop();
    if(seen[tmp.second]) continue;
    int nv = tmp.second;
    dijkstra(G, nv);
  }

  return;
}

int main(){
  cin >> n;

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

  seen.assign(n, false);
  dist.assign(n, INF);
  dist[0] = 0;
  dijkstra(G, 0);

  rep(i, n) cout << i << " " << dist[i] << endl;

  return 0;
}

C++: #include<bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (n); ++i) 
#define PI acos(-1)

using namespace std;
using ll = long long;
using P = pair<int, int>;
using LP = pair<ll, ll>;

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);

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

    priority_queue<P, vector<P>, greater<P>> q;
    vector<int> wmap(n, -1);
    q.push(P(0, 0));
    while (!q.empty()) {
        P p = q.top(); q.pop();
        int w = p.first;
        int v = p.second;
        if (wmap[v] != -1) continue;

        wmap[v] = w;
        for (auto e : adj[v]) {
            q.push(P(e.first + w, e.second));
        }
    }

    rep(i, n) cout<<i<<" "<<wmap[i]<<endl;
}