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++: // AtCoder template
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i,n) for(int i = 0; i < n; ++i)

/*
* グラフ構造体
*/
template<typename U>
struct edge{
    int to;
    int from;
    U cost; // 変更
    edge(int to, int from, U cost):to(to), from(from), cost(cost){}
    edge(int to, int from):to(to), from(from), cost(1){}
};

template<typename T>
class Graph{
public:
    vector<vector<edge<T>>> graph;
    int v_size;
    
    // 無向グラフならunDirected = true
    Graph(int n, vector<int> from, vector<int> to, vector<T> cost, bool unDirected){
        if(from.size() != to.size() || to.size() != cost.size()) cout << "Graph constructer detected error.\n";
        graph.assign(n, vector<edge<T>>());
        v_size = n;
        for(int i = 0; i < from.size(); ++i){
            edge<T> tmp(to[i], from[i], cost[i]);
            graph[from[i]].push_back(tmp);
            if(unDirected){
                swap(tmp.from, tmp.to);
                graph[to[i]].push_back(tmp);
            }
        }
    }
    Graph(int n, vector<int> from, vector<int> to, bool unDirected){
        if(from.size() != to.size()) cout << "Graph constructer detected error.\n";
        graph.assign(n, vector<edge<T>>());
        for(int i = 0; i < from.size(); ++i){
            edge<T> tmp(to[i], from[i]);
            graph[from[i]].push_back(tmp);
            if(unDirected){
                swap(tmp.from, tmp.to);
                graph[to[i]].push_back(tmp);
            }
        }
    }

    // BFS, DFS
    vector<bool> visited;
    bool BFS(int start, int goal){
        visited.assign(graph.size(), false);
        queue<pair<int, T>> que;
        que.emplace(start, 0);
        while(!que.empty()){
            int now = que.front().first;
            T depth = que.front().second;
            que.pop();
            visited[now] = true;
            
            if(now == goal){ // 処理記述

                return true;
            }
            
            for(int i = 0; i < graph[now].size(); ++i){
                int next = graph[now][i].to;
                int cost = graph[now][i].cost;
                if(visited[next]) continue;
                que.emplace(next, depth+cost);
            }
        }
        return false;
    }

    bool DFS(int start, int goal){
        visited.assign(v_size, false);
        stack<pair<int, T>> sta;
        sta.emplace(start, 0);
        while(!sta.empty()){
            int now = sta.top().first;
            T depth = sta.top().second;
            sta.pop();
            visited[now] = true;
    
            if(now == goal){ // 処理記述
                
                return true;
            }
            for(int i = 0; i < graph[now].size(); ++i){
                int next = graph[now][i].to;
                int cost = graph[now][i].cost;
                if(visited[next]) continue;
                sta.emplace(next, depth+cost);
            }
        }
        return false;
    }
    
    // ダイクストラ法（による最短経路木構築）
    vector<T> d_d;
    void Dijkstra(int start, int goal, T t_max){
        d_d.assign(graph.size(), t_max);
        d_d[start] = 0;
        priority_queue<pair<T,int>, vector<pair<T,int>>, greater<pair<T, int>> > que;
        que.emplace(0, start);
        while(!que.empty()){
            T dist = que.top().first;
            int now = que.top().second;
            que.pop();
            if(d_d[now] < dist) continue;
            //if(now == goal) return ; // ここの行を失くせばstart全頂点への距離が求められる
            for(int i = 0; i < graph[now].size(); ++i){
                int next = graph[now][i].to;
                int next_cost = graph[now][i].cost;
                if(d_d[next] > d_d[now] + next_cost){
                    d_d[next] = d_d[now] + next_cost;
                    que.emplace(d_d[next], next);
                }
            }
        }
    }

    // ワーシャルフロイド法
    vector<vector<T>> w_d;
    void Warshal_Floyd(T u_max){
        int n = graph.size();
        w_d.assign(n, vector<T>(n, u_max));
        for(int i = 0; i < n; ++i){
            w_d[i][i] = 0;
            for(int j = 0; j < graph[i].size(); ++j){
                int next = graph[i][j].to, dist = graph[i][j].cost;
                w_d[i][next] = dist;
            }
        }
        for(int i = 0; i < n ; ++i){
            for(int j = 0; j < n; ++j){
                for(int k = 0; k < n; ++k){
                    w_d[j][k] = min(w_d[j][k], w_d[j][i] + w_d[i][k]);
                }
            }
        }
    }
};




int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);

    int n; cin >> n;
    vector<int> from,to;
    vector<ll> cost;
    rep(i,n){
        int u,k; cin >> u >> k;
        rep(j,k){
            int v,c; cin >> v >> c;
            from.push_back(u);
            to.push_back(v);
            cost.push_back(c);
        }
    }
    Graph<ll> graph(n, from, to, cost, false);
    graph.Dijkstra(0, 0, INT_MAX);
    rep(i,n) cout << i << " " << graph.d_d[i] << "\n";
}