Problem:
Score : 200 points

Problem Statement

There are N apple trees in a row. People say that one of them will bear golden apples.

We want to deploy some number of inspectors so that each of these trees will be inspected.

Each inspector will be deployed under one of the trees. For convenience, we will assign numbers from 1 through N to the trees. An inspector deployed under the i-th tree (1 \leq i \leq N) will inspect the trees with numbers between i-D and i+D (inclusive).

Find the minimum number of inspectors that we need to deploy to achieve the objective.

Constraints

All values in input are integers.

1 \leq N \leq 20

1 \leq D \leq 20

Input

Input is given from Standard Input in the following format:

N D

Output

Print the minimum number of inspectors that we need to deploy to achieve the objective.

Sample Input 1

6 2

Sample Output 1

2

We can achieve the objective by, for example, placing an inspector under Tree 3 and Tree 4.

Sample Input 2

14 3

Sample Output 2

2

Sample Input 3

20 4

Sample Output 3

3

Solution in Go (1.6) (judge verdict: Accepted)

package main

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

const (
	initialBufSize = 10000
	maxBufSize     = 1000000
	mod            = 1e9 + 7
)

var (
	sc *bufio.Scanner = func() *bufio.Scanner {
		sc := bufio.NewScanner(os.Stdin)
		buf := make([]byte, initialBufSize)
		sc.Buffer(buf, maxBufSize)
		sc.Split(bufio.ScanWords)
		return sc
	}()
)

func main() {
	N := getInt()
	D := getInt()

	num := N / (2*D+1)
	if N % (2*D+1) != 0 {
		num++
	}

	fmt.Println(num)
}

type Graph struct {
	n     int
	edges [][]int
}

func NewGraph(n int) *Graph {
	g := &Graph{
		n:     n,
		edges: make([][]int, n),
	}
	return g
}

func (g *Graph) AddEdge(u, v int) {
	g.edges[v] = append(g.edges[v], u)
	g.edges[u] = append(g.edges[u], v)
}

func dfs(c int, edges [][]int, visited map[int]struct{}) {
	visited[c] = struct{}{}

	for _, v := range edges[c] {
		_, flag := visited[v]
		if flag {
			continue
		}
		dfs(v, edges, visited)
	}
}

func getInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

func getIntArray(n int) []int {
	array := make([]int, n)
	for i := 0; i < n; i++ {
		array[i] = getInt()
	}
	return array
}

func getString() string {
	sc.Scan()
	return sc.Text()
}

func abs(a int) int {
	return int(math.Abs(float64(a)))
}

func pow(p, q int) int {
	return int(math.Pow(float64(p), float64(q)))
}

func powMod(n, p int) int {
	if p == 0 {
		return 1
	} else if p%2 == 0 {
		t := powMod(n, p/2)
		return calcMod(t * t)
	} else {
		return calcMod(n * powMod(n, p-1))
	}
}

func min(nums ...int) int {
	if len(nums) == 0 {
		panic("funciton min() requires at least one argument.")
	}
	res := nums[0]
	for i := 0; i < len(nums); i++ {
		res = int(math.Min(float64(res), float64(nums[i])))
	}
	return res
}

func max(nums ...int) int {
	if len(nums) == 0 {
		panic("funciton max() requires at least one argument.")
	}
	res := nums[0]
	for i := 0; i < len(nums); i++ {
		res = int(math.Max(float64(res), float64(nums[i])))
	}
	return res
}

func strSearch(a []string, b string) bool {
	for i := 0; i < len(a); i++ {
		if a[i] == b {
			return true
		}
	}
	return false
}

func printIntArray(array []int) {
	strArray := fmt.Sprint(array)
	fmt.Println(strArray[1 : len(strArray)-1])
}

func calcMod(x int) int {
	return x % mod
}

func reverse(s string) string {
	runes := []rune(s)
	for i, j := 0, len(runes)-1; i < j; i, j = i+1, j-1 {
		runes[i], runes[j] = runes[j], runes[i]
	}
	return string(runes)
}

func isPrime(n int) bool {
	if n < 2 {
		return false
	} else if n == 2 {
		return true
	} else if n % 2 == 0 {
		return false
	}

	sqrtN := int(math.Sqrt(float64(n)))
	for i := 3; i <= sqrtN; i += 2 {
		if n % i == 0 {
			return false
		}
	}

	return true
}

func contains(s []int, e int) bool {
	for _, v := range s {
		if e == v {
			return true
		}
	}
	return false
}

func makeRange(min, max int) []int {
	a := make([]int, max-min+1)
	for i := range a {
		a[i] = min + i
	}
	return a
}

func powerset2(nums []int) [][]int {
	length := int(math.Pow(2, float64(len(nums))))
	result := make([][]int, length)

	index := 0
	result[index] = []int{}
	index++

	for _, n := range nums {
		max := index
		for i := 0; i < max; i++ {
			result[index] = copyAndAppend(result[i], n)
			index++
		}
	}

	return result
}

func copyAndAppend(nums []int, n int) []int {
	dst := make([]int, len(nums)+1)
	copy(dst, nums)
	dst[len(nums)] = n
	return dst
}

func calcGcd(x, y int) int {
	if y == 0 {
		return x
	} else if x >= y {
		return calcGcd(y, x % y)
	} else {
		return calcGcd(x, y % x)
	}
}

func getDivisor(n int) []int {
	var divisor []int
	divisor = append(divisor, 1)
	if n != 1 {
		divisor = append(divisor, n)
	}

	sqrt := int(math.Sqrt(float64(n)))
	for i := 2; i <= sqrt; i++ {
		if n % i == 0 {
			divisor = append(divisor, i)
			divisor = append(divisor, n/i)
		}
	}
	return divisor
}

type intHeap []int

func (h intHeap) Len() int {
	return len(h)
}

func (h intHeap) Less(i, j int) bool {
	return h[i] > h[j]
}

func (h intHeap) Swap(i, j int) {
	h[i], h[j] = h[j], h[i]
}

func (h *intHeap) Push(x interface{}) {
	*h = append(*h, x.(int))
}

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

func initHeap() *intHeap {
	ih := &intHeap{}
	heap.Init(ih)
	return ih
}

func (h *intHeap) pushHeap(n int) {
	heap.Push(h, n)
}

func (h *intHeap) popHeap() int {
	return heap.Pop(h).(int)
}

func factMod(n int) int {
	value := 1
	for ; n > 1; n-- {
		value = calcMod(value * n)
	}
	return value
}

func combinationMod(n, k int) int {
	factN := factMod(n)
	factK := factMod(k)
	factNK := factMod(n - k)
	factKR := powMod(factK, mod - 2)
	factNKR := powMod(factNK, mod - 2)
	return calcMod(factN * calcMod(factKR * factNKR))
}