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 <queue>
#include <vector>

using namespace std;

#define MAX_V 10000
#define INF 1e9

struct edge{ int to,cost; };
typedef pair<int,int> P;

int V;
vector<edge> G[MAX_V];
int dist[MAX_V];

void dijkstra(){
  priority_queue<P, vector<P>, greater<P> > Q;
  fill(dist,dist+V,INF);
  dist[0] = 0;
  Q.push(P(0,0));

  while(!Q.empty()){
    P p = Q.top(); Q.pop();
    int v = p.second;

    if(dist[v] < p.first){
      continue;
    }

    for(int i = 0 ; i < (int)G[v].size() ; i++){
      edge e = G[v][i];
      
      if(dist[e.to] > dist[v] + e.cost){
	dist[e.to] = dist[v] + e.cost;
	Q.push(P(dist[e.to],e.to));
      }
    }

  }
}

int main(){
  cin >> V;
 
  for(int i = 0 ; i < V ; i++){
    int u,k;

    cin >> u >> k;
    for(int j = 0 ; j < k ; j++){
      int v,c;

      cin >> v >> c;

      edge e = {v,c};
      G[u].push_back(e);
    }
  }

  dijkstra();
  for(int i = 0 ; i < V ; i++){
    cout << i << " " << dist[i] << endl;
  }

  return 0;
}

C++: #include<iostream>
#include<cstdio>
#define INF 1<<30
#define FinishFunction return 0
#define MAX 1000000
using namespace std;
     
struct edge {
  int from,to,cost,k;
};
   
edge es[MAX];
   
int main(){
  int n,u,k,E,c,v;
  E = 0;
  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);
      es[E].from = u;
      es[E].to = v;
      es[E++].cost = c;
    }
  }
   
  // Ika berumanfo-do  
  int d[MAX];
  for(int i=0;i<n;i++)d[i] = INF;
  d[0] = 0;
  while(true){
    bool update = false;
    for(int i=0;i<E;i++){
      edge e = es[i];
      if(d[e.from] != INF && d[e.to] > d[e.from] + e.cost){
    d[e.to] = d[e.from] + e.cost;
    update = true;
      }
    }
    if(!update)break;
  }
  for(int i=0;i<n;i++)cout << i << " " << d[i] << endl;
  FinishFunction;// return 0
}

C++: #include<iostream>
#include<algorithm>
#include<vector>
#include<stack>
#include<queue>
#include<list>
#include<string>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<cmath>
using namespace std;

const int NIL = -1;
const int MAX = 1 << 21;

int color[10001], d[10001];

struct Node {
	int node, weight;
};
vector<Node>M[10001];

struct cmp {
	bool operator () (Node a, Node b)
	{
		return a.weight > b.weight;
	}
};

int next(int u) {
	for (int i = 0; i < M[u].size(); i++) {
		if (color[M[u][i].node] == 0) {
			color[M[u][i].node] = 1;
			return i;
		}
	}
	return -1;
}

int main(void)
{
	int n, u, k, v, c;
	priority_queue<Node, vector<Node>, cmp>PQ;
	Node s;
	cin >> n;
	for (int i = 0; i < n; i++) {
		cin >> u >> k;
		for (int j = 0; j < k; j++) {
			cin >> v >> c;
			s.node = v;
			s.weight = c;
			M[u].push_back(s);
		}
	}
	for (int i = 0; i < n; i++) {
		color[i] = 0;
		d[i] = MAX;
	}
	d[0] = 0;
	s.node = s.weight = 0;
	PQ.push(s);
	while (!PQ.empty()) {
		Node u = PQ.top();
		PQ.pop();
		color[u.node] = 2;
		for (int i = 0; i < n; i++) {
			if (color[i] != 2)
				color[i] = 0;
		}
		if (d[u.node] < u.weight)
			continue;
		while ((v = next(u.node)) != NIL) {
			int tmp = M[u.node][v].node;
			if (color[tmp] != 2) {
				if (d[u.node] + M[u.node][v].weight < d[tmp]) {
					d[tmp] = M[u.node][v].weight + d[u.node];
					s.node = tmp;
					s.weight = d[tmp];
					PQ.push(s);
				}
			}
		}
	}
	for (int i = 0; i < n; i++) {
		cout << i << " " << d[i] << endl;
	}
	return 0;
}

C++: #include <bits/stdc++.h>
using namespace std;

typedef long long ll;

struct Edge {
    ll t,w;
};

struct State {
    ll v;
    ll score;
    bool operator < (const State& tgt) const {
	return score > tgt.score;
    }
};

vector<ll> dijkstra(vector<vector<Edge>>& G, const int start) {
    const ll V = G.size();

    vector<ll>res(V,INT_MAX);
    priority_queue<State> q;
    q.push( State{0,0} );
    while( q.size() ) {
	State s = q.top(); q.pop();
	if( res[s.v] != INT_MAX ) continue;
	res[s.v] = s.score;
	for(auto& e : G[s.v]) {
	    if( res[e.t] != INT_MAX ) continue;
	    q.push( State{e.t, s.score + e.w} );
	}
    }
    return res;
}


int main () {

    ll V; cin >> V;
    vector<vector<Edge>> G(V);
    for(int i=0; i<V; i++) {
	ll u,k; cin >> u >> k;
	for(int j=0; j<k; j++) {
	    ll v,w; cin >> v >> w;
	    G[i].push_back( Edge{v,w} );
	}
    }
    vector<ll> res = dijkstra(G,0);
    for(int i=0; i<V; i++) {
	cout << i << " " << res[i] << endl;
    }    
    return 0;
}

C++: #include <bits/stdc++.h>
using namespace std;

typedef pair<int, int> P;

struct Edge {
  int to, cost;
};

int n;
vector<vector<Edge> > G;

vector<int> dij() {
  priority_queue<P, vector<P>, greater<P> > Q;
  vector<int> d(n, -1);
  Q.push({0, 0});
  while ( !Q.empty() ) {
    P p = Q.top(); Q.pop();
    int v = p.second, c = p.first;

    if ( d[v] >= 0 ) continue;
    d[v] = c;
    
    for ( Edge e: G[v] ) {
      Q.push({c+e.cost, e.to});
    }    
  }

  return d;
}

int main() {
  cin >> n;

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

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