Go: package main

import (
	"bufio"
	"container/heap"
	"fmt"
	"os"
	"strconv"
)

// I/O
type Scanner struct {
	sc *bufio.Scanner
}

func NewScanner() *Scanner {
	sc := bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)
	sc.Buffer(make([]byte, 1024), int(1e+9))
	return &Scanner{sc}
}

func (s *Scanner) nextStr() string {
	s.sc.Scan()
	return s.sc.Text()
}

func (s *Scanner) nextInt() int {
	i, e := strconv.Atoi(s.nextStr())
	if e != nil {
		panic(e)
	}
	return i
}

func (s *Scanner) nextFloat() float64 {
	f, e := strconv.ParseFloat(s.nextStr(), 64)
	if e != nil {
		panic(e)
	}
	return f
}

func (s *Scanner) nextRuneSlice() []rune {
	return []rune(s.nextStr())
}

func (s *Scanner) nextIntSlice(n int) []int {
	res := make([]int, n)
	for i := 0; i < n; i++ {
		res[i] = s.nextInt()
	}
	return res
}

func (s *Scanner) nextFloatSlice(n int) []float64 {
	res := make([]float64, n)
	for i := 0; i < n; i++ {
		res[i] = s.nextFloat()
	}
	return res
}

// Arithmetic
func max(nums ...int) int {
	m := nums[0]
	for _, i := range nums {
		if m < i {
			m = i
		}
	}
	return m
}

func min(nums ...int) int {
	m := nums[0]
	for _, i := range nums {
		if m > i {
			m = i
		}
	}
	return m
}

func abs(x int) int {
	if x > 0 {
		return x
	}
	return -x
}

func pow(x, y int) int {
	res := 1
	for i := 0; i < y; i++ {
		res *= x
	}
	return res
}

func ceil(a, b int) int {
	if a%b == 0 {
		return a / b
	} else {
		return a/b + 1
	}
}

// Sort
type RuneSlice []rune

func (a RuneSlice) Len() int           { return len(a) }
func (a RuneSlice) Less(i, j int) bool { return a[i] < a[j] }
func (a RuneSlice) Swap(i, j int)      { a[i], a[j] = a[j], a[i] }

// Main
const INF = 1 << 60

type Edge struct {
	to, cost int
}

type Node struct {
	id, cost int
}

type PQ []Node

func (pq PQ) Len() int           { return len(pq) }
func (pq PQ) Less(i, j int) bool { return pq[i].cost < pq[j].cost }
func (pq PQ) Swap(i, j int)      { pq[i], pq[j] = pq[j], pq[i] }

func (pq *PQ) Push(x interface{}) {
	*pq = append(*pq, x.(Node))
}

func (pq *PQ) Pop() interface{} {
	old := *pq
	n := len(old)
	x := old[n-1]
	*pq = old[0 : n-1]
	return x
}

func main() {
	sc := NewScanner()
	wtr := bufio.NewWriter(os.Stdout)
	N := sc.nextInt()
	E := make([][]Edge, N)
	for i := 0; i < N; i++ {
		id, k := sc.nextInt(), sc.nextInt()
		E[id] = make([]Edge, k)
		for j := 0; j < k; j++ {
			to, cost := sc.nextInt(), sc.nextInt()
			E[id][j] = Edge{to, cost}
		}
	}

	d := make([]int, N)
	for i := 0; i < N; i++ {
		d[i] = INF
	}
	done := make([]bool, N)
	pq := &PQ{}
	heap.Init(pq)
	d[0] = 0
	heap.Push(pq, Node{0, 0})
	for pq.Len() > 0 {
		cur := heap.Pop(pq).(Node).id
		if done[cur] {
			continue
		}
		done[cur] = true
		for i := 0; i < len(E[cur]); i++ {
			to, cost := E[cur][i].to, E[cur][i].cost+d[cur]
			if !done[to] && cost < d[to] {
				d[to] = cost
				heap.Push(pq, Node{to, cost})
			}
		}
	}

	for i := 0; i < N; i++ {
		fmt.Fprintln(wtr, i, d[i])
	}
	wtr.Flush()
}

C++: #include <stdio.h>
#include <stdint.h>
#include <iostream>
#include <fstream>
#include <cassert>
#include <climits>

#include <memory>
#include <queue>
using namespace std;

#define DEBUG (0)

#if DEBUG
#define DPRINTF(...) do { \
    printf("D(L%d) %s: ", __LINE__, __func__); \
    printf(__VA_ARGS__); \
  } while (false)
#else
#define DPRINTF(...)
#endif // DEBUG


const int kMaxVertex = 10000;
int g_num_of_vertex;
int g_min_weight[kMaxVertex];

struct Edge {
    Edge(int num_vertex)
        : num_vertex_(num_vertex)
    {
        const int size_of_ptr_ = num_vertex_ * num_vertex_;
        weight_ = unique_ptr<int>(new int[size_of_ptr_]);

        for (int i = 0; i < num_vertex_; i++)
            for (int j = 0; j < num_vertex_; j++)
                setWeight(i, j, kInvalidWeight);

        for (int i = 0; i < num_vertex_; i++)
            setWeight(i, i, 0);
    }

    const int kInvalidWeight = INT_MAX;

    bool isConnected(int v0, int v1) const;
    vector<int> getConnectedVertices(int v) const;
    int getWeight(int v0, int v1) const;
    void setWeight(int v0, int v1, int w);

    void printWeight() const;

    int num_vertex_;
    int size_of_ptr_;
    unique_ptr<int> weight_;
};

bool Edge::isConnected(int v0, int v1) const
{
    if (v0 == v1)
        return false;

    if (getWeight(v0, v1) == kInvalidWeight)
        return false;

    return true;
}

vector<int> Edge::getConnectedVertices(int v) const
{
    vector<int> vertices;

    for (int i = 0; i < num_vertex_; i++)
        if (isConnected(v, i))
            vertices.push_back(i);

    return vertices;
}

void Edge::setWeight(int v0, int v1, int w)
{
    assert(0 <= v0 && v0 < num_vertex_);
    assert(0 <= v1 && v1 < num_vertex_);

    int *p = weight_.get() + (v0 * num_vertex_) + v1;
    *p = w;
}

int Edge::getWeight(int v0, int v1) const
{
    int *p = weight_.get() + (v0 * num_vertex_) + v1;
    return *p;
}

void Edge::printWeight() const
{
    DPRINTF("\n");
    for (int i = 0; i < num_vertex_; i++)
    {
        printf("    [%d]", i);
        for (int j = 0; j < num_vertex_; j++)
        {
            const int w = getWeight(i, j);
            if (w != kInvalidWeight)
                printf(" %d", getWeight(i, j));
            else
                printf(" -");
        }
        cout << endl;
    }
}


struct VtxAndWeight {
    VtxAndWeight(int vtx, int weight)
        : vtx_(vtx)
        , weight_(weight)
    {}

    int vtx_;
    int weight_;

    bool operator>(const VtxAndWeight& rhs)
    {
        return (*this).weight_ > rhs.weight_;
    };

    bool operator<(const VtxAndWeight& rhs)
    {
        return (*this).weight_ < rhs.weight_;
    };
};

struct LessThanByWeight
{
    bool operator()(const VtxAndWeight& lhs, const VtxAndWeight& rhs) const
    {
        return lhs.weight_ > rhs.weight_;
    }

};


/* Dijkstra's algorithm */
void calcShortestPath(int start, const Edge &edge)
{
    priority_queue<VtxAndWeight, vector<VtxAndWeight>, LessThanByWeight> priority_queue;

    const int init_weight = 0;
    g_min_weight[start] = 0;
    priority_queue.push(VtxAndWeight(start, init_weight));

    while (!priority_queue.empty())
    {
        // select the minimum weight from the priority queue
        const int vtx = priority_queue.top().vtx_;
        const int weight = priority_queue.top().weight_;
        priority_queue.pop();

        DPRINTF("vtx %d  weight %d\n", vtx, weight);

        if (weight > g_min_weight[vtx])
            continue;

        // find connected vertices
        vector<int> connectedVertices = edge.getConnectedVertices(vtx);

        // update min weight for the vertices
        for (int neighbour : connectedVertices)
        {
            const int updated_weight= weight + edge.getWeight(vtx, neighbour);

            if (updated_weight < g_min_weight[neighbour])
            {
                g_min_weight[neighbour] = updated_weight;
                priority_queue.push(VtxAndWeight(neighbour, g_min_weight[neighbour]));
            }

            DPRINTF("g_min_weight[%d] %d\n", neighbour, g_min_weight[neighbour]);
        }
    }

}


int main()
{
    cin >> g_num_of_vertex;
    cin.ignore();

    assert(kMaxVertex >= g_num_of_vertex);

    // init
    for (int i = 0; i < g_num_of_vertex; i++)
    {
        g_min_weight[i] = INT_MAX;
    }

    Edge edge(g_num_of_vertex);

    // input
    for (int i = 0; i < g_num_of_vertex; i++)
    {
        int start, degree;
        cin >> start >> degree;

        for (int j = 0; j < degree; j++)
        {
            int dst, weight;
            cin >> dst >> weight;

            edge.setWeight(start, dst, weight);
        }

        cin.ignore();
    }

#if DEBUG
    edge.printWeight();
#endif

    // process
    const int start = 0;
    calcShortestPath(start, edge);

    // output
    for (int i = 0; i < g_num_of_vertex; i++)
        printf("%d %d\n", i, g_min_weight[i]);

    return 0;
}