用Java递归定义一个序列

Question

Need help with this problem, I am very bad at recursion. I need to write a method that does this:

The input variable X is an integer between 1 and 50. The function should return as Y the X-th term of a sequence defined recursively by:

f(1) = 1 f(2) = 3 f(X) = 2*f(X-1) – 2*f(X-2) for X = 3,4,5,...

Your function code should use recursion (not a loop)

TBH I dont even know where to get started. Any help would be appreciated. Here is my current code:

package p1parta;

import java.util.Scanner;

public class RecursiveSeq
{
    public static void main(String args[])
    {
       System.out.println("Please enter a number:");
       Scanner input = new Scanner(System.in);

       int x = input.nextInt();

       System.out.println(sequence(x));
    }

    public static int sequence(int x)
    {
        if(x == 1){
           return 1;
        }
        if (x == 2){
           return 3;
        }
        return 2 * sequence(x - 1) - 2 * sequence(x - 2);
    }
}

I tried to implement the solution shown but the output I get from the program do not match what I am calculating by hand. In fact just testing inputs 3,4,5,and 6 The only one that matches is 5

Answer 1

Your problem is a perfect use case for recursion. In general the recursive pattern is:

func(context)
    if simple case
        return simple answer
    else
        call func(simpler context)
        and return combined results

Have a go at implementing using this pattern and come back if you have issues.