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 REP(i,n) for(long long i=0;i<n;++i)
#define FOR(i,a,b) for(long long i=a;i<b;++i)
#define F first
#define S second
using namespace std;

typedef pair< int,int > point;
vector< point > graph[10001];
vector< int > v(10001);
int n;
const int INF=1<<30;

void dijkstra(int s){
    priority_queue< point,vector< point >,greater< point > >pq;
    pq.push({0,s});
    fill(v.begin(),v.end(),INF);
    v[s]=0;
    while(!pq.empty()){
        point p=pq.top();
        pq.pop();
        REP(i,graph[p.S].size()){
            int nex=graph[p.S][i].S;
            int cost=p.F+graph[p.S][i].F;
            if(v[nex]>cost){
                v[nex]=cost;
                pq.push({cost,nex});
            }
        }
    }
}

int main(){
    scanf("%d",&n);
    int u,k,to,c;
    REP(i,n){
        scanf("%d%d",&u,&k);
        REP(j,k){
            scanf("%d%d",&to,&c);
            graph[u].push_back({c,to});
        }
    }
    dijkstra(0);
    REP(i,n){
        printf("%d ",i);
        printf("%d\n",v[i]);
    }
    return 0;
}

C++: // ダイクストラ法
// Dijkstra's Algorithm
// priority_queue
// Single Source Shortest Path 2 単一始点最短経路
#include <iostream>
#include <cstring>
#include <algorithm>
#include <queue>
#include <stack>
#include <cstdio>
#include <cstdlib>
#include <vector>
using namespace std;

static const int MAX = 10000;
static const int INF = (1 << 21);
static const int WHITE = 0;
static const int GRAY = 1;
static const int BLACK = 2;

int n;
vector<pair<int, int>> adj[MAX]; //重み付き有向グラフ

void dijkstra() {

    priority_queue<pair<int, int>> PQ;
    int d[MAX], color[MAX];

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

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

    while (!PQ.empty()) {
        
        pair<int, int> f = PQ.top();
        PQ.pop();
        int u = f.second;

        color[u] = BLACK;

        // 最小値を取り出し、それが最短でなければ無視
        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[v] > d[u] + adj[u][j].second) {
                d[v] = d[u] + adj[u][j].second;
                // priority_queueのため-1を掛ける
                PQ.push(make_pair(d[v]*(-1), v));
                color[v] = GRAY;
            }
        }
    }

    for(int i = 0; i < n; i++) {
        cout << i << " " << (d[i] == INF ? -1 : d[i]) << endl;
    }
}

int main() {

    cin >> n;
    int k, c, u, v;

    for(int i = 0; i < n; i++) {
        cin >> u >> k;
        for(int j = 0; j < k; j++) {
            cin >> v >> c;
            adj[u].push_back(make_pair(v, c));
        }
    }


    dijkstra();

    return 0;
}

C++: #include<bits/stdc++.h>
using namespace std;
static const int MAX = 10000;
static const int WHITE = 0;
static const int GRAY = 1;
static const int BLACK = 2;
static const int INFTY = (1<<20);
int n;
vector<pair<int,int> >adj[MAX];


void dijkstra(){
    priority_queue<pair<int,int> >PQ;
    int color[MAX],d[MAX];
    
    for (int i = 0; i < n; i++)
    {
        color[i] = WHITE;
        d[i] = INFTY;
        
    }
    d[0] = 0;color[0] = GRAY;
    PQ.push(make_pair(0,0));

    while (!PQ.empty())
    {
        pair<int,int> f = PQ.top();PQ.pop();
        int u = f.second;
        color[u] = BLACK;
        //最小値を取り出し、それが最短でなければ無視
        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[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;
            }
            
        }
    }
    for (int  i = 0; i < n; i++)
        {
            cout << i << " " << (d[i]==INFTY?-1:d[i]) << endl;
        }  
}


int main(){
    cin >> n;
    int u,k,c,v;
    
    
    
    for (int i = 0; i < n; i++){
        cin >> u >> k;
        for (int j = 0; j < k; j++){
            cin >> v>> c;
           adj[u].push_back(make_pair(v,c));
        }
    }
    dijkstra();
    return 0;
    
}