Go: package main

import (
	"fmt"
	"container/heap"
)

type Node struct {
	Id int
	Dis int
}

type PriorityQueue []*Node

func (pq PriorityQueue) Len() int { return len(pq) }

func (pq PriorityQueue) Less(i, j int) bool {
	return pq[i].Dis < pq[j].Dis
}

func (pq PriorityQueue) Swap(i, j int) {
	pq[i], pq[j] = pq[j], pq[i]
}

func (pq *PriorityQueue) Push(x interface{}) {
	*pq = append(*pq, x.(*Node))
}

func (pq *PriorityQueue) Pop() interface{} {
	n := len(*pq)
	pop := (*pq)[n-1]
	*pq = (*pq)[0:n-1]
	return pop
}

func main() {
	var n int
	fmt.Scan(&n)

	g := make([][]int, n)
	c := make([][]int, n)
	pq := make(PriorityQueue, 0, n)
	d := make([]int, n)
	for i := 0; i < n; i++ {
		var u,k int
		fmt.Scan(&u)
		fmt.Scan(&k)
		g[u] = make([]int, k)
		c[u] = make([]int, k)
		for j := 0; j < k; j++ {
			fmt.Scan(&g[u][j])
			fmt.Scan(&c[u][j])
		}

		if u == 0 {
			d[u] = 0
		} else {
			d[u] = 1 << 30
		}
		pq.Push(&Node{u, d[u]})
	}
	heap.Init(&pq)

	for pq.Len() > 0 {
		node := heap.Pop(&pq).(*Node)
		for i := 0; i < len(g[node.Id]); i++ {
			nextId := g[node.Id][i]
			nextDis := node.Dis + c[node.Id][i]
			if nextDis < d[nextId] {
				d[nextId] = nextDis
				heap.Push(&pq, &Node{nextId, nextDis})
			}
		}
	}

	for i := 0; i < n; i++ {
		fmt.Println(i, d[i])
	}
}

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

#define rep(i, a, b) for (int i = (a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (a); i >= (int)(b); i--)
#define all(x) (x).begin(), (x).end()
using i32 = int32_t;
using i64 = int64_t;
using f32 = float;
using f64 = double;
using P   = pair<int, int>;

template <class T>
bool chmin(T& a, T b) {
    if (a > b) {
        a = b;
        return true;
    } else {
        return false;
    }
}
template <class T>
bool chmax(T& a, T b) {
    if (a < b) {
        a = b;
        return true;
    } else {
        return false;
    }
}

template <class T>
void dump_vec(const vector<T>& v) {
    auto len = v.size();
    rep(i, 0, len) {
        cout << v[i] << (i == (int)len - 1 ? "\n" : " ");
    }
}

struct FastIO {
    FastIO() {
        cin.tie(0);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(20);
    }
} FASTIO;

//---------------------------------------------------------------------------------------------------

struct Edge {
    int from, to;
    i64 cost;
    Edge() {}
    Edge(int t, i64 c) : from(-1), to(t), cost(c) {}
    Edge(int f, int t, i64 c) : from(f), to(t), cost(c) {}

    bool operator<(const Edge& r) const {
        return cost < r.cost;
    }
    bool operator>(const Edge& r) const {
        return cost > r.cost;
    }
};

using Vertex = vector<Edge>;
using Graph  = vector<Vertex>;

// 無向
void link(Graph& g, int from, int to, int cost = 1) {
    g[from].push_back(Edge(from, to, cost));
    g[to].push_back(Edge(to, from, cost));
    return;
}

// 有向
void connect(Graph& g, int from, int to, int cost = 1) {
    g[from].push_back(Edge(from, to, cost));
    return;
}

vector<i64> dijkstra(const Graph& g, int start) {
    const auto inf = numeric_limits<i64>::max();
    vector<i64> dist(g.size(), inf);

    using Pi = pair<i64, int>;
    priority_queue<Pi, vector<Pi>, greater<Pi>> que;
    dist[start] = 0;
    que.push(make_pair(0, 0));
    while (!que.empty()) {
        const auto e    = que.top();
        const auto cost = e.first;
        const auto from = e.second;
        que.pop();
        if (dist[from] < cost) continue;

        for (const auto& e : g[from]) {
            const auto next_cost = e.cost + cost;
            if (chmin(dist[e.to], next_cost)) {
                que.push(make_pair(next_cost, e.to));
            }
        }
    }

    return dist;
}

//---------------------------------------------------------------------------------------------------

signed main() {
    int N;
    cin >> N;
    Graph G(N);
    rep(i, 0, N) {
        int u, k;
        cin >> u >> k;
        rep(j, 0, k) {
            int v, c;
            cin >> v >> c;
            connect(G, u, v, c);
        }
    }
    auto dist = dijkstra(G, 0);
    rep(i, 0, N) {
        cout << i << " " << dist[i] << "\n";
    }
}

C++: /*
　　　  ∧＿∧　やあ
　　 （´・ω・｀)　　　　　/　　　　　ようこそ、バーボンハウスへ。
　　 ／∇y:::::＼　　　 [￣]　　　　　このテキーラはサービスだから、まず飲んで落ち着いて欲しい。
　　 |:⊃:|:::::|　　　|──|
￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣|　うん、「また」なんだ。済まない。
￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣|￣　  仏の顔もって言うしね、謝って許してもらおうとも思っていない。
￣￣￣￣￣￣￣￣￣￣￣￣￣￣／|
　　　　∇　∇　∇　∇　　　／.／|　　　でも、この提出を見たとき、君は、きっと言葉では言い表せない
　　　　┴　┴　┴　┴　／ ／　  |　　　「ときめき」みたいなものを感じてくれたと思う。
￣￣￣￣￣￣￣￣￣￣|／　　  |　　　殺伐としたコンテストの中で、そういう気持ちを忘れないで欲しい
￣￣￣￣￣￣￣￣￣￣　　　　 |　　　そう思って、この提出を投げたんだ。
　　　(⊆⊇)　(⊆⊇)　(⊆⊇)　　|
　    ||　　 ||　　||　　|　　　 じゃあ、判定を聞こうか。
　　.／|＼　／|＼ ／|＼
*/

#include <iostream>
#include <cstdlib>
#include <algorithm>
#include <array>
#include <bitset>
#include <climits>
#include <cmath>
#include <cstdio>
#include <functional>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <string>
#include <vector>
using namespace std;
#define fst first
#define snd second
#define mp make_pair
#define ALL(obj) (obj).begin(),(obj).end()
#define FOR(i,a,b) for(int i=(a);i<(b);i++)
#define RFOR(i,a,b) for(int i = (b-1);i>=a;i--)
#define REP(i,n)  FOR(i,0,n)
#define RREP(i,n) RFOR(i,0,n) 
#define SIZE(x) ((int)(x).size())
#define debug(x) cerr << #x << " -> " << x << " (line:" << __LINE__ << ")" << '\n';
#define debugpair(x, y) cerr << "(" << #x << ", " << #y << ") -> (" << x << ", " << y << ") (line:" << __LINE__ << ")" << '\n';
typedef long long lint;
typedef pair<int, int> pint;
typedef pair<lint, lint> plint;
typedef vector<lint> vec;
typedef vector<vector<lint>> matrix;
typedef priority_queue<lint> p_que;
typedef priority_queue<lint, vector<lint>, greater<lint>> p_que_rev;
const lint INF = INT_MAX;
const lint LINF = LLONG_MAX;
const lint MOD = 1000000000 + 7;
const double EPS = 1e-9;
const double PI = acos(-1);
const int di[]{0, -1, 0, 1, -1, -1, 1, 1};
const int dj[]{1, 0, -1, 0, 1, -1, -1, 1};

// Graph Templates
using Weight = lint;
// using Flow = int;
struct Edge {
    int src, dst;
    Weight weight;
    // Flow cap;
    Edge() : src(0), dst(0), weight(0) {}
    Edge(int s, int d, Weight w) : src(s), dst(d), weight(w) {}
};
using Edges = vector<Edge>;
using Graph = vector<Edges>;
using Array = vector<Weight>;
using Matrix = vector<Array>;
// const Weight INF = numeric_limits<Weight>::max() / 8;

// add edge a <--(weight = w)--> b
void add_edge(Graph &g, int a, int b, Weight w) {
    g[a].push_back(Edge(a, b, w));
    g[b].push_back(Edge(b, a, w));
}

// add edge a --(weight = w)--> b
void add_arc(Graph &g, int a, int b, Weight w) { g[a].push_back(Edge(a, b, w)); }

// Dijkstra
// g is graph, s is start
vector<Weight> dijkstra(const Graph &g, int s) {
    // const Weight INF = numeric_limits<Weight>::max() / 8;
    using state = tuple<Weight, int>;
    priority_queue<state> q;
    vector<Weight> dist(g.size(), LINF);
    dist[s] = 0;
    q.emplace(0, s);
    while (q.size()) {
        Weight d;
        int v;
        tie(d, v) = q.top();
        q.pop();
        d *= -1;
        /* if(v == t) return d; */
        if (dist[v] < d) continue;
        for (auto &e : g[v]) {
            if (dist[e.dst] > dist[v] + e.weight) {
                dist[e.dst] = dist[v] + e.weight;
                q.emplace(-dist[e.dst], e.dst);
            }
        }
    }
    return dist;
}

int main(){
    int n;
    cin >> n;
    int u, k, v;
    Weight c;
    Graph g;
    vector<Weight> dist;
    g.resize(n);
    for (int i=0; i<n; ++i){
        cin >> u >> k;
        for (int j=0; j<k; ++j){
            cin >> v >> c;
            add_arc(g, u, v, c);
        }
        // add_edge(g, s, t, d);
    }
    dist = dijkstra(g, 0);
    for (int i=0; i<(int)dist.size(); ++i){
        cout << i << " ";
        if(dist[i] != INF){
            cout << dist[i] << endl;
        }
        else {
            cout << "INF" << endl;
        }
    }
    
    return 0;
}