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 <string.h>
#include <algorithm>
#include <iostream>
#include <string>
#include <math.h>
#include <ctype.h>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <functional>
using namespace std;

typedef long long ll;
typedef pair<ll, int> pp;
#define mp(a, b) make_pair(a, b)

struct edge {
	int v, w;
	int next;
	edge() {}
	edge(int v_, int w_, int n_) : v(v_), w(w_), next(n_) {}
};

int n, cnt;
int head[10001];
edge e[600000];
bool vis[10001];
ll dis[10001];

void init()
{
	cnt = 0;
	memset(head, -1, sizeof head);
}
void addedge(int u, int v, int w)
{
	e[++cnt] = edge(v, w, head[u]); head[u] = cnt;
}
void dijkstra(int s)
{
	for (int i = 0; i < n; i++)
		vis[i] = 0, dis[i] = ll(1e18);
	dis[s] = 0; vis[s] = 1;
	for (int i = head[s]; i != -1; i = e[i].next)
		dis[e[i].v] = e[i].w;
	while(1)
	{
		int idx = -1;
		ll dist = 1e18;
		for (int j = 0; j < n; j++)
			if (!vis[j] && dist > dis[j])
			{
				idx = j;
				dist = dis[j];
			}
		if (idx == -1)
			break;
		vis[idx] = 1;
		for (int j = head[idx]; j != -1; j = e[j].next)
		{
			int v = e[j].v;
			ll w = e[j].w;
			if (dis[v] > dis[idx] + w)
				dis[v] = dis[idx] + w, vis[v] = 0;
		}
	}
}

int id[10001];

int main()
{
	int s;
	while (scanf("%d", &n) == 1)
	{
		init();
		for (int i = 0; i < n; i++)
		{
			int u, k;
			scanf("%d%d", &u, &k);
			id[i] = u;
			if (u == 0)
				s = i;
			while (k--)
			{
				int v, w;
				scanf("%d%d", &v, &w);
				addedge(u, v, w);
			}
		}
		dijkstra(s);
		for (int i = 0; i < n; i++)
			printf("%d %lld\n", id[i], dis[i]);
	}
	return 0;
}

C++: // #define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define all(v) v.begin(), v.end()
#define Graph vector< vector<P> >
typedef long long ll;
typedef pair<int, int> P;
const int INF = 1000000007;

int main(){
    int N;
    cin >> N;
    Graph M(N);
    rep(i, N){
        int u, k;
        cin >> u >> k;
        rep(j, k){
            int v, c;
            cin >> v >> c;
            M[u].push_back(P(v, c));
        }
    }

    vector<int> d(N, INF), p(N, -1);
    vector<bool> seen(N, false);
    d[0] = 0;

    while(1){
        int mincost = INF;
        int u;

        rep(i, N){
            if(!seen[i] && d[i] < mincost){
                mincost = d[i];
                u = i;
            }
        }

        if(mincost == INF) break;
        seen[u] = true;

        rep(i, M[u].size()){
            int v = M[u][i].first, c = M[u][i].second;
            if(!seen[v] && d[u] + c < d[v]){
                d[v] = d[u] + c;
                p[v] = u;
            }
        }
    }

    rep(i, N){
        cout << i << ' ' << d[i] << endl;
    }

}

C++: // Ref : https://book.mynavi.jp/ec/products/detail/id=35408

#include <iostream>
#include <algorithm>
#include <queue>
using namespace std;
static const int MAX = 10000;
static const int INFTY = (1 << 20);
static const int WHITE = 0;
static const int GRAY = 1;
static const int BLACK = 2;

int n;
vector<pair<int, int> > adj[MAX];

void dijkstra() {
	priority_queue<pair<int, int> > PQ;
	int color[MAX];
	int d[MAX];
	for (int i = 0; i < n; i++) {
		d[i] = INFTY;
		color[i] = WHITE;
	}

	d[0] = 0;
	PQ.push(make_pair(0, 0));
	color[0] = GRAY;

	while (!PQ.empty()) {
		pair<int, int> f = PQ.top(); PQ.pop();
		int u = f.second;
		color[u] = BLACK;

		if (d[u] < (f.first * (-1))) continue;

		for (unsigned int j = 0; j < adj[u].size(); j++) {
			int v = adj[u][j].first;
			if (color[v] == BLACK) continue;
			if (d[v] > d[u] + adj[u][j].second) {
				d[v] = d[u] + adj[u][j].second;
				// priority queue order is converted from descending to ascending with -1.
				PQ.push(make_pair(d[v] * (-1), v));
				color[v] = GRAY;
			}
		}
	}
	
	for (int i = 0; i < n; i++) {
		cout << i << " " << (d[i] == INFTY ? -1 : d[i]) << endl;
	}
}

int main() {
	int k, u, v, c;

	cin >> n;
	for (int i = 0; i < n; i++) {
		cin >> u >> k;
		for (int j = 0; j < k; j++) {
			cin >> v >> c;
			adj[u].push_back(make_pair(v, c));
		}
	}

	/*
	for (int i = 0; i < n; i++) {
		vector<pair<int, int> >::iterator begin = adj[i].begin();
		vector<pair<int, int> >::iterator end = adj[i].end();
		cout << i << " ";
		for (; begin != end; begin++) {
			cout << (*begin).first << " " << (*begin).second << " ";
		}
		cout << endl;
	}
	*/

	dijkstra();

	return 0;
}