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 <cstdint>
#include <queue>
#include <vector>

using namespace std;

#define GRAPH_SIZE 10000
#define WEIGHT_MAX UINT32_MAX

enum state_t { WHITE, GRAY, BLACK };

static state_t state[GRAPH_SIZE];
static priority_queue<pair<uint32_t, uint32_t>, vector<pair<uint32_t, uint32_t>>, greater<pair<uint32_t, uint32_t>>> min_queue;
static vector<pair<uint32_t, uint32_t>> graph[GRAPH_SIZE];
static uint32_t dist[GRAPH_SIZE];

void single_source_shortest_path(size_t num)
{
  for (uint32_t i = 0; i < num; i++) {
    // dist[i] = WEIGHT_MAX;
    state[i] = WHITE;
  }

  state[0] = GRAY;
  min_queue.push(make_pair(0, 0));

  while (!min_queue.empty()) {
    pair<uint32_t, uint32_t> vertex = min_queue.top();
    min_queue.pop();
    if (state[vertex.first] != BLACK) {
      state[vertex.first] = BLACK;
      dist[vertex.first] = vertex.first;

      for (uint32_t i = 0; i < graph[vertex.first].size(); i++) {
        pair<uint32_t, uint32_t> to = graph[vertex.first][i];
        if (state[vertex.first] != BLACK) {
          min_queue.push(make_pair(vertex.first, vertex.second + to.second));
          state[vertex.first] = GRAY;
        }
      }
    }
  }
}

#include <iostream>

int32_t main()
{
  uint32_t num;
  cin >> num;

  for (uint32_t i = 0; i < num; i++) {
    uint32_t index, len;
    cin >> index >> len;
    for (uint32_t j = 0; j < len; j++) {
      uint32_t connect, weight;
      graph[index].push_back(make_pair(connect, weight));
    }
  }

  single_source_shortest_path(num);

  for (uint32_t i = 0; i < num; i++) {
    cout << i << " " << dist[i] << endl;
  }

  return 0;
}

C++: #include <iostream>
#include <cstdio>
#include <vector>
#include <queue>
#define MAX 10000
#define INF (1<<30)

using namespace std;
enum state{
  BLACK,
  WHITE
};

int main(){
  vector<pair<int,int>> a[MAX];
  int n; cin>>n;
  int d[MAX];
  state s[MAX];

  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;
      a[u].push_back(make_pair(v,c));
    }
  }

  for(int i=0;i<n;i++){
    s[i]=WHITE;
    d[i]=INF;
  }
  d[0]=0;

  priority_queue<pair<int,int>> q;
  q.push(make_pair(0,0));

  while(!q.empty()){
    pair<int,int> p;
    p = q.top(); q.pop();
    if(s[p.second]==BLACK) continue;
    d[p.second]=p.first*-1;
    s[p.second]=BLACK;
    
    for(auto it = a[p.second].begin(); it!=a[p.second].end(); it++){
      int i = it->first;
      int cost = it->second;
      if(s[i]==WHITE && d[i] > d[p.second] + cost ){
        d[i]=d[p.second]+cost;
        q.push(make_pair(d[i]*-1,i));
      }
    }
  }
  
  for(int i=0;i<n;i++){
    printf("%d %d\n",i,d[i]);
  }


}

C++: #include <iostream>
#include <queue>
#include <utility>
#include <vector>

#define MAX_NODE 10000
#define INF 1000000000

using namespace std;

struct Edge {int to, w;};
typedef pair<int, int> PII;

vector<Edge> adj[MAX_NODE];
int d[MAX_NODE];

void dijkstra(int n, int start) {
	priority_queue<PII, vector<PII>, greater<PII>> que;
	fill(d, d + n, INF);

	d[start] = 0;
	que.emplace(0, start);
	while (!que.empty()) {
		PII p = que.top();
		que.pop();
		int from = p.second;

		if (d[from] < p.first)
			continue;

		for (auto& e : adj[from])
			if (d[from] + e.w < d[e.to]) {
				d[e.to] = d[from] + e.w;
				que.emplace(d[e.to], e.to);
			}
	}
}

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

	int n;

	cin >> n;

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

	dijkstra(n, 0);

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

	return 0;
}