Classic interview questions: the factorial in question 100 has a few ending zeros.

100! = 100*99*98*97 *... * 2*1 first, let's take a look at how the zero end is formed: the zero end is formed when a multiples of 5 and a multiple of 2 are multiplied. So we only need to calculate a few () pairs, and we can know that there are a few ending zeros. There are several 5 factors first: within 100, 5 as the factor has 5, 10, 15, 20, 25... a total of 20. However, we note that 25, 50, and 75,100 both contain 2 5 as the factor (25 = 5*5, 50 = 2*5*5). Therefore, we need to do this most once. Therefore, there are 24 5 factors in total. From the formula point of view: the number of 5 factors = 100/5 + 100/(5 ^ 2) + 100/(5 ^ 3) +... = 24 (must be an integer) Now there are several factors in the number 2: 2, 4, 6, 8, 10 ,... A total of 100/2 = 50 2 factors, 100/4 = 25 4 factors (count more once), 100/8 = 12 8 factors (count more once ),... so the number of 2 factors = 100/2 + 100/(2 ^ 2) + 100/(2 ^ 3) + 100/(2 ^ 4) + 100/(2 ^ 5) + 100/(2 ^ 6) + 100/(2 ^ 7) +... = 97 In summary, there are 24 5 factors and 97 2 factors in total, so 24 (2, 5) pairs can be merged. Therefore, it is easy to write a program after 24 factorial ends with zero knowledge of ideas and formulas. When is there any time to complete the program Update: 11.16 now complete the program, respectively on the two OJ test, no problem. The POJ http://poj.org/problem? Id = 1401

Import java. io. *; import java. util. *; public class Main {public static void main (String args []) {program cin = new program (System. in); int cnt = cin. nextInt (); int input; for (int I = 0; I <cnt; I ++) {input = cin. nextInt (); System. out. println (trailingZeros (input);} // you can only calculate the number of five factors, because the number of five factors must be less than the number of two factors public static int trailingZeros (int input) {int quotient; int fiveFactors = 0; quotient = input/ 5; int I = 1; while (quotient! = 0) {fiveFactors + = quotient; I ++; quotient = (int) (input/Math. pow (5, I);} return fiveFactors ;}}

 

Package Factorial; import java. io. *; import java. util. *; public class Main {public static void main (String args []) {program cin = new program (System. in); int input = cin. nextInt (); while (input! = 0) {System. out. println (trailingZeros (input); input = cin. nextInt ();} System. out. println () ;}// you only need to calculate the number of 5 factors, because the number of 5 factors must be less than the number of 2 factors. public static int trailingZeros (int input) {int quotient; int fiveFactors = 0; quotient = input/5; int I = 1; while (quotient! = 0) {fiveFactors + = quotient; I ++; quotient = (int) (input/Math. pow (5, I);} return fiveFactors ;}}