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 <vector>
#include <cassert>

using size_t = std::size_t;

template<class id_type>
class Graph{
public:
  using vertex_type = size_t;
  struct Edge{
    vertex_type to;
    id_type id;
  };

  struct Edge_Pair{
    vertex_type from;
    vertex_type to;
    id_type id;
  };
private:
  std::vector<vertex_type> ver;
  std::vector<Edge_Pair> edges;
  std::vector<std::vector<Edge>> G;
  std::vector<std::vector<Edge>> rG;
public:
  Graph(size_t sz) : ver(sz) , G(sz) , rG(sz){
    for(size_t i = 0;i < ver.size();i++) ver[i] = i;
  }

  const std::vector<vertex_type>& V() const{
    return ver;
  }

  const std::vector<Edge_Pair>& E() const{
    return edges;
  }

  void add_edge(const Edge_Pair& e){
    edges.push_back(e);
    G[e.from].push_back({e.to,e.id});
    rG[e.to].push_back({e.from,e.id});
  }

  void add_edge(vertex_type from,vertex_type to,id_type id){
    add_edge({from,to,id});
  }

  Graph operator+=(const Edge_Pair& e){
    add_edge(e);
    return *this;
  }


  const std::vector<Edge>& delta_p(vertex_type v) const{
    return G[v];
  }

  const std::vector<Edge>& delta_m(vertex_type v) const{
    return rG[v];
  }

  const std::vector<Edge>& operator[](vertex_type v) const{
    return this->delta_p(v);
  }
};

#include <set>
#include <queue>
#include <functional>

template<class dist_type,class id_type>
std::vector<dist_type> dijkstra(const Graph<id_type>& g,std::function<dist_type(id_type)> cost,size_t s,dist_type init,dist_type INF){
    using vt = typename Graph<id_type>::vertex_type;
    using P = std::pair<dist_type,vt>;
    std::vector<dist_type> dist(g.V().size(),INF);
    dist[s] = init;

    std::priority_queue<P,std::vector<P>,std::greater<P>> que;

    que.push({dist[s],s});

    while(!que.empty()){
      vt v = que.top().second;
      dist_type d = que.top().first;
      que.pop();
      if(dist[v] < d) continue;
      for(const auto & e : g.delta_p(v)){
        if(dist[e.to] > dist[v] + cost(e.id)){
          dist[e.to] = dist[v] + cost(e.id);
          que.push({dist[e.to],e.to});
        }
      }
    }

    return dist;
}

#include <bits/stdc++.h>
using namespace std;
using i64 = long long;
#define rep(i,s,e) for(int (i) = (s);(i) <= (e);(i)++)
#define all(x) x.begin(),x.end()

int main(){
  int n;
  cin >> n;
  Graph<size_t> g(n);
  vector<i64> cost;
  for(int i = 0;i < n;i++){
    size_t u,t;
    cin >> u >> t;
    for(int j = 0;j < t;j++){
      size_t v;
      i64 c;
      cin >> v >> c;
      g.add_edge(u,v,cost.size());
      cost.push_back(c);
    }
  }

  auto res = dijkstra<i64,size_t>(g,[&](size_t id)->i64{return cost[id];},0UL,0LL,(i64)1e9);
  for(int i = 0;i < n;i++){
    cout << i << " " << res[i] << endl;
  }
}

C++: #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]; // 重み付き有向グラフの隣接リスト表現

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;
        
        // 最小値を取り出し、それが最短でなければ無視
        if (d[u] < f.first * (-1)) continue;
        
        for (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はデフォルトで大きい値を優先するため-1をかける
                PQ.push(make_pair(d[v]*(-1), v));
                color[v] = GRAY;
            }
        }
    }
    
    for (int i=0; i<n; i++) {
        printf("%d %d\n", i, d[i]);
    }
}

int main() {
    int k, u, v, c;
    
    scanf("%d", &n);
    for (int i=0; i<n; i++) {
        scanf("%d %d", &u, &k);
        for (int j=0; j<k; j++) {
            scanf("%d %d", &v, &c);
            adj[u].push_back(make_pair(v, c));
        }
    }
    
    dijkstra();
    
    return 0;
}