2-5 半数集问题
问题描述
给定一个自然数n,由n开始可以依次产生半数集set(n)中的数如下:
(1)set(n)中包含n;
(2)在n的左边加上一个自然数,但该自然数不能超过最近添加的数的一半;
(3)按此规则进行处理,直至不能添加自然数为止。
例如,set(6)={6,16,26,126,36,136}。
注意:该半数集是多重集。
编程任务:对于给定的自然数n,编程计算半数集set(n)中元素的个数。
分析
设
中的元素个数为
,则显然有:
Java: version-1
import java.util.Scanner;
public class Main {
public static void main(String[] args) {
Scanner input = new Scanner(System.in);
int number;
int count;
while (true){
System.out.println("Please input a number: ");
number = input.nextInt();
count = halfNumber(number);
System.out.println("There are "+count+" elements!");
System.out.println("----------------------------");
}
}
private static int halfNumber(int number){
int count = 1;
if(number > 1){
for(int i=1; i<=number/2; i++){
count += halfNumber(i);
}
}
return count;
}
}
Java: version-2
import java.util.Scanner;
public class Main {
private static int[] countArray = new int[1001];
public static void main(String[] args) {
Scanner input = new Scanner(System.in);
int number;
int count;
countArray[1] = 1;
while (true){
System.out.println("Please input a number: ");
number = input.nextInt();
count = halfNumber(number);
System.out.println("There are "+count+" elements!");
System.out.println("----------------------------");
}
}
private static int halfNumber(int number){
int count = 1;
if(countArray[number] > 0)
return countArray[number];
for(int i=1; i<=number/2; i++){
count += halfNumber(i);
}
countArray[number] = count;
return count;
}
}
Output
Please input a number:
1
There are 1 elements!
----------------------------
Please input a number:
2
There are 2 elements!
----------------------------
Please input a number:
3
There are 2 elements!
----------------------------
Please input a number:
4
There are 4 elements!
----------------------------
Please input a number:
5
There are 4 elements!
----------------------------
Please input a number:
6
There are 6 elements!
----------------------------
Please input a number:
34
There are 238 elements!
----------------------------
Please input a number:
23
There are 74 elements!
----------------------------
Please input a number:
999
There are 1955133450 elements!
----------------------------
Please input a number:
1000
There are 1981471878 elements!
----------------------------
Please input a number:
Reference
王晓东《计算机算法设计与分析》(第3版)P43