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 <list>
#include <vector>

class TNode
{
	std::list<std::pair<TNode*, int> > FNexts;
	int  FDistance;
public:
	TNode()
	: FDistance(-1)
	{
	}
	
	int GetDistance()const {return FDistance;}
	
	void Push(TNode* New, int Weight)
	{
		FNexts.push_back(std::make_pair(New, Weight));
	}
	
	void Visit(int Distance)
	{
		if(FDistance >= 0 && Distance > FDistance) return;
		FDistance = Distance;
		for(std::list<std::pair<TNode*, int> >::iterator It = FNexts.begin(); It != FNexts.end(); ++It){
			It->first->Visit(Distance + It->second);
		}
	}
};

class TGraph
{
	std::vector<TNode*> FNodes;
public:
	TGraph(int Count)
	: FNodes(Count)
	{
		for(int i = 0; i < Count; ++i){
			FNodes[i] = new TNode();
		}
	}
	
	~TGraph()
	{
		for(unsigned int i = 0; i < FNodes.size(); ++i){
			delete FNodes[i];
		}
	}
	
	void InputNode()
	{
		int Index;
		std::cin >> Index;
		int BranchCount;
		std::cin >> BranchCount;
		for(int i = 0; i < BranchCount; ++i){
			int Target, Weight;
			std::cin >> Target >> Weight;
			FNodes[Index]->Push(FNodes[Target], Weight);
		}
	}
	
	void BreathFirstSearch()
	{
		FNodes[0]->Visit(0);
	}
	
	int Distance(int Target)const
	{
		return FNodes[Target]->GetDistance();
	}
};

int main()
{
	int Count;
	std::cin >> Count;
	TGraph Graph(Count);
	for(int i = 0; i < Count; ++i){
		Graph.InputNode();
	}
	Graph.BreathFirstSearch();
	
	for(int i = 0; i < Count; ++i){
		std::cout << i << " " << Graph.Distance(i) << std::endl;
	}
	return 0;
}

C++: #include <bits/stdc++.h>
using namespace std;

#define INF (INT64_MAX/2)
typedef pair<long long, int> P;

int main()
{
	int n;
	cin >> n;
	vector<vector<P>> g( n );
	for( int i = 0; i < n; i++ ) {
		int u, k;
		cin >> u >> k;
		g[u].resize( k );
		for( int j = 0; j < k; j++ ) {
			int v, c;
			cin >> v >> c;
			g[u][j] = P( c, v );
		}
	}

	vector<long long> d( n, INF );
	d[0] = 0;
	priority_queue<P, vector<P>, greater<P>> que;
	que.push( P( 0, 0 ) );
	while( !que.empty() ) {
		P p = que.top();
		que.pop();
		int c = p.first;
		int u = p.second;
		for( P e : g[u] ) {
			int cost = e.first;
			int v = e.second;
			if( d[v] <= d[u] + cost ) continue;
			d[v] = d[u] + cost;
			que.push( e );
		}
	}

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

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

using namespace std;

static const int N = 100;
static const int WHITE = 0;
static const int BLACK = 1;
int n, colors[N], d[N];
vector<pair<int, int> > G[N];

void dijkstra() {
    int u, mind;
    for(int i = 0; i < N; i++) {
        colors[i] = WHITE;
        d[i] = INT_MAX;
    }
    d[0] = 0;
    while(1) {
        u = -1;
        mind = INT_MAX;
        for(int i = 0; i < n; i++) {
            if(colors[i] == WHITE && d[i] < mind) {
                u = i;
                mind = d[i];
            }
        }
        if(u == -1) break;
        colors[u] = BLACK;
        for(int i = 0; i < G[u].size(); i++) {
            d[G[u][i].first] = min(d[G[u][i].first], mind + G[u][i].second);
        }
    }
}

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

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

C++: #define _USE_MATH_DEFINES
#include <bits/stdc++.h>
#define USE_LLONG_AS_INT
#ifdef USE_LLONG_AS_INT
#define int long long
#define inf (1ll<<60)
#else
#define inf (1<<30)
#endif
#define rep(i,n) for(int i=0;i<(n);i++)
#define Rep(i,a,b) for(int i=(a);i<(b);i++)
#define REP(i,a,b) for(int i=(a);i<=(b);i++)
#define rev(i,n) for(int i=(n)-1;i>=0;i--)
#define vi vector<int>
#define vvi vector<vi>
#define pb push_back
#define eb emplace_back
#define pi pair<int,int>
#define vp vector<pair<int,int>>
#define mp make_pair
#define all(v) (v).begin(),(v).end()
#define fi first
#define se second
#define MEMSET(a) memset(a,0,sizeof(a))
#define Yes(f) cout<<(f?"Yes":"No")<<endl
#define yes(f) cout<<(f?"yes":"no")<<endl
#define YES(f) cout<<(f?"YES":"NO")<<endl
#define SORT(v) sort(all(v))
#define RSORT(v) sort(all(v), greater<int>())

using namespace std;

const int mod=1e9+7;
const string sp=" ";

void run();

void init() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout<<fixed<<setprecision(12);
}

signed main(){
    init();
    run();
    return 0;
}

int n;
vector<vp> g;

void solve(){
    vi d(n,inf);
    priority_queue<pi,vp,greater<pi>> q;
    d[0]=0;
    q.push({0,0});
    while(!q.empty()){
        pi p=q.top();
        q.pop();
        int v=p.se;
        if(d[v]<p.fi)continue;
        for(pi e:g[v]){
            if(d[e.se]>d[v]+e.fi){
                d[e.se]=d[v]+e.fi;
                q.push({d[e.se],e.se});
            }
        }
    }
    rep(i,n){
        cout<<i<<sp<<d[i]<<endl;
    }
}

void run(){
    cin>>n;
    g.resize(n);
    rep(i,n){
        int u,k;
        cin>>u>>k;
        rep(j,k){
            int v,c;
            cin>>v>>c;
            g[u].eb(pi(c,v));
        }
    }
    solve();
}