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 <deque>
#include <queue>
#include <list>
#include <stack>
#include <string>
#include <tuple>
#include <functional>
#include <numeric>
#include <cmath>
#include <iomanip>
#include <map>
#include <random>
#include <cstdlib>
#define INT_MAX 2147483647
#define INT_MIN -2147483646
#define Loop(i, n) for(int i = 0; i < (int)n; i++)
#define Loop1(i, n) for(int i = 1; i <= (int)n; i++)
#define Loopr(i, n) for(int i = (int)n - 1; i >= 0; i--)
#define Loopr1(i, n) for(int i = (int)n; i >= 1; i--)
using namespace std;
typedef long long int ll;
typedef vector<int> vi;
typedef vector<vector<int>> vvi;
void fastios() { ios_base::sync_with_stdio(0); cin.tie(0); }

static const int N = 10005;

struct vertex {
	int id;
	int d;
	bool operator<(const vertex & another) const {
		return (d != another.d ? d>another.d : id>another.id);
	}
};

struct edge {
	int end;
	int w;
};

int main() {
	fastios();
	int n;
	cin >> n;
	vector<vector<edge>> E(N);
	Loop(i, n) {
		int u, k;
		cin >> u >> k;
		Loop(i, k) {
			int v, c;
			cin >> v >> c;
			E[u].push_back({ v,c });
		}
	}

	priority_queue<vertex> pq;
	vi color(N, 0), dist(N, 0);
	pq.push({ 0,0 });
	int cnt = 0;
	while (pq.size() > 0) {
		if (cnt == n) break;
		vertex v = pq.top();
		pq.pop();
		if (color[v.id] == 1) continue;
		dist[v.id] = v.d;
		color[v.id] = 1;
		cnt++;
		Loop(j, E[v.id].size()) {
			pq.push({ E[v.id][j].end, dist[v.id] + E[v.id][j].w });
		}
	}
	Loop(i, n) {
		cout << i << " " << dist[i] << endl;
	}
	return 0;
}

C++: #include <iostream>
#include <vector>
#include <queue>
#define INF 1000000
using namespace std;

class vertex{
public:
  class edge{
  public:
    int to;
    int weight;
    edge(int to, int weight){
      this->to = to;
      this->weight = weight;
    }
  };

  vector<edge> edges;
  int num;
  int dis;

  vertex(){
    n++;
    vertexes.push_back(this);
  }

  bool operator< (const vertex& v) const{
    return dis < v.dis;
  }

  bool operator> (const vertex& v) const{
    return dis > v.dis;
  }

  static void dijkstra(int start){
    //距離の初期化
    for(int i=0; i<n; i++) vertexes[i]->dis=INF;
    vertexes[start]->dis=0;

    //プライオリティキューを初期化、始点を格納
    priority_queue<vertex, vector<vertex>, greater<vertex> > pq; pq.push(*vertexes[start]);


    while(!pq.empty()){
      vertex now = pq.top(); pq.pop(); //キューの先頭をポップ
      if(now.dis>vertexes[now.num]->dis) continue;

      //ポップしたキューの頂点集合について最短距離更新
      for(int i=0; i<now.edges.size(); i++){
        int newDis = now.dis+now.edges[i].weight;
        vertex* next = vertexes[now.edges[i].to];
        if(newDis < next->dis){
          next->dis = newDis;
          pq.push(*next);
        }
      }

    }


  }

  static void print(){
    for(int i=0; i<n; i++){
      cout << vertexes[i]->num << " " << vertexes[i]->dis << endl;
    }
  }
private:
  static int n;
  static vector<vertex*> vertexes;
};

int vertex::n=0;
vector<vertex*> vertex::vertexes;

int main(){
  int n; cin >> n;

  vertex graph[n];

  //入力を隣接リストのようなものに格納
  int v, k, to, weight;
  for(int i=0; i<n; i++){
    cin >> v >> k;
    graph[i].num=v;
    for(int j=0; j<k; j++){
      cin >> to >> weight;
      vertex::edge e(to, weight);
      graph[v].edges.push_back(e);
    }
  }

  vertex::dijkstra(0); //0始点のダイクストラ法

  vertex::print();

  return 0;
}

C++: #include<iostream>
#include<climits>
using namespace std;

typedef struct{
  int A[10005];
  int ans;
  bool c;
}node;
node T[10005];
int Q[100000000];
int head=0;
int tail=1;
int n;

void function(int num){
  while(true){
    if(head==tail)break;
    num=Q[head++];
    if(head==99999999)head=1;
    T[num].c=true;
    for(int i=0;i<n;i++){
      if(T[num].A[i]!=0){
	if(T[i].ans>T[num].ans+T[num].A[i]){
	  T[i].ans=T[num].ans+T[num].A[i];
	Q[tail++]=i;
	if(tail==99999999)tail=1;
	}
      }
    }
  }
}

int main(){
  int num,son,z,w;
  cin>>n;
  for(int i=0;i<n;i++){
    cin>>num>>son;
    T[num].ans=INT_MAX;
    for(int j=0;j<son;j++){
      cin>>z>>w;
      T[num].A[z]=w;
      }
  }
  Q[0]=0;
  T[0].ans=0;
  function(0);
 
  for(int i=0;i<n;i++){
      cout<<i<<" "<<T[i].ans<<endl;
  }
  return 0;
}

C++: //Dijkstra
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<queue>
#include<vector>
using namespace std;
typedef pair<int, int> P;
int n, dis[10001], n_left;
vector< vector<P> > G(10001);
priority_queue< P, vector<P>, greater<P> > heap;
bool visited[10001];

int main(){
    int u, v, k, w;

    scanf("%d", &n);
    n_left = n;
    for(int i=0; i<n; i++){
        scanf("%d %d", &u, &k);
        for(int j=0; j<k; j++){
            scanf("%d %d", &v, &w);
            G[u].push_back(P(w, v));
        }
    }
    memset(visited, 0, sizeof(visited));
    memset(dis, 127, sizeof(dis));

    dis[0] = 0;
    heap.push(P(0, 0));
    while(!heap.empty() && n_left>0){
        P top = heap.top();
        heap.pop();
        if(!visited[top.second]){
            u = top.second;
            visited[u] = true;
            --n_left;
            for(int i=0; i<G[u].size(); i++){
                v = G[u][i].second;
                w = dis[u] + G[u][i].first;
                if(!visited[v] && w < dis[v]){
                    heap.push(P(w, v));
                    dis[v] = w;
                }
            }
        }
    } 
    for(int i=0; i<n; i++){
        printf("%d %d\n", i, dis[i]);
    }
    return 0;
}