大整数阶乘位数计算-优快云博客

本文链接：https://blog.youkuaiyun.com/ljf_study/article/details/67068462

本文介绍了一个计算大整数阶乘位数的方法，通过输入一系列整数，利用对数特性计算每个整数阶乘后的位数，并提供了一个具体的C++实现案例。

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Big Number

Time Limit: 20000/10000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)

Total Submission(s): 1294 Accepted Submission(s): 884

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

Source

Asia 2002, Dhaka (Bengal)

#include <iostream>
#include <stdio.h>
#include <cmath>
using namespace std;

int main()
{
    int n;
    cin >> n;
    while(n--){
        int temp;
        cin >> temp;
        double sum = 0;
        for(int i = 1; i <= temp; i++){
            sum += log10(i);
        }
        sum ++;
        cout << (int)sum <<endl;
    }
    return 0;
}