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<algorithm>
#include<iostream>
#include<cstdlib>
#include<cstring>
#include<cstdio>
#include<vector>
#include<queue>
#include<stack>
#include<cmath>
#include<list>
#include<map>
#include<set>
using namespace std;
 
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<string> VS;
typedef stack<int> SI;
typedef queue<int> QI;
typedef pair<int,int> PII;
typedef long long LL;
 
#define d(x)  cout<<#x<<" = "<<(x)<<endl;
#define ALL(a)  (a).begin(),(a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define PB push_back
#define MP make_pair
#define EMP empty()
#define SZ(a) int((a).size())
#define EACH(i,c) for(typeof((c).begin()) i=(c).begin(); i!=(c).end(); ++i)
#define REACH(i,c) for(typeof((c).rbegin()) i=(c).rbegin(); i!=(c).rend(); ++i)
#define EXIST(s,e) ((s).find(e)!=(s).end())
#define SORT(c,n) sort(c,c+n)
#define VSORT(c) sort((c).begin(),(c).end())
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n)  FOR(i,0,n)
#define DFOR(i,b,a) for(int i=(b)-1;i>=(a);--i)
#define DREP(i,n) DFOR(i,n,0)
#define INF 1000000000
 
const double EPS = 1e-10;
const double PI  = acos(-1.0);
////////////////////////////////////////////////
static const int MAX=10000;
static const int WHITE=0;
static const int GRAY=1;
static const int BLACK=2;
 
int n;
vector<PII> adj[MAX];
void dijkstra()
{
    priority_queue<PII> PQ;
    int color[MAX];
    int d[MAX];
    REP(i,n)
    {
        d[i]=INF;
        color[i]=WHITE;
    }
     
    d[0]=0;
    PQ.push(MP(0,0));
    color[0]=GRAY;
     
    while(!PQ.EMP)
    {
        PII f=PQ.top();
        PQ.pop();
        int u=f.second;
        color[u]=BLACK;
         
        if(d[u]<f.first*(-1))continue;
         
        REP(j,SZ(adj[u]))
        {
            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(MP(d[v]*(-1),v));
                color[v]=GRAY;
            }
        }
    }
    REP(i,n)
    {
        cout<<i<<" "<<(d[i]==INF?-1:d[i])<<endl;
    }
}
 
int main()
{
    int k,u,c,v;
    cin>>n;
    REP(i,n)
    {
        cin>>u>>k;
        REP(j,k)
        {
            cin>>v>>c;
            adj[u].PB(MP(v,c));
        }
    }
     
    dijkstra();
     
    return 0;
}

C++: //Single Source Shortest Path II
#include <iostream>
#include <vector>
#include <queue>
#include <climits>

using namespace std;

static const int N = 10000;
static const int WHITE = 0;
static const int BLACK = 1;
int d[N];

void dijkstra(vector<vector<pair<int, int>>> G, int n) {
    int colors[n];
    for(int i = 0; i < n; i++) {
        colors[i] = WHITE;
        d[i] = INT_MAX;
    }

    priority_queue<pair<int, int>, vector<pair<int, int> >, greater<pair<int, int> > > pq;

    d[0] = 0;
    pq.push(make_pair(0, 0));
    while(!pq.empty()) {
        pair<int, int> f = pq.top();
        pq.pop();
        
        int u = f.second;
        if(d[u] < f.first) continue;
        if(colors[u] == BLACK) continue;
        for(int i = 0; i < G[u].size(); i++) {
            if(d[G[u][i].first] > f.first + G[u][i].second) {
                d[G[u][i].first] = f.first + G[u][i].second;
                pq.push(make_pair(d[G[u][i].first], G[u][i].first));
            }

        }
    }
}

int main() {
    int n, u, k, v, c;
    cin >> n;
    vector<vector<pair<int, int>>> G(n);

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

    dijkstra(G, n);

    for(int i = 0; i < n; i++) cout << i << " " << d[i] << endl;

    return 0;
}

C++: #include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i=0; i<(n); i++)
using ll = long long;
using P = pair<int, int>;
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;
vector<pair<int, int>> adj[MAX]; // 重みつき有向グラフの隣接リスト表現

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

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

    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 はデフォルトで大きい値を優先するため -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] == INFTY ? -1 : d[i]) << endl;
    }
}

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

    cin >> n;
    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;
}