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 <climits>
#include <functional>
#include <iostream>
#include <queue>
#include <utility>
#include <vector>
using namespace std;

int main() {
	int n, u, k, v, c;
	cin >> n;
	vector<vector<pair<int, int>>> a(n);
	for (int i = 0; i < n; ++i) {
		cin >> u >> k;
		for (int j = 0; j < k; ++j) {
			cin >> v >> c;
			a[u].emplace_back(v, c);
		}
	}
	priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> b;
	b.emplace(0, 0);
	vector<bool> d(n);
	vector<int> e(n, INT_MAX);
	e[0] = 0;
	while (!b.empty()) {
		pair<int, int> f = b.top();
		b.pop();
		d[f.second] = true;
		for (int i = 0; i < a[f.second].size(); ++i) {
			if (!d[a[f.second][i].first]) {
				if (a[f.second][i].second + e[f.second] < e[a[f.second][i].first]) {
					e[a[f.second][i].first] = a[f.second][i].second + e[f.second];
					b.emplace(e[a[f.second][i].first], a[f.second][i].first);
				}
			}
		}
	}
	for (int i = 0; i < n; ++i) cout << i << ' ' << e[i] << endl;
}

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

#define INF 100000000

typedef struct state {
  int pos, cost;
} state;

state A[2000001];
int N = 0;

int parent (int i) { return i/2;}
int left ( int i) {return i * 2;}
int right ( int i ) {return i * 2 + 1;}

void swap( state* a, state* b ) {
  state tmp = *a;
  *a = *b;
  *b = tmp;
}

void minHeapify ( int i ) {
  int l = left(i);
  int r = right(i);
  int small;

  if ( l <= N && A[l].cost < A[i].cost ) small = l;
  else small = i;

  if ( r <= N && A[r].cost < A[small].cost ) small = r;

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

state heapExtractMin() {
  if ( N < 1 ) return (state) {0,0};
  state min = A[1];
  A[1] = A[N];
  N--;
  minHeapify(1);
  return min;
}

void heapIncreaseKey( int i , state key ) {
  if ( key.cost > A[i].cost) return;

  A[i] = key;
  while ( i > 1 && A[parent(i)].cost > A[i].cost ) {
    swap( &A[i], &A[parent(i)]);
    i = parent(i);
  }
}

void minHeapInsert( state key ) {
  N++;
  A[N] = (state) { INF, INF };
  heapIncreaseKey(N, key);
}

typedef struct edge{
  int to,cost;
} edge;

edge* G[10000];
int size[10000];
int n;
int d[10000];
edge e;
state s;

int main() {
  int a,b;
  cin >> n;
  for ( int i = 0; i < n; i++ ) {
    cin >> a >> b;
    G[a] = (struct edge*)malloc( sizeof(edge )*b );
    size[a] = b;
    for ( int j = 0; j < b; j++ ) {
      cin >> G[a][j].to >> G[a][j].cost;
    }
    d[i] = INF;
  }
  d[0] = 0;
  minHeapInsert ( (state{0,0} ) );
  while(N!=0) {
    s = heapExtractMin();
    if ( s.cost > d[s.pos]) continue;
    for ( int i = 0; i < size[s.pos]; i++ ) {
      e = G[s.pos][i];
      if ( d[e.to] <= d[s.pos] + e.cost ) continue;
      d[e.to] = d[s.pos] + e.cost;
      minHeapInsert((state){e.to,d[e.to]});
    }
  }
  for ( int i = 0; i < n; i++ ) {
    cout << i << " " << d[i] << endl;
  }
}

C++: #include <algorithm>
#include <iostream>
#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];

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;

    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;
        PQ.push(make_pair(d[v] * (-1), v));
        color[v] = GRAY;
      }
    }
  }

  for (int i = 0; i < n; i++) {
    cout << i << " " << (d[i] == INFTY ? -1 : d[i]) << endl;
  }
}

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

  dijkstra();

  return 0;
}