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 <vector>
#include <algorithm>


using namespace std;

short heap_index[10000];

struct Info{
	Info(){
		to=0;
		weight = 0;
	}
	Info(short arg_to,int arg_weight){
		to = arg_to;
		weight = arg_weight;
	}
	short to;
	int weight;
};

class InfoPQ{
public:
	InfoPQ(){
		array = new Info[10000];
		n = 0;
	}
	void push(Info arg_info){
		array[n] = arg_info;
		int tmp = n;
		while(tmp != 0 && array[tmp].weight < array[(tmp-1)/2].weight){
			std::swap(array[tmp], array[(tmp-1)/2]);
			tmp = (tmp-1)/2;
		}
		n++;
	}

	bool isEmpty(){
		return n == 0;
	}

	void writeHeapIndex(){
		for(int i=0;i<n;i++){
			heap_index[array[i].to] = i;
		}
	}

	void update(short update_index,int new_weight){
		array[heap_index[update_index]].weight = new_weight;
		int tmp = heap_index[update_index];
		while(tmp != 0 && array[tmp].weight < array[(tmp-1)/2].weight){
			std::swap(heap_index[array[tmp].to],heap_index[array[(tmp-1)/2].to]);
			std::swap(array[tmp], array[(tmp-1)/2]);
			tmp = (tmp-1)/2;
		}
	}

	Info pop(){
		Info ret = array[0];
		n--;
		heap_index[array[n].to] = 0;
		std::swap(array[0],array[n]);
		int tmp = 0;
		while(2*tmp+1 <= n-1){
			if(2*tmp+2 <= n-1){
				if(array[2*tmp+2].weight < array[tmp].weight && array[2*tmp+2].weight <= array[2*tmp+1].weight){
					std::swap(heap_index[array[tmp].to],heap_index[array[2*tmp+2].to]);
					std::swap(array[2*tmp+2],array[tmp]);
					tmp = 2*tmp+2;
				}else if(array[2*tmp+1].weight < array[tmp].weight && array[2*tmp+1].weight <= array[2*tmp+2].weight){
					std::swap(heap_index[array[tmp].to],heap_index[array[2*tmp+1].to]);
					std::swap(array[2*tmp+1],array[tmp]);
					tmp = 2*tmp+1;
				}else{
					break;
				}
			}else{
				if(array[tmp].weight > array[2*tmp+1].weight){
					std::swap(heap_index[array[tmp].to],heap_index[array[2*tmp+1].to]);
					std::swap(array[tmp],array[2*tmp+1]);
					tmp = 2*tmp+1;
				}else{
					break;
				}
			}
		}
		return ret;
	}

private:
	Info* array;
	int n;
};



int main(){
	int n,count=0,tmp,left_node,right_node,dist;
	short size;
	scanf("%d",&n);
	vector<Info> V[n];
	Info catcher;
	InfoPQ A;

	int P[n],zero_dist[n];

	for(int i=0;i<n;i++){
		P[i]=0;
		zero_dist[i] = 10000001;
	}
	zero_dist[0] = 0;
	P[0]=1;

	for(int i=0;i<n;i++){
		scanf("%d %d",&left_node,&tmp);
		if(left_node == 0){
			for(int k=0;k<tmp;k++){
				scanf("%d %d",&right_node,&dist);
				zero_dist[right_node] = dist;
			}
		}else{
			for(int k=0;k<tmp;k++){
				scanf("%d %d",&right_node,&dist);
				V[left_node].push_back(Info(right_node,dist));
			}
		}
	}

	for(short k=1;k<n;k++){
		A.push(Info(k,zero_dist[k]));
	}

	A.writeHeapIndex();

	while(count<n-1){

		catcher = A.pop();
		P[catcher.to]=1;
		count++;
		size = V[catcher.to].size();
		for(int k=0;k<size;k++){
			if(zero_dist[V[catcher.to][k].to] > catcher.weight+V[catcher.to][k].weight){
				zero_dist[V[catcher.to][k].to] = catcher.weight+V[catcher.to][k].weight;
				A.update(V[catcher.to][k].to,catcher.weight+V[catcher.to][k].weight);
			}
		}
	}

	for(int i=0;i<n;i++){
		printf("%d %d\n",i,zero_dist[i]);
	}

    return 0;
}

C++: #include <iostream>
#include <iomanip>
#include <vector>
#include <set>
#include <string>
#include <queue>
#include <algorithm>
#include <map>
#include <cmath>
#include <list>
#include <stack>
#include <cstdio>
#include <cstdlib>
#include <cstring>

#define rep(i, n) for (int i = 0; i < n; i++)

using namespace std;
typedef vector<int> vi;
typedef pair<int, int> pii;

const int INF = 1 << 30;
const long long INFL = 1LL << 60;
const int MOD = 1000000007;
const int MAX = 100000;
const int N = 10000;

vector<pii> G[N];
long long d[N];

int main() {
	int n; cin >> n;
	rep(i, n) {
		int _, n2; cin >> _ >> n2;
		rep(j, n2) {
			int v, c; cin >> v >> c;
			G[i].push_back(pii(c, v));
		}
	}
	rep(i, n) d[i] = INFL;

	priority_queue<pii, vector<pii>, greater<pii>> Q;
	d[0] = 0;
	Q.push(pii(0, 0));
	while (!Q.empty()) {
		pii p = Q.top(); Q.pop();
		for (auto i : G[p.second]) {
			if (d[i.second] <= d[p.second] + i.first) continue;
			d[i.second] = d[p.second] + i.first;
			Q.push(i);
		}
	}
	rep(i, n) cout << i << ' ' << d[i] << endl;
}