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 <cassert>

#include <cctype>
#include <cerrno>
#include <cfloat>
#include <ciso646>
#include <climits>
#include <clocale>
#include <cmath>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <ccomplex>
#include <cfenv>
#include <cinttypes>
#include <cstdbool>
#include <cstdint>
#include <ctgmath>
#include <cwchar>
#include <cwctype>

// C++
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>
#include <array>
#include <atomic>
#include <chrono>
#include <condition_variable>
#include <forward_list>
#include <future>
#include <initializer_list>
#include <mutex>
#include <random>
#include <ratio>
#include <regex>
#include <scoped_allocator>
#include <system_error>
#include <thread>
#include <tuple>
#include <typeindex>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
// #include <boost/foreach.hpp>
// #include <boost/range/algorithm.hpp>
#define rep(i,j,k) for(int i=(int)j;i<(int)k;i++)
#define ll long long
#define Sort(v) sort(all(v))
//#define INF 1e9
#define LINF 1e18
#define END return 0
#define pb push_back
#define se second
#define fi first
#define pb push_back
#define all(v) (v).begin() , (v).end()
#define MP make_pair
#define int long long
using namespace std;
int day[12]={31,28,31,30,31,30,31,31,30,31,30,31};
// int dx[]={0,1,0,-1};
// int dy[]={1,0,-1,0};
struct edge{int to,cost;};
//typedef pair<int,int> P;

const long long MOD=1000000007LL;
bool isupper(char c){if('A'<=c&&c<='Z')return 1;return 0;}
bool islower(char c){if('a'<=c&&c<='z')return 1;return 0;}
bool isPrime(int x){if(x==1)return 0;if(x==2)return 1;if(x%2==0)return 0;for(int i=3;i*i<=x;i++)if(x%i==0)return 0;return 1;}
bool iskaibun(string s){for(int i=0;i<s.size()/2;i++)if(s[i]!=s[s.size()-i-1])return 0;return 1;}
bool isnumber(char c){return ('0'<=c&&c<='9');}
bool isalpha(char c){return (isupper(c)||islower(c));}
template<typename T> 
void print(vector<T> v){
    for(int i=0;i<v.size();i++){
        if(i)cout<<" ";
        cout<<v[i];
    }
    cout<<endl;
}
int INF=1e18;

template<typename T>
void printendl(vector<T> v){
    for(auto date:v)cout<<date<<endl;
}

template<typename T>
void printvv(vector<vector<T>> v){
    for(int i=0;i<v.size();i++){
        for(int j=0;j<v[i].size();j++){
            if(j)cout<<" ";
            cout<<v[i][j];
        }
        cout<<endl;
    }
}
int gcd(int a,int b){
    if(a<b)swap(a,b);
    if(b==0)return a;
    else return gcd(b,a%b);
}

struct Edge{
    int to,cost;
};

struct Dijk{
    vector<int> d;
    vector<vector<Edge>> v;
    Dijk(int n){
        d.assign(n,INF);
        v.assign(n, vector<Edge>(0));
    }

    void input(int e){
        for(int i=0;i<e;i++){
            int a,b,c;
            cin>>a>>b>>c;
            //a--; b--; //1-indexなら
            v[a].push_back(Edge{b,c});
            //v[b].push_back(Edge{a,c}); //無向グラフ
        }
    }

    void solve(int s){
        d[s]=0;
        typedef pair<int,int> P;
        priority_queue<P, vector<P> , greater<P>> que;
        que.push(P(0,s));
        while(!que.empty()){
            P now = que.top();
            que.pop();
            int now_d=now.first, idx=now.second;
            if(d[idx] < now_d)continue;
            for(int j=0;j<v[idx].size();j++){
                Edge e = v[idx][j];
                if(d[e.to] > d[idx] + e.cost){
                    d[e.to] = d[idx] + e.cost;
                    que.push(P(d[e.to], e.to));
                }
            }
        }
    }

    int get_cost(int n){
        return d[n];
    }
};

signed main (){
    int n;cin>>n;
    Dijk di(n);
    rep(i,0,n){
        int u;cin>>u;
        int k;cin>>k;
        rep(j,0,k){
            int v,c;cin>>v>>c;
            di.v[u].push_back(Edge{v,c});
        }
    }
    di.solve(0);
    rep(i,0,n){
        cout<<i<<" "<<di.get_cost(i)<<endl;
    }
    

}
/*

*/