一个数的阶乘中的第一个数字-yiteyi-C++库

给定一个正整数n，求其阶乘中的第一个数字。

null

例如：

Input  : n = 5Output : 1Factorial of 5 is 120 and firstdigit is 1.Input  : 1000Output : 4

推荐：请尝试你的方法 {IDE} 首先，在进入解决方案之前。

A. 简单解决方案 就是计算数字的阶乘，然后找到其中的第一个数字。上述解决方案导致溢流很快更好的解决方案是利用以下事实：阶乘包含尾随的0 删除尾随的0不会改变第一个数字。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 <bits/stdc++.h>                       
                         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

                         <?php                       
                         // PHP program for finding                       
                         // the First digit of the                       
                         // large factorial number                       
           
                         function                                     firstDigit(                                     $n                                     )                       
                         {                       
                                                 $fact                                     = 1;                       
           
                                                 for                                     (                                     $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                                     floor                                     (                                     $fact                                     );                       
                         }                       
           
                         // Driver Code                       
                         $n                                     = 5;                       
                         echo                                     firstDigit(                                     $n                                     );                       
           
                         // This code is contributed by aj_36.                       
                         ?>                       

Javascript

                         <script>                       
           
                         // 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                       
           
                         </script>                       

输出：

对于稍高的值，上述代码也会失败。最好的办法似乎是求大数的阶乘然后找到第一个数字。

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