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 <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, long weight);
	void SetWeight(int weight);
	void DistributeWeight();
	long 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, long 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;
}

C++: #include <bits/stdc++.h>
#define rep(i,n) for (int i = 0; i < (n); ++i)
#define sz(x) int(x.size())
#define ALL(c) (c).begin(), (c).end()
#define SUM(x) std::accumulate(ALL(x), 0LL)
#define MIN(v) *std::min_element(v.begin(), v.end())
#define MAX(v) *std::max_element(v.begin(), v.end())
#define EXIST(v, x) (std::find(v.begin(), v.end(), x) != v.end())

using namespace std;
typedef long long ll;

template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }
const int INF = 1001001001;
const long long INFL = (1LL<<60);
const double eps = (1e-9);

typedef pair<int, int> P;

// @param [in] n: ノード数
// @param [in] cost: 重みの隣接表現
// @param [in] s: スタートするノード
// @param [out] d: s からの距離
void dijkstra(const int& n, const vector<vector<pair<int, int>>>& cost, const int& s, vector<int>& d) {
  priority_queue<P, vector<P>, greater<P>> que;  // P#first が小さい順に取り出せる
  d[s] = 0;
  que.push(P(0, s));

  while (!que.empty()) {
    P p = que.top(); que.pop();
    int v = p.second;
    if (d[v] < p.first) continue;
    for (int j = 0; j < cost[v].size(); j++) {  // v から移動できる全ての node について
      int t = cost[v][j].first;
      int c = cost[v][j].second;
      if (d[t] > d[v] + c) {
        d[t] = d[v] + c;
        que.push(P(d[t], t));
      }
    }
  }
}

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

  int n;
  cin >> n;
  vector<vector<pair<int, int>>> cost(n);

  rep(i, n) {
    int u, k;
    cin >> u >> k;
    vector<pair<int, int>> tmp(k);
    rep(j, k) {
      int v, c;
      cin >> v >> c;
      tmp[j] = make_pair(v, c);
    }
    cost[i] = tmp;
  }

  // 求めるのは 0 からの距離
  vector<int> d(n, INF);
  dijkstra(n, cost, 0, d);

  rep(i, n) {
    cout << i << " " << d[i] << endl;
  }

  return 0;
}

C++: #include <bits/stdc++.h>

#define REP(i, n) for(int i=0;i<(int)(n);i++)
#define ALL(x) (x).begin(),(x).end()
const int INF = 1e9;

using namespace std;
int n;
int res = 0;
struct node {
    int id;
    int dist;
    bool searched;
};

node v[100];
int edge[100][100];

int main() {
    cin >> n;
    REP(i, n) {
        int u, k;
        cin >> u >> k;
        v[u].id = u;
        v[u].dist = INF;
        v[u].searched = false;
        REP(j, n) edge[i][j] = INF;
        REP(j, k){
            int to, cost;
            cin >> to >> cost;
            edge[i][to] = cost;
        }
    }
    v[0].dist = 0;
    int prev = 0;
    REP(i, n){
        int minimum = INF;
        REP(j, n){
            if(!v[j].searched && minimum >= v[j].dist){
                prev = j;
                minimum = v[j].dist;
            }
        }
        REP(j, n){
            if(!v[j].searched && edge[prev][j] != INF){
                v[j].dist = min(v[j].dist, v[prev].dist + edge[prev][j]);
            }
        }
        v[prev].searched = true;
    }
    REP(i, n) cout << i << " " << v[i].dist << endl;
    return 0;
}