我想从斐波那契数列中减去最大可能的数字

Question

I want to get n from user and subtract the largest possible number from the Fibonacci sequence by decreasing it in sequence and continue this process until it reaches zero. Our Fibonacci sequence starts from 1. The number 88 can be The form 1 + 3 + 8 + 21 + 55 wrote that these numbers are the sentences 1, 3, 5, 7 and 9 of the Fibonacci sequence, respectively.

Input: 88

Output: 9 7 5 3 1

My code:

class Main {
    public static void main(String args[]) {
        Scanner input = new Scanner(System.in);

        int n = input.nextInt();
        int[] fibo = new int[1000];
        int[] arr = new int [100];
        int d = 0;
        int b = 0;
        fibo[1] = 1;
        fibo[2] = 2;

        for (int i = 3, j = 1; i <= 20; i++, j++)
            fibo[i] = fibo[i - 1] + fibo[i - 2];

        b = n;

        for (int i = 1, j = 1; i <= 20 && b >= 0; i++, j++) {
            if (b == fibo[i] || b + 1 == fibo[i] || b - 1 == fibo[i]) {
                d = i;
                b -= fibo[d - 1];
                System.out.println("B= " + b);
                arr[j] = d - 1;
                System.out.println("arr= " + arr[j]);
            }
        }
    }
}

Answer 1

The first problem is that, every time you subtract something from your number, the next number you will subtract will have to be smaller - because your number itself is smaller now - whereas in your code, the numbers just keep getting bigger.

For instance, after you try the 9th fibonacci number 55, you are trying 89, whereas you should be trying 34.

This can be solved by iterating backwards through the fibonacci numbers, as in starting from the biggest number at the end of the array, so that as the loop iterates, the numbers get smaller.

The second problem is your check in the if statement, which is only satisfied if there happens to be a fibonacci number very close to the number you are at.

Instead, if you want to select the largest fibonacci number that is smaller than your number, you can just check for the 'smaller than your number' part, since 'the largest fibonacci' part is already taken care of by how the for loop works.

Here is the working code. You will also notice a lot fewer variables. Also I hard-coded the input number for testing, you'll have to add the scanner stuff back in. Sorry.

public class Main {
    public static int len = 20; // the program considers this many fibonacci numbers
    
    public static void main(String args[])
    {
        int n = 88;
        int[] fibo = new int[len];
        
        for(int i=0; i<len; i++)
        {
            if (i < 2) fibo[i] = i+1; // for 1 and 2
            else fibo[i] = fibo[i-1] + fibo[i-2]; // for 3 and 5 and ...
        }
        
        for(int i=len-1; i>=0; i--)
        {
            if (fibo[i] <= n)
            {
                System.out.format("%d: %d - %d = %d\n",
                    i+1, // to correct for 0-indexing
                    n, fibo[i], n-fibo[i]);
                n -= fibo[i];
            }
        }
    }
}