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++: //
//  main.cpp
//
//
//  Created by ???????????? on 2017/10/23.
//  Copyright ?? 2017 ????????????. All rights reserved.
//

#include <iostream>
#include <stdio.h>
#include <queue>
#include <algorithm>


#define n_max 100
#define WHITE 0
#define GRAY 1
#define BLACK 2
#define INFTY (1<<20)

using namespace std;

int n, M[n_max][n_max], color[n_max], d[n_max], p[n_max];

void init(){
    int i, j, id, num, node;
    scanf("%d", &n);
    for(i = 0; i < n; i++){
        for(j = 0; j < n; j++){
            M[i][j] = INFTY;
        }
    }
    
    
    for(i = 0; i < n; i++){
        scanf("%d %d", &id, &num);
        for(j = 0; j < num; j++){
            scanf("%d", &node);
            scanf("%d", &M[id][node]);
        }
        color[i] = WHITE;
        d[i] = INFTY;
    }
}

void dijkstra(){
    //initializing
    d[0] = 0;
    p[0] = -1;
    
    priority_queue<pair<int, int>> PQ;
    
    PQ.push(make_pair(0, 0));
    
    int u;
    while(!PQ.empty()){
        int mincost = INFTY;
        //first weight, second idx
        pair<int, int> f= PQ.top(); PQ.pop();
        u = f.second;
        color[u] = BLACK;
        
        if(d[u] < f.first*(-1)) continue;
        
        for(int v = 0; v < n; v++){
            if((color[v] != BLACK) && (M[u][v] != INFTY)){
                if((d[u] + M[u][v]) < d[v]){
                    d[v] = M[u][v] + d[u];
//                    p[v] = u;
                    PQ.push(make_pair(d[v]*(-1), v));
                    color[v] = GRAY;
                }
            }
        }
    }
    for(int i = 0; i < n; i++){
        cout<<i<<" "<<d[i]<<endl;
    }
}

int main(int argc, const char * argv[]) {
    init();
    dijkstra();
    //    std::cout << "Hello, World!\n";
    return 0;
}

C++: #include<iostream>
#include<cstring>
#include<algorithm>
using namespace std;

int x[10000][2000];
int x2[10000][2000];
int y[10000];
int z[10000];

int main() {
	memset(x, 1, sizeof(x));
	memset(y, 1, sizeof(y));
	int n, a, b, c, d;
	cin >> n;
	for (int i = 0; i < n; i++) {
		cin >> a >> b;
		for (int i = 0; i < b; i++) {
			cin >> c >> d;
			x[a][z[a]] = c;
			x2[a][z[a]] = d;
			z[a]++;
		}
	}
	y[0] = 0;
	for (int i = 0; i < n; i++) {
		for (int j = 0; j < n; j++) {
			for (int k = 0; k < z[j]; k++) {
				y[x[j][k]] = min(y[x[j][k]], y[j] + x2[j][k]);
			}
		}
	}
	for (int i = 0; i < n; i++) {
		cout << i << ' ' << y[i] << endl;
	}
	return 0;
}

C++: #include <iostream>
#include <vector>
#include <utility>
#include <queue>
#define INF 10000000
#define MAX 10000
using namespace std;

// ====== Implement of Heap ======
int heap[2000000]={INF};
int eoh=1;

void minHeapify(int* A, int i){
  int h = eoh-1;
  int l = 2*i;
  int r = 2*i+1;
  int smallest;
  if ( l <= h && A[l] < A[i] )
    smallest = l;
  else
    smallest = i;

  if ( r<= h && A[r] < A[smallest])
    smallest = r;

  if (smallest != i){
    swap(A[i], A[smallest]);
    minHeapify(A, smallest);
  }
}

void insert(int v, int p=-1){
  if (p == -1){
    p = eoh++;
    heap[p] = v;
    insert(v, p);
    return;
  }
  if (p == 1)
    return;
  int parent = heap[p/2];
  if (parent < v)
    return;
  swap(heap[p/2], heap[p]);
  insert(v, p/2);
}

int del(void){
  if (eoh == 1)
    return -1;
  int res = heap[1];
  heap[1] = heap[eoh-1];
  eoh--;
  minHeapify(heap, 1);
  return res;
}
// ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 

// ====== Implement of List Structure ======
struct Node {
    int to, cost;
    struct Node * next;
};

typedef struct Node * NodePointer;

NodePointer NIL;

NodePointer makeNode(int to, int cost){
    NodePointer newNode = (NodePointer)malloc(sizeof(struct Node));
    newNode->to = to;
    newNode->cost = cost;
    newNode->next = NIL;
    return newNode;
}

NodePointer insert(NodePointer head, int to, int cost){
    NodePointer ite, newNode;
    for (ite=head;ite->next!=NIL;ite=ite->next);
    newNode = makeNode(to, cost);
    ite->next = newNode;
    return newNode;
}


// decl vals
int dist[MAX];

void dijkstraAlgorithm(NodePointer vertex[], int n){
  auto compare = [=](int i, int j){return dist[i] >= dist[j];};
  priority_queue<int, vector<int>,  decltype(compare)> searchQueue {compare}; 

  // Initialize of distance, previous and Push all of vectex to queue 
  dist[0] = 0;
  for (int i=0;i<n;i++){
    if (i!=0) dist[i] = INF;
    searchQueue.push(i);
  }

  while(!searchQueue.empty()){
    int current = searchQueue.top();
    NodePointer ite;
    searchQueue.pop();
    for (ite=vertex[current]->next;ite!=NIL;ite=ite->next){
      int alt = dist[current]+ite->cost;
      if ( dist[ite->to] > alt ){
        dist[ite->to] = alt;
        searchQueue.push(ite->to);
      }
    }
  }
}

int main(){
  NodePointer vertex[MAX];
  int i, n;
  cin >> n;
  NIL = makeNode(0, 0);
  for(i=0;i<n;++i) vertex[i] = makeNode(-1,INF);
  
  for (int i=0;i<n;++i){
    int id, k;
    scanf("%d%d", &id, &k);
    for (int j=0;j<k;++j){
      int node, cost;
      scanf("%d%d", &node, &cost);
      insert(vertex[id], node, cost);
    }
  }

  dijkstraAlgorithm(vertex, n);

  for (int i=0;i<n;++i){
    cout << i << " " << dist[i] << endl;
  }

  return 0;
}