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 <stdio.h>
#include <iostream>
#include <queue>
using namespace std;

class Vertice;
class Edge;

class Vertice{
private:
	int id;
	int edge_num;
	int *vertice_id_list;
	Edge **edges;
	bool flag_fixed;
	int distance_min;
public:
	Vertice(int id, int edge_num_max);
	~Vertice(){ delete[] edges, vertice_id_list; }
	int getDistanceMin() const { return distance_min; }
	void addEdge(int vertice_id, Edge *edge);
	void addVertices(Vertice *vertices[]);
	void setDistance(int d);
	void serveDistance();
	void setFlagFixed(){ flag_fixed = true; }
};

class Edge{
private:
	int distance;
	Vertice *vertice;
public:
	Edge(int distance){ this->distance = distance; }
	void addVertice(Vertice *vertice){ this->vertice = vertice; }
	void setDistance(int distance){ vertice->setDistance(distance + this->distance); }
};

struct verticeComp {
	bool operator()(const Vertice *v1, const Vertice *v2)
	{
		return v1->getDistanceMin() > v2->getDistanceMin();
	}
};

priority_queue<Vertice*, vector<Vertice*>, verticeComp> PQ; 

Vertice::Vertice(int id, int edge_num_max)
{
	this->id = id;
	edge_num = 0;
	vertice_id_list = new int[edge_num_max];
	edges = new Edge*[edge_num_max];
	flag_fixed = false;
	distance_min = 100000000;
}

void Vertice::addEdge(int vertice_id, Edge *edge)
{
	edges[edge_num] = edge;
	vertice_id_list[edge_num] = vertice_id;
	edge_num++;
}

void Vertice::addVertices(Vertice *vertices[])
{
	for (int i = 0; i < edge_num; i++) {
		edges[i]->addVertice(vertices[vertice_id_list[i]]);
	}
}

void Vertice::setDistance(int d)
{
	if (flag_fixed) return;
	if (d < distance_min) distance_min = d;
	PQ.push(this);
}

void Vertice::serveDistance()
{
	for (int i = 0; i < edge_num; i++) {
		edges[i]->setDistance(distance_min);
	}
	if (PQ.empty()) return;
	Vertice *fixed_vertice = PQ.top();
	PQ.pop();
	fixed_vertice->setFlagFixed();
	fixed_vertice->serveDistance();
}

int main(void)
{
	Vertice **vertices;

	int n;
	cin >> n;
	vertices = new Vertice*[n];
	for (int i = 0; i < n; i++) {
		int u, k;
		cin >> u >> k;
		vertices[u] = new Vertice(u, k);
		for (int j = 0; j < k; j++) {
			int v, c;
			cin >> v >> c;
			vertices[u]->addEdge(v, new Edge(c));
		}
	}

	for (int i = 0; i < n; i++) {
		vertices[i]->addVertices(vertices);
	}

	vertices[0]->setDistance(0);
	vertices[0]->setFlagFixed();
	PQ.pop();
	vertices[0]->serveDistance();

	for (int i = 0; i < n; i++) {
		cout << i << " ";
		cout << vertices[i]->getDistanceMin() << endl;
	}

	return 0;
}

C++: #include<iostream>
#include<vector>
#include<algorithm>
#include<queue>
#define N 100000
const int INF = 1 << 30; // > 10^9
int n;
using namespace std;
struct edge : vector<pair<int, int> > {
    void add_edge(int to, int cost) {
        push_back(pair<int, int>(to, cost));
    }
} info[N];
void bfs();
int hoge[N];
int main() {
    cin >> n;
    for (int i = 0; i < n; i++) {
        int u, k;
        cin >> u >> k;
        while (k--) {
            int v, c;
            cin >> v >> c;
            info[u].add_edge(v, c);
        }
    }
    bfs();
    for (int i = 0; i < n; i++) {
        cout << i << " " << hoge[i] << endl;
    }
}
void bfs() {
    fill_n(hoge, n, INF); //hoge ~ hoge + v <- INF
    queue<int> que;
    que.push(0);
    hoge[0] = 0;
    while (!que.empty()) {
        int p = que.front();
        que.pop();
        for (int i = 0; i < info[p].size(); i++) {
            if (info[p][i].second + hoge[p] < hoge[info[p][i].first]) {
                que.push(info[p][i].first);
                hoge[info[p][i].first] = info[p][i].second + hoge[p];
            }
        }
    }
    
}

C++: #define RangeFor(i,n) for(int i=0; i<n; ++i)
#define RvRngFor(i,n) for(int i=n-1; i>=0; --i)

#include <iostream>
#include <vector>
#include <queue>
#include <utility>
#include <numeric>

using std::vector;
using std::cin;
using std::priority_queue;
using std::pair;
using std::make_pair;


vector<int> sssp(vector<vector<pair<int, int> > > c, int start_node = 0){
    int n = c.size();
    priority_queue<pair<int, int>, vector<pair<int,int> >, std::greater<pair<int, int>> > pq;
    vector<int> temp_dist(n, std::numeric_limits<int>::max());
    pq.push(make_pair(0, start_node));

    for(;!pq.empty();pq.pop()){
        auto t = pq.top();
        auto d = t.first;
        auto u = t.second;


        if(d < temp_dist[u]){
            temp_dist[u] = d;
            auto k = c[u].size();
            RangeFor(j, k) {
                pq.push(make_pair(d + c[u][j].second, c[u][j].first));
            }
        }
    }

    return temp_dist;
}

int main(){
    int n; cin >> n;
    vector<vector< pair<int,int> > > c(n);
    RangeFor(i, n) {
        int u;
        cin >> u;
        int k;
        cin >> k;
        c[u] = vector<pair<int, int> >(k);
        RangeFor(j, k) {
            int v;
            cin >> v;
            int d;
            cin >> d;
            c[u][j] = make_pair(v, d);
        }
    }

//    RangeFor(i, n){
//        RangeFor(j, c[i].size()){
//            std::cout << c[i][j].first << ' ' << c[i][j].second;
//        }
//        std::cout << std::endl;
//    }

    auto res = sssp(c);
    RangeFor(i, n){
        std::cout << i << ' ' << res[i] << std::endl;
    }
    return 0;
}