Program to find number of zero's in factorial of a number...

Resently a came accross this problem of finding the number of zero's in factorial of a number....

Well i think the logic is really simple...we have to find out the factors that contributes to 1 or more number of 0's.Whenever there are 1 or more zero's at the end of a number it always results in 0's at the end factorial number also.And the number of 5 also gives same number of 0's as there are many more numbers of the 2's compared to 5's.Similarly one 0 from 25 and two 0's from 50 and and soo on....

Hence we can compute the number of zero's by finding a value though the formula

value = (number/5^1+number/5^2+..............+number/5^n)

where

n = number/5;

Hope the idea is clear....

Now as far as the implementation in java is concerned here i also give the code for implementing it in java...

package com.lara;

import java.util.Arrays;

import java.util.Scanner;

public class Main

{

public static void main(String[] args)

{

Scanner sc = new Scanner(System.in);

System.out.println("Enter the number for which you want to find zeros");

System.out.println("Enter the total number of the cases");

int cas = sc.nextInt();

long result[]=new long [cas];

System.out.println("Enter the long elements one by one");

long num[] = new long[cas];

for(int i =0 ;i

{

num[i] = sc.nextLong();

}

for(int i=0; i

{

long n = num[i]/5;

for(int i1=1;i1

{

System.out.println("i1: "+i1);

System.out.println("i; "+ i);

result[i] += (long) (num[i]/Math.pow(5, i1));

}

}

System.out.println("number of the zeros are "+ Arrays.toString(result));

}

}

Well the fact remains that the execution time of this program in java is definitly more than that in C/C++....