factorial of given number-CodePudding

i would like to find the smallest factorial of a given long number. for example, if you enter the number 100, the code should give the factorial 5, since 5! = 1 * 2 * 3 * 4 * 5 = 120 is closer than the factorial 4! = 1 * 2 * 3 * 4 = 24. i have written the code below. but when i enter 100, i only get the factorial 3.

import java.util.Scanner;

class Main {

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        long number = scanner.nextLong();
        long factorial = 1;
        long sum;
        do {
            sum = number / factorial;
            factorial  ;
        } while (number <= sum);
        System.out.println(factorial);
    }
}

What am I doing wrong here?

CodePudding user response：

you should calculate the factorial of numbers, untill you find an equal or smaller number than the number you entered, as shown in the following code :

import java.util.Scanner;

class Main {
    public Long factorial (int n){
      long p = 1L;
      for(int i = 1; i<= n ; i  ){
        p=p*i;
      }
    }
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        long number = scanner.nextLong();
        long i = 1;
       while (factorial(i) < number) {
           i  ;
        }
        System.out.println(i);
    }

CodePudding user response：

Here is one way. This will return the factorial closest to the number. If there is a tie, the lowest factorial will be returned.

int[] data = {0,1,2,5,10,200,500,2520,1000,2520, 2000, 3000, 10_000};
for (int d :data) {
    System.out.println(d   ":  closest factorial = "   closestFactorial(d));
}

prints

0:  closest factorial = 1!
1:  closest factorial = 1!
2:  closest factorial = 1!
5:  closest factorial = 3!
10:  closest factorial = 3!
100:  closest factorial = 5!
200:  closest factorial = 5!
500:  closest factorial = 6!
2520:  closest factorial = 6!
1000:  closest factorial = 6!
2520:  closest factorial = 6!
2000:  closest factorial = 6!
3000:  closest factorial = 7!
10000:  closest factorial = 7!

This method calculates the factorial while comparing to the passed argument.

continue calculating factorials until the factorial exceeds the argument.
compare the factorial - argument to the argument - previous factorial. Return the proper factorial based on the comparison.

public static int closestFactorial(long n) {
   if (n <= 2) {
       return 1;
   }
   long fact = 2;
   int k = 2;
   while (n > fact) {
       fact*=  k;
   }
   long previousFact = fact/k;
   return fact - n  < n - previousFact ? k : k-1; 
}

If you want to see the actual factorial you can replace the last statement with.

return fact - n  < n - previousFact ? fact : previousFact;