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<cstdio>
#include<queue>
#include<vector>
#include<algorithm>
static const int kMaxVertices = 10000;
static const int kInfinity = 100010;
using namespace std;

void Dijkstra(int n, vector<pair<int, int> > Adjacency_list[], int first_vertex){
	bool has_not_been_added[kMaxVertices];
	int distance[kMaxVertices];
	for (int i = 0; i < n; ++i)	{
		has_not_been_added[i] = true;
		distance[i] = kInfinity;
	}
	distance[first_vertex] = 0;

	priority_queue<pair<int, int>, vector<pair<int, int> >, greater<pair<int, int> > > PQ;
	PQ.push(make_pair(0, first_vertex));

	while(!PQ.empty()){
		pair<int, int> f = PQ.top(); PQ.pop();
		int u = f.second;
		has_not_been_added[u] = false;
		if (distance[u] < f.first) continue;
		for(vector<pair<int, int> >::iterator it = Adjacency_list[u].begin(); it != Adjacency_list[u].end(); it++){
			int v = (*it).second;
			if(has_not_been_added[v] && distance[u] + (*it).first < distance[v]){
				distance[v] = distance[u] + (*it).first;
				PQ.push(make_pair(distance[v], v));
			}
		}
	}
	for (int i = 0;i < n;++i)
		printf("%d %d\n", i, distance[i]);
}

int main(){
	int number_of_vertices;
	scanf("%d", &number_of_vertices);
	vector<pair<int, int> > Adjacency_list[number_of_vertices];
	for (int vertex_from_i = 0; vertex_from_i < number_of_vertices; ++vertex_from_i)	{
		int vertex_from_id, degree_out;
		scanf("%d %d", &vertex_from_id, &degree_out);
		for (int vertex_to_i = 0; vertex_to_i < degree_out; ++vertex_to_i){
			int vertex_to_id, cost_of_route;
			scanf("%d %d", &vertex_to_id, &cost_of_route);
			Adjacency_list[vertex_from_id].push_back(make_pair(cost_of_route, vertex_to_id));
		}
	}
	Dijkstra(number_of_vertices, Adjacency_list, 0);
	return 0;
}

C++: #include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < n; i++)

const int INF = 1e8;

int n, m; // 頂点の数、辺の数

struct edge {int from, to, cost;}; // 辺の始点・終点・重み

vector<vector<int>> adj_matrix; // 隣接行列
vector<vector<edge>> adj_list; // 隣接リスト

vector<int> dist;
vector<bool> visited;

void dijkstra(int start) {
    dist.resize(n);
    visited.resize(n);
    rep(i, n) {
        if (i == start) dist[i] = 0;
        else dist[i] = INF;
        visited[i] = false;
    }
    priority_queue<pair<int,int>, vector<pair<int,int>>, greater<pair<int,int>>> pq;
    pq.push({dist[start], start});
    while (not pq.empty()) {
        int cur = pq.top().second;
        pq.pop();
        visited[cur] = true;
        for (edge e : adj_list[cur]) {
            // int adj = e.to;
            if (visited[e.to] == false) {
                if (dist[e.to] > dist[e.from] + e.cost) {
                    dist[e.to] = dist[e.from] + e.cost;
                    pq.push({dist[e.to], e.to});
                }
            }
        }
    }
}

void solve_ALDS1_12_C() {
    cin >> n;
    adj_list.resize(n);
    rep(i, n) {
        int u, k;
        cin >> u;
        cin >> k;
        rep(j, k) {
            edge e;
            e.from = u;
            cin >> e.to;
            cin >> e.cost;
            adj_list[e.from].push_back(e);
        }
    }
    dijkstra(0);
    rep(i, n) {
        cout << i << " " << dist[i] << endl;
    }
}

int main() {
    // cin >> n;
    // cin >> m;
    // adj_matrix.resize(n, vector<int>(n, INF));
    // rep(i, n) {
    //     adj_matrix[i][i] = 0;
    // }
    // adj_list.resize(n);
    // rep(i, m) {
    //     edge e;
    //     cin >> e.from;
    //     cin >> e.to;
    //     cin >> e.cost;
    //     adj_matrix[e.from][e.to] = e.cost;
    //     adj_list[e.from].push_back(e);
    // }
    solve_ALDS1_12_C();
}

C++: #include <bits/stdc++.h>
#define FOR(i,a,b) for (int i=(a);i<(b);i++)
#define RFOR(i,a,b) for (int i=(b)-1;i>=(a);i--)
#define REP(i,n) for (int i=0;i<(n);i++)
#define RREP(i,n) for (int i=(n)-1;i>=0;i--)
#define INF INT_MAX/3
#define SORT(v, n) sort(v, v+n);
#define VSORT(v) sort(v.begin(), v.end());
#define llong long long
#define pb(a) push_back(a)
using namespace std;
typedef pair<int, int> P;
typedef pair<llong, llong> LP;
typedef pair<int, P> PP;
typedef pair<llong, LP> LPP;

int dy[]={0, 0, 1, -1, 0};
int dx[]={1, -1, 0, 0, 0};

#define MAX_N 10000
int G[MAX_N][MAX_N];
int MIN_COSTS[MAX_N];

int main() {
  int n;
  cin >> n;
  REP(i, n) {
    REP(j, n) {
      G[i][j] = INT_MAX;
    }
    MIN_COSTS[i] = INT_MAX;
  }
  int u, k;
  int v, c;
  REP(i, n) {
    cin >> u >> k;
    REP(j, k) {
      cin >> v >> c;
      G[u][v] = c;
    }
  }

  priority_queue<P> q;
  int position;
  int new_cost;
  q.push(P(0, 0));
  while (q.size() != 0){
    position = q.top().first;
    MIN_COSTS[position] = q.top().second;
    q.pop();
    REP(i, n) {
      if (G[position][i] != INT_MAX) {
        new_cost = MIN_COSTS[position] + G[position][i];
        if (new_cost < MIN_COSTS[i]) {
          MIN_COSTS[i] = new_cost;
          q.push(P(i, new_cost));
        }
      }
    }
  }

  REP(i, n) {
    cout << i << ' ' << MIN_COSTS[i] << endl;
  }

  return 0;
}