数字阶乘的第一个数字

给定正整数n，请找到其阶乘中的第一个数字。

例子 ：

Input  : n = 5
Output : 1
Factorial of 5 is 120 and first
digit is 1.

Input  : 1000
Output : 4

一个简单的解决方案是计算数字的阶乘，然后在其中找到第一个数字。
上述解决方案很快就会导致溢出。更好的解决方案是使用阶乘包含尾随0并删除尾随0不会更改第一位的事实。例如，对于x> 0和y> 0，x * y的第一位数字与x * y * 100相同。

C++

// A C++ program for finding the First digit
// of the large factorial number
#include 
using namespace std;
 
int firstDigit(int n)
{
    long long int fact = 1;
 
    for (int i = 2; i <= n; i++) {
        fact = fact * i;
 
        // Removing trailing 0s as this
        // does not change first digit.
        while (fact % 10 == 0)
            fact = fact / 10;       
    }
 
    // loop for divide the fact until it
    // become the single digit and return
    // the fact
    while (fact >= 10)
        fact = fact / 10;
     
    return fact;
}
 
// derive main
int main()
{
    int n = 5;
    cout << firstDigit(n);
    return 0;
}

Java

// A Java program for finding the First digit
// of the large factorial number
class GFG{
static int firstDigit(int n)
{
    int fact = 1;
 
    for (int i = 2; i <= n; i++) {
        fact = fact * i;
 
        // Removing trailing 0s as this
        // does not change first digit.
        while (fact % 10 == 0)
            fact = fact / 10;    
    }
 
    // loop for divide the fact until it
    // become the single digit and return
    // the fact
    while (fact >= 10)
        fact = fact / 10;
     
    return fact;
}
 
// derive main
public static void main(String[] args)
{
    int n = 5;
    System.out.println(firstDigit(n));
}
}
//This code is contributed by Smitha Dinesh Semwal

Python3

# Python3 program for finding
# the First digit of the
# large factorial number
import math
def firstDigit(n) :
    fact = 1
 
    for i in range(2, n + 1) :
        fact = fact * i
 
        # Removing trailing 0s
        # as this does not
        # change first digit.
        while (fact % 10 == 0) :
            fact = int(fact / 10)
 
    # loop for divide the fact
    # until it become the single
    # digit and return the fact
 
    while (fact >= 10) :
        fact = int(fact / 10)
     
    return math.floor(fact)
 
# Driver Code
n = 5
print (firstDigit(n))
 
# This code is contributed by
# Manish Shaw(manishshaw1)

C#

// A C# program for finding the First digit
// of the large factorial number
using System;
 
class GFG {
     
    static int firstDigit(int n)
    {
        int fact = 1;
     
        for (int i = 2; i <= n; i++)
        {
            fact = fact * i;
     
            // Removing trailing 0s as this
            // does not change first digit.
            while (fact % 10 == 0)
                fact = fact / 10;    
        }
     
        // loop for divide the fact until
        // it become the single digit and
        // return the fact
        while (fact >= 10)
            fact = fact / 10;
         
        return fact;
    }
     
    // driver function
    public static void Main()
    {
        int n = 5;
         
        Console.Write(firstDigit(n));
    }
}
 
// This code is contributed by parashar.

PHP

= 10)
        $fact = $fact / 10;
     
    return floor($fact);
}
 
// Driver Code
$n = 5;
echo firstDigit($n);
 
// This code is contributed by aj_36.
?>

Javascript

 
// JavaScript program for finding the
// First digit of the large factorial number
function firstDigit(n)
{
    let fact = 1;
   
    for(let i = 2; i <= n; i++)
    {
        fact = fact * i;
   
        // Removing trailing 0s as this
        // does not change first digit.
        while (fact % 10 == 0)
            fact = fact / 10;    
    }
   
    // Loop for divide the fact until it
    // become the single digit and return
    // the fact
    while (fact >= 10)
        fact = fact / 10;
       
    return (Math.round(fact));
}
 
// Driver code
let n = 5;
 
document.write(firstDigit(n));
 
// This code is contributed by splevel62
 

输出 ：

1

上面的代码对于稍高的值也失败。最好的主意似乎是找到大数的阶乘，然后找到第一个数字。