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 <iostream>
#include <algorithm>
#include <vector>
#include <deque>
#include <queue>
#include <list>
#include <stack>
#include <string>
#include <tuple>
#include <functional>
#include <numeric>
#include <cmath>
#include <iomanip>
#include <map>
#include <random>
#include <cstdlib>
#define INT_MAX 2147483647
#define INT_MIN -2147483646
#define Loop(i, n) for(int i = 0; i < (int)n; i++)
#define Loop1(i, n) for(int i = 1; i <= (int)n; i++)
#define Loopr(i, n) for(int i = (int)n - 1; i >= 0; i--)
#define Loopr1(i, n) for(int i = (int)n; i >= 1; i--)
using namespace std;
typedef long long int ll;
typedef vector<int> vi;
typedef vector<vector<int>> vvi;
void fastios() { ios_base::sync_with_stdio(0); cin.tie(0); }

static const int N = 10005;

struct vertex {
	int id;
	int p;
	int d;
	bool operator<(const vertex & another) const {
		return (d != another.d ? d>another.d : id>another.id);
	}
};

struct edge {
	int end;
	int w;
};

int main() {
	fastios();
	int n;
	cin >> n;
	vector<vector<edge>> E(N);
	Loop(i, n) {
		int u, k;
		cin >> u >> k;
		Loop(i, k) {
			int v, c;
			cin >> v >> c;
			E[u].push_back({ v,c });
		}
	}
	//
	priority_queue<vertex> pq;
	vi color(N, 0), dist(N, 0);
	pq.push({ 0,-1,0 });
	int cnt = 0;
	while (pq.size() > 0) {
		if (cnt == n) break;
		vertex v = pq.top();
		pq.pop();
		if (color[v.id] == 1) continue;
		dist[v.id] = v.d;
		color[v.id] = 1;
		cnt++;
		Loop(j, E[v.id].size()) {
			pq.push({ E[v.id][j].end, v.id, dist[v.id] + E[v.id][j].w });
		}
	}
	Loop(i, n) {
		cout << i << " " << dist[i] << endl;
	}
	return 0;
}

C++: #include <iostream>
#include <iomanip>
#include <algorithm>
#include <cfloat>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <functional>
#include <sstream>
#include <string>
#include <utility>
#include <map>
#include <memory>
#include <set>
#include <vector>
#include <deque>
#include <list>
#include <stack>
#include <queue>

using namespace std;

class SSSPath
{
public:
  int solve();
};

int SSSPath::solve()
{
  int n;
  cin >> n;

  vector<vector<pair<int, int>>> adj( n );

  for ( auto i = 0; i < n; ++i )
    {
      int k, u, v, w;

      cin >> u >> k;

      for ( auto j = 0; j < k; ++j )
        {
          cin >> v >> w;
          adj[u].push_back( make_pair( v, w ) );
        }
    }

  const int infty = 2000000000;
  
  vector<int> d( n, infty );
  vector<bool> vs( n, true );
  
  d[0] = 0;

  while ( true )
    {
      int u, mc = infty;

      for ( auto i = 0; i < n; ++i )
        {
          if ( vs[i] && d[i] < mc )
            {
              mc = d[i];
              u = i;
            }
        }

      if ( mc == infty ) break;
      
      vs[u] = false;

      for ( auto it = adj[u].begin(); it != adj[u].end(); ++it )
        {
          if ( d[(*it).first] > d[u] + (*it).second )
            {
              d[(*it).first] = d[u] + (*it).second;
            }
        }
    }

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

int main()
{
  SSSPath s;

  s.solve();

  return 0;
}

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

#define MAX 10000
#define INF (1<<20)
#define WHITE 0
#define GRAY 1
#define BLACK 2

int n;
vector<pair<int,int> > adj[MAX];

void dijkstra(int s){
    priority_queue<pair<int,int> > PQ;
    int d[MAX], color[MAX];

    rep(i,n){
        color[i] = WHITE;
        d[i] = INF;
    }

    d[s] = 0;
    PQ.push(make_pair(0, s));

    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 i = 0; i < adj[u].size(); i++){
            int v = adj[u][i].first;
            int c = adj[u][i].second;
            if(color[v] == BLACK) continue;
            if(d[v] > d[u] + c){
                d[v] = d[u] + c;
                PQ.push(make_pair((-1)*d[v], v));
            }
        }
    }

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

int main(){
    cin >> n;
    int u, k, v, c;
    rep(i,n){
        cin >> u >> k;
        rep(j,k){
            cin >> v >> c;
            adj[u].push_back(make_pair(v, c)); 
        }
    }

    dijkstra(0);

    return 0;
}