Go: package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

const BIG_COST = 200000

type Path struct {
	node int
	cost int
}

func main() {
	sc := bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)

	nNodes := scanInt(sc)

	// 各頂点につながる頂点一覧を得るための隣接リスト
	graph := make([][]Path, nNodes)

	for i := 0; i < nNodes; i++ {
		u := scanInt(sc)
		k := scanInt(sc)
		graph[i] = make([]Path, k)
		for d := 0; d < k; d++ {
			graph[u][d] = Path{
				node: scanInt(sc),
				cost: scanInt(sc),
			}
		}
	}

	// 0 から各頂点への最小コストを保存する配列
	minCosts := make([]int, nNodes)

	minCosts[0] = 0
	for i := 1; i < nNodes; i++ {
		minCosts[i] = BIG_COST
	}

	// 各頂点が調査済みかどうかを保持する配列
	checked := make([]bool, nNodes)

	// 最小コストのパスを高速に取得するためのヒープ。
	// コストが小さいものほどルートに来るようにする。
	heap := NewHeap(func(a, b Path) bool {
		return a.cost < b.cost
	})

	heap.insert(Path{node: 0, cost: 0})
	for heap.size > 0 {
		u := heap.extractMax()

		// 隣接行列を使っていた時とは違い、ヒープには
		// 同じノードへのパスが複数含まれうる。そのため既によりコストの低い
		// パスが見つかっている場合は無視する。
		if minCosts[u.node] < u.cost {
			continue
		}

		checked[u.node] = true

		for _, v := range graph[u.node] {
			cost := v.cost + u.cost
			if !checked[v.node] && cost < minCosts[v.node] {
				minCosts[v.node] = cost
				heap.insert(Path{node: v.node, cost: cost})
			}
		}
	}

	w := bufio.NewWriter(os.Stdout)
	for i, cost := range minCosts {
		fmt.Fprintf(w, "%d %d\n", i, cost)
	}
	w.Flush()
}

func scanInt(sc *bufio.Scanner) int {
	sc.Scan()
	v, _ := strconv.Atoi(sc.Text())
	return v
}

// --- From ALDS1_9_C: Priority Queue

type Heap struct {
	size   int
	heap   []Path
	isHigh func(a, b Path) bool
}

func NewHeap(isHigh func(a, b Path) bool) Heap {
	heap := make([]Path, 1) // 先頭は不使用
	return Heap{size: 0, heap: heap, isHigh: isHigh}
}

func (h *Heap) insert(v Path) {
	h.size += 1
	if h.size > len(h.heap)-1 {
		h.heap = append(h.heap, v)
	} else {
		h.heap[h.size] = v
	}

	for i := h.size; i > 1; {
		parent := i / 2
		if h.isHigh(h.heap[parent], h.heap[i]) {
			break
		}
		h.heap[i], h.heap[parent] = h.heap[parent], h.heap[i]
		i = parent
	}
}

func (h *Heap) extractMax() Path {
	if h.size <= 0 {
		panic("cannot extract from empty heap")
	}

	max := h.heap[1]
	h.heap[1] = h.heap[h.size]
	h.size -= 1
	h.maxHeapify(1)

	return max
}

func (h *Heap) maxHeapify(idx int) {
	left := idx * 2
	right := left + 1
	largest := idx

	if left <= h.size {
		if h.isHigh(h.heap[left], h.heap[idx]) {
			largest = left
		}
		if right <= h.size && h.isHigh(h.heap[right], h.heap[largest]) {
			largest = right
		}
	}

	if largest != idx {
		h.heap[idx], h.heap[largest] = h.heap[largest], h.heap[idx]
		h.maxHeapify(largest)
	}
}

C++: #include<map>
#include<list>
#include<cmath>
#include<stack>
#include<queue>
#include<vector>
#include<cstring>
#include<iostream>
#include<functional>
#include<algorithm>
using namespace std;
#define LOOP1(n) for(int i=0;i<n;i++)
#define LOOP2(n) for(int j=0;j<n;j++)
#define LOOP3(n) for(int k=0;k<n;k++)
#define Psi pair<string,int>
#define Pis pair<int,string>
#define Pii pair<int,int>
// ??????????????????memset(a,0,sizeof(a));
// ?´???°?????? if(x<2)return0;else if(x==2)return1;if(x%2==0)return0;for(i=3;i*i<=x;i+=2){if(x%i==0)return0;}return1;}p440
//vector size();push_back(x);pop_back();begin();end();insert(p,x);erase(p);clear();
//stack  size();top();pop();push(x);emtpy();
//queue  size();front();pop();push(x);empty();
//priority_queue< ??? , ??\???????????? , less<???> or greater<???> > <int , vector<int> , greater<int> >
/*******************************************/
/* vector<int> v     vector<int> v[100]    */
/* ???[1]          ?????? [1,1][1,2][1,3]     */
/*   [2]               [2,1][2,2][3,3]     */
/*   [3]               [3,1][2,2][3,3]     */
/*******************************************/
static const int MAX = 10000;
static const int WHITE = 1;
static const int GRAY = 2;
static const int BLACK = 3;
static const int INFTY = (1 << 21);
int d[MAX]; int color[MAX]; 
int main(){
	vector<pair<int, int>> v[MAX];
	int n, k, uu;
	cin >> n;
	for (int i = 0; i < n; i++){
		cin >> uu >> k;
		for (int j = 0; j < k; j++){
			Pii p;
			cin >> p.first >> p.second;
			v[i].push_back(p);
		}
	}
	for (int i = 0; i < n; i++){
		d[i] = INFTY;
		color[i] = WHITE;
	}
	d[0] = 0; int u = 0;
	while (1){
		int mincost = INFTY;
		LOOP1(n){
			if (color[i] != BLACK && mincost > d[i]){
				mincost = d[i];
				u = i;
			}
		}
		if (mincost == INFTY) break;
		color[u] = BLACK;
		for (int j = 0; j < v[u].size(); j++){
			if (color[v[u][j].first] != BLACK && d[u] + v[u][j].second < d[v[u][j].first]){
				color[v[u][j].first] = GRAY;
				d[v[u][j].first] = d[u] + v[u][j].second;
			}
		}
	}
	LOOP1(n){
		cout << i << ' ' << d[i] << endl;
	}
	return 0;
}

C++: #include<iostream>
#include<vector>
#include<list>
#define INF 2e9
using namespace std;

void Dikstra(const vector<vector<pair<int, int> > >& G, vector<int>& d){
    d[0] = 0;
    list<int> i_gray;
    i_gray.push_back(0);
    vector<bool> is_black(d.size(), false);
    is_black[0] = true;
    while (!i_gray.empty()) {
        list<int>::iterator min_it = i_gray.begin();
        for (list<int>::iterator it = i_gray.begin(); it != i_gray.end(); it++) {
            if (d[*it] < d[*min_it]) min_it = it;
        }
        is_black[*min_it] = true;
        for (int i = 0; i < G[*min_it].size(); i++) {
            int v = G[*min_it][i].first;
            int w = G[*min_it][i].second;
            if (!is_black[v] && d[*min_it] + w < d[v]) {
                if (d[v] == INF) i_gray.push_back(v);
                d[v] = d[*min_it] + w;
            }
        }
        i_gray.erase(min_it);
    }
}

int main(){
    int n;
    cin >> n;
    vector<vector<pair<int, int> > > G(n);
    for (int i = 0; i < n; i++) {
        int u, k;
        cin >> u >> k;
        for (int j = 0; j < k; j++) {
            int v, c;
            cin >> v >> c;
            G[u].push_back(make_pair(v, c));
        }
    }
    vector<int> d(n, INF);
    Dikstra(G, d);
    for (int i = 0; i < n; i++) {
        cout << i << " " << d[i] << endl;
    }

    return 0;
}

C++: #include <stdio.h>
#include <iostream>
#include <queue>
#include <list>
using namespace std;

class Node
{
private:
	list<int> next_node_list;
	list<int> next_weight_list;
public:
	Node();
	void AddNextNode(int id, int weight);
	void SetWeight(int weight);
	void DistributeWeight();
	int weight_from_0;
	bool check;
};

Node::Node()
{
	weight_from_0 = -1;
	check = false;
}

Node *Node_list;

struct GreatNode
{
	bool operator()(const Node *n1, const Node *n2) const;
};
bool GreatNode::operator()(const Node *n1, const Node *n2) const
{
	return n1->weight_from_0 > n2->weight_from_0;
}
priority_queue<Node*, vector<Node*>, GreatNode > que;

void Node::AddNextNode(int id, int weight)
{
	next_node_list.push_back(id);
	next_weight_list.push_back(weight);
}

void Node::SetWeight(int weight)
{
	if (weight_from_0 == -1 || weight < weight_from_0) {
		weight_from_0 = weight;
	}
}

void Node::DistributeWeight()
{
	check = true;
	list<int>::iterator itr2 = next_weight_list.begin();
	for(list<int>::iterator itr = next_node_list.begin(); itr != next_node_list.end(); itr++){	
		if (Node_list[*itr].check == false) {
			Node_list[*itr].SetWeight(weight_from_0 + *itr2);
			que.push(&Node_list[*itr]);
		}
		itr2++;
	}
	next_node_list.clear();
	next_weight_list.clear();
}

int main(void)
{
	//input
	int n;
	cin >> n;
	Node_list = new Node[n]();
	for (int i = 0; i < n; i++) {
		int u, k;
		cin >> u >> k;
		for (int j = 0; j < k; j++) {
			int v, c;
			cin >> v >> c;
			Node_list[i].AddNextNode(v, c);
		}
	}

	//weight from 0 ?
	Node_list[0].check = true;
	Node_list[0].weight_from_0 = 0;
	Node_list[0].DistributeWeight();
	while (!que.empty()) {
		Node *node = que.top();
		que.pop();
		node->DistributeWeight();
	}

	//output
	for (int i = 0; i < n; i++) {
		cout << i << " " << Node_list[i].weight_from_0 << endl;
	}
	
	return 0;
}