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++: #pragma region _head

#include<iostream>
#include<fstream>
#include<string>
#include<vector>
#include<algorithm>
#include<cmath>
#include<map>
#include<set>
#include<iomanip>
#include<queue>
#include<stack>
#include<numeric>
#include<utility>
#include<regex>

void Init() {
	std::cin.tie(0); std::ios::sync_with_stdio(false);
	struct Init_caller { Init_caller() { Init(); } }caller;
}

#pragma region _define

#define int LL
#define f(i,a,b) for(LL i=a;i<b;i++)
#define rep(i,n) for(LL i=0;i<n;i++)
#define rep2(i,j,a,h,w) for(LL i=0;i<h;i++)for(LL j=0;j<w;j++)cin>>a[i][j]
#define f_vI(v,n) f(i,0,n)cin>>v[i]
#define f_v2I(v1,v2,n) f(i,0,n)cin>>v1[i]>>v2[i]
#define f_v3I(v1,v2,v3,n) f(i,0,n)cin>>v1[i]>>v2[i]>>v3[i]
#define f_vO(v,n) f(i,0,n)cout<<v[i]<<endl
#define ei else if
#define all(a) a.begin(),a.end()
#define size(s) ((LL)s.size())
#define F first
#define S second
#define check() cout<<"! ! !"
#define endl "\n"
#define _y() cout<<"Yes"<<endl
#define _Y() cout<<"YES"<<endl
#define _n() cout<<"No"<<endl
#define _N() cout<<"NO"<<endl
#define INT_INF 1<<29
#define LL_INF 1LL<<60
#define MOD (int)pow(10,9)+7

#pragma endregion





#pragma region _using

using namespace std;

using LL = long long;
using st = string;
using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vd = vector<double>;
using vvd = vector<vd>;
using vvvd = vector<vvd>;
using vc = vector<char>;
using vvc = vector<vc>;
using vs = vector<st>;
using vb = vector<bool>;
using vvb = vector<vb>;
using vvvb = vector<vvb>;
using qi = queue<int>;
using qc = queue<char>;
using qs = queue<st>;
using si = stack<int>;
using sc = stack<char>;
using ss = stack<st>;
using pi = pair<int, int>;
using ppi = pair<pi, int>;
using mll = map<int, int>;
using mcl = map<char, int>;
using msb = map<st, bool>;
using vpi = vector<pi>;
using vppi = vector<ppi>;
using qpi = queue<pi>;

#pragma endregion

//4,2,8,6,1,7,3,9の順
int arround_x[] = { -1,0,0,1,-1,-1,1,1 };
int arround_y[] = { 0,1,-1,0,1,-1,1,-1 };



void y_n(bool p) {
	p ? _y() : _n();
}

void Y_N(bool p) {
	p ? _Y() : _N();
}

LL vmax(vi v, LL n) {
	int MAX = 0;
	f(i, 0, n) {
		MAX = max(MAX, v[i]);
	}
	return MAX;
}

LL vmin(vi v, LL n) {
	int MIN = LL_INF;
	f(i, 0, n) {
		MIN = min(MIN, v[i]);
	}
	return MIN;
}

LL gcd(LL a, LL b) {
	if (b == 0) {
		swap(a, b);
	}
	LL r;
	while ((r = a % b) != 0) {
		a = b;
		b = r;
	}
	return b;
}
LL lcm(LL a, LL b) {
	return (a / gcd(a, b) * b);
}

bool is_square(int n) {
	if ((int)sqrt(n)*(int)sqrt(n) == n) {
		return true;
	}
	else {
		return false;
	}
}

//素数判定
bool is_prime(int n) {
	if (n == 1) {
		return false;
	}
	else {
		for (int i = 2; i*i <= n; i++) {
			if (n % i == 0) {
				return false;
			}
		}
	}
	return true;
}


//素因数分解
void dec_prime(int n) {
	int a = 2;
	while (a*a <= n) {
		if (n % a == 0) {
			cout << a << endl;
			n /= a;
		}
		else {
			a++;
		}
	}
	cout << n << endl;
}

//エラトステネスの篩 （区間[a,b]の篩）
int sieve_prime(LL a,LL b) {
	if (a > b)swap(a, b);
	vb s(b + 1, true);
	int cnt_a=0,cnt_b = 0;
	f(i, 2, b + 1) {
		for (int j = 2; i*j <= b; j++) {
			s[i*j] = false;
		}
	}
	//cout << "2から" << n << "までの素数" << endl;
	f(i, 2, b + 1) {
		if (s[i]) {
			//cout << i << " ";
			if (i < a) {
				cnt_a++;
			}
			cnt_b++;
		}
	}
	return cnt_b - cnt_a;
}

//階乗計算
LL factorial(LL n) {
	LL a = 1, ret = 1;
	while (a < n) {
		a++;
		ret *= a;
		ret %= MOD;
	}
	return ret;
}


#pragma endregion 

vi par;

int root(int x) {
	if (par[x] == x) {
		return x;
	}
	else {
		return par[x] = root(par[x]);
	}
}

void unite(int x, int y) {
	if (root(x) == root(y)) {
		return;
	}
	else {
		par[root(x)] = root(y);
		return;
	}
}

bool same(int x, int y) {
	return root(x) == root(y);
}

struct edge {
	int to;
	int cost;
};

/*****************************************************************************/
vector<vector<edge>> G;
int n;
vi d;
void dijkstra(int s) {
	priority_queue<pi, vpi, greater<pi>>q;
	rep(i, n) {
		d[i] = INT_INF;
	}
	d[0] = 0;
	q.push({ 0,0 });
	while (!q.empty()) {
		pi p = q.top(); q.pop();
		int v = p.second;
		if (d[v] < p.F) {
			continue;
		}
		for (int i = 0; i < size(G[v]); i++) {
			edge e = G[v][i];
			if (d[e.to] > d[v] + e.cost) {
				d[e.to] = d[v] + e.cost;
				q.push({ d[e.to], e.to });
			}
		}
	}
}
signed main() {

	cin >> n;
	G.resize(n);
	d.resize(n);
	for (int i = 0; i < n; i++) {
		int u, k;
		cin >> u >> k;
		for (int j = 0; j < k; j++) {
			int a, b;
			cin >> a >> b;
			G[u].push_back({ a,b });
		}
	}
	dijkstra(0);
	for (int i = 0; i < n; i++) {
		cout << i << " " << d[i] << endl;
	}
	return 0;
}