求阶乘的第一个非零数字

Problem statement:

问题陈述：

Find the number of trailing zeros in n! (Where, n is the given input).

在n中找到尾随零的数目！ (其中， n是给定的输入)。

Solution:

解：

Computing a factorial is of course expansive. Though using dynamic programming the computing expanse can be managed, for the large value of n, the factorial value is going exceed normal data size. Needless to say, computing the whole factorial is not the way to find the number of trailing zeros. There must be some advanced algorithm to find the no of trailing zeros.

计算阶乘当然是可扩展的。 尽管使用动态编程可以管理计算范围，但是对于较大的n值，阶乘值将超过正常数据大小。 不用说，计算整个阶乘不是找到尾随零的数量的方法 。 必须有一些高级算法来找到尾随零 。

Firstly, we need to understand what causes trailing zeroes. A pair of 2 & 5 is the reason behind a trailing zero. Thus a pair of 2 & 5 in the factorial expression leads to a trailing zero. Thus we simply need to check how many pairs (different) of 2 & 5 are there.

首先，我们需要了解导致尾随零的原因。 一对2和5是尾随零后面的原因。 因此，阶乘表达式中的2和5对导致尾随零。 因此，我们只需要检查2和5有多少对(不同)。

Let's say 5!
5!= 5*4*3*2*1 (thus only one pair)
5!=120 ( only one trailing zero)

假设5！
5！= 5 * 4 * 3 * 2 * 1 (因此只有一对)
5！= 120 (仅一个尾随零)

Intuition says that we don’t even need to find the number of pairs as the occurrence of 2 as a factor is obvious if a 5 is present as a factor. Thus we only need to check how many 5 is there as a factor in the factorial.

直觉说，我们甚至不需要找到对的数量，因为如果5作为一个因素，则2作为一个因素的出现就很明显。 因此，我们仅需要检查阶乘中有5个因素。

Algorithm:

算法：

    Set count to 0
For(i=5;n/i>0;i=i*5)
count=count+ n/i;
Return count

C ++代码查找数字阶乘中的尾随零 (C++ code to find trailing zeros in factorial of a number)

#include<bits/stdc++.h>
using namespace std;
int trailingZeros(int n){int count=0;
if(n<0)
return -1;
for(int i=5;n/i>0;i*=5){count+=n/i;
}
return count;
}
int main(){int n;
cout<<"enter input,n"<<endl;
cin>>n;
if(trailingZeros(n))
cout<<"no of trailing zero in "<<n<<"! is "<<trailingZeros(n)<<endl;
else
cout<<"input is negative, can't proceed"<<endl;
return 0;
}

Output

输出量

First run:
enter input,n
15
no of trailing zero in 15! is 3
Second run:
enter input,n
100
no of trailing zero in 100! is 24

翻译自: https://www.includehelp.com/algorithms/find-trailing-zeros-in-factorial-of-a-number.aspx

求阶乘的第一个非零数字