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HDU 1018 Big Number 数学题解

2024-07-13 21:15:56   230人阅读

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 ≤ 107 on each line.
 

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

Sample Input
2
10
20
 

Sample Output
7
19

本题就考查斯特林公式。因为斯特林公式是求解n！的近似公式，而本题只需要求解有多少位。

底层数学原理就是求一个数n的数位可以使用 digits = log10(n)

然后利用斯特林公式求出n！的近似值就可以利用log10来求得数位了。

斯特林公式百度百科有，这里不重复了。

float不能AC的时候，就使用double吧。

#include <stdio.h>
#include <math.h>
const float PI = 3.14159265358979323846f;

inline int getDigits(int n)
{
	float num = float(n);
	int ans = (int)(0.5*log10(2.0*PI*num) + num*(log(num)-1)/log(10.0)) + 1;
	return ans;
}

int main()
{
	int T, n;
	scanf("%d", &T);
	while (T--)
	{
		scanf("%d", &n);
		printf("%d\n", getDigits(n));
	}
	return 0;
}


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