HDU 1018Big Number（简单题目，JAVA练手）

最新推荐文章于 2021-03-02 02:42:55 发布

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最新推荐文章于 2021-03-02 02:42:55 发布

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文章标签： JAVA 斯特林公式

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本文深入探讨了如何利用斯特林公式来高效计算阶乘的位数，详细介绍了输入输出规范和代码实现，包括直接位数求解和斯特林公式求解两种方法，适合对算法优化感兴趣的读者。

Big Number

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 21108 Accepted Submission(s): 9500

Problem Description

In many applications very large integers numbers are required. Some of these applications are using keys for secure transmission of data, encryption, etc. In this problem you are given a number, you have to determine the number of digits in the factorial of the number.

Input

Input consists of several lines of integer numbers. The first line contains an integer n, which is the number of cases to be tested, followed by n lines, one integer 1 ≤ n ≤ 10 ⁷ on each line.

Output

The output contains the number of digits in the factorial of the integers appearing in the input.

Sample Input

Sample Output

  
   7
19

题目大意：问你n!有多少位。

解题思路：最先想到的就是对10求余，n!=1*2*3*4*……*n 不过也可以使用斯特林公式直接求解。斯特林公式：n! 约等于 sqrt(2*PI*n)*(n/e)^n.

题目地址：Big Number

直接一位一位求AC代码：

import java.util.Scanner;
import java.math.*;

public class Main
{
    public static void main(String args[])
    {
    	 
    	 Scanner cin = new Scanner(System.in);
         int tes,i,p,j;
         tes=cin.nextInt();
         for(i=0;i<tes;i++)
         {
        	 p=cin.nextInt();
        	 double sum=0;
        	 for(j=1;j<=p;j++)
        	 	 sum+=Math.log((double)j)/Math.log(10.0);
        	 int res=(int)sum+1;
             System.out.println(res);
         }
    }
}

使用斯特林公式AC代码：

import java.util.Scanner;
import java.math.*;

public class Main
{
    public static void main(String args[])
    {
    	 
    	 Scanner cin = new Scanner(System.in);
         int tes,i,p,j;
         tes=cin.nextInt();
         double PI=Math.acos(-1.0);
         double e=Math.E;
         for(i=0;i<tes;i++)
         {
        	 p=cin.nextInt();
        	 double res1=1.0/2.0*Math.log(2.0*PI*p)/Math.log(10.0)+p*Math.log(p/e)/Math.log(10.0);
        	 int res=(int)res1+1;
             System.out.println(res);
         }
    }
}