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 <algorithm>
#include <queue>
using namespace std;
static const int INFTY = (1 << 21);
static const int WHITE = 0;
static const int GRAY = 1;
static const int BLACK = 2;

int n;
vector<pair<int, int>> *adj;
int *d;

void dijkstra() {
    priority_queue<pair<int, int>> PQ;
    int d[n], color[n];

    for (int i = 0; i < n; i++) {
        d[i] = INFTY;
        color[n] = WHITE;
    }
    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] = BLACK;

        if (d[u] < f.first * (-1)) { continue; }

        for (int j = 0; j < adj[u].size(); j++) {
            int v = adj[u][j].first;
            if (color[v] == BLACK) { continue; }
            if (d[u] + adj[u][j].second < d[v]) {
                d[v] = d[u] + adj[u][j].second;
                // printf("d[%d] = %d\n", v, d[v]);
                PQ.push(make_pair(d[v] * (-1), v));
                color[v] = GRAY;
            }
        }
    }
    
    for (int i = 0; i < n; i++) {
        printf("%d %d\n", i, d[i]);
    }
}

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

    adj = new vector<pair<int, int>>[n];

    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);
            adj[u].push_back(make_pair(v, c));
        }
    }

    dijkstra();

    return 0;
}

C++: #include <cstdio>
#include <vector>
#include <queue>

int main(void){

	int n, count, next_node, num_neighbors;
	std::vector< std::vector<int> > edges;
	std::vector< std::vector<int> > neighbors;
	std::vector<bool> isUsed;
	std::vector<int> distance;
	std::priority_queue< std::pair<int, int> > distance_heap;
	
	scanf("%d", &n);
	
	edges.resize(n);
	isUsed.resize(n);
	neighbors.resize(n);
	distance.resize(n);
	
	for(int i=0;i<n;i++){
		scanf("%d %d", &next_node, &num_neighbors);
		edges[next_node].resize(num_neighbors);
		neighbors[next_node].resize(num_neighbors);
		for (int j=0;j<num_neighbors;j++){
			scanf("%d %d", &neighbors[next_node][j], &edges[next_node][j]);
		}
		isUsed[next_node]=-false;
		distance[next_node]=300000;
	}
	isUsed[0] = true;
	count=0;
	distance[0] = 0;
	for(int i=0;i<neighbors[0].size();i++){
		distance[neighbors[0][i]] = edges[0][i];
		distance_heap.push(std::make_pair(distance[neighbors[0][i]]*(-1), neighbors[0][i]));
	}
	count=1;
	while(count<n-1){
		std::pair<int, int> p = distance_heap.top();
		distance_heap.pop();
		next_node = p.second;
		if (isUsed[next_node]) continue;
		isUsed[next_node] = true;
		for(int i=0; i<neighbors[next_node].size();i++){
			int neighbor = neighbors[next_node][i];
			if ((!isUsed[neighbor]) && (distance[neighbor] > distance[next_node] + edges[next_node][i])){
				distance[neighbor] = distance[next_node] + edges[next_node][i];
				distance_heap.push(std::make_pair(distance[neighbor]*(-1), neighbor));
			}
		}
		count ++;
	}
	for(int i=0;i<n;i++){
		printf("%d %d\n", i, distance[i]);
	}
	return 0;
}

C++: #include<iostream>
#include<string>
#include<vector>
#include<algorithm>
#include<cmath>
#include<queue>

#define FOR(i,a,b) for(int i=(a);i<(b);++(i))
#define REP(i,n) FOR(i,0,n)

#define dump(x) cerr << #x << " = " <<(x)<<endl;
#define debug(x) cerr << #x << " = " <<(x) << "(L" << __LINE__ << ")" << __FILE__ << endl;

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;
typedef pair<int,int> P;
vector<P> adj[MAX];

void dijkstra(){
  priority_queue<P> PQ;
  int color[MAX];
  int d[MAX];
  REP(i,n){
    d[i] = INFTY;
    color[i] = WHITE;
  }

  d[0] = 0;
  PQ.push(make_pair(0,0));
  color[0] = GRAY;

  while(!PQ.empty()){
    P f = PQ.top(); PQ.pop();
    int u = f.second;
    color[u] = BLACK;
    
    if(d[u]<f.first*(-1) ) continue;
    REP(j,(int)adj[u].size()){
      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;
      }
    }
  }

  REP(i,n){
    cout << i << " "<< (d[i]==INFTY?-1:d[i]) << endl;
  }
}

int main(void){
   
  return 0;
}

C++: #include <bits/stdc++.h>
using namespace std;
struct Point{
	int v,e;
	bool operator<(const Point b)const{
		return this->e > b.e;
	}
	Point(int a,int b):v(a),e(b){}
	Point():v(0),e(0){}
};

long long d[10000];
bool visit[10000] = {0};
vector <Point> G[10000];
priority_queue <Point> PQ;

const long long INF = 1e19;

void dj(int n){
	for(int i=0; i<n; i++) d[i] = INF;
	d[0] = 0;
	PQ.push(Point(0,0));
	Point p, q;
	while(!PQ.empty()){
		p = PQ.top(); PQ.pop();
		visit[p.v] = 1;
		if(d[p.v] < p.e) continue;
		int du = G[p.v].size();
		for(int i=0; i<du; i++){
			q = G[p.v][i];
			if(!visit[q.v] && q.e+d[p.v]<d[q.v]){
				d[q.v] = q.e + d[p.v];
				PQ.push(Point(q.v,d[q.v]));
			}
		}
	}
}
int main()
{	
	int n,u,du; cin>>n;
	for(int i=0; i<n; i++){
		scanf("%d%d",&u,&du);
		int v,e;
		while(du--){
			scanf("%d%d",&v,&e);
			G[u].push_back(Point(v,e));
		}
	}
	dj(n);
	for(int i=0;i<n;i++)
		printf("%d %d\n",i,d[i]);
	return 0;
}