HDU 1018Big Number（大数的阶乘的位数，利用公式）

发布时间：2020-12-14 03:21:08 所属栏目：大数据来源：网络整理

导读：传送门：http://acm.hdu.edu.cn/showproblem.php?pid=1018 Big Number Time Limit: 2000/1000 MS (Java/Others)????Memory Limit: 65536/32768 K (Java/Others) Total Submission(s): 42715????Accepted Submission(s): 20844 Problem Description In many a

传送门：http://acm.hdu.edu.cn/showproblem.php?pid=1018

Big Number

Time Limit: 2000/1000 MS (Java/Others)????Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 42715????Accepted Submission(s): 20844

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

Source

Asia 2002,Dhaka (Bengal)

分析：

问你一个数的阶乘是多少位

n比较大

是大数问题

一开始不知道写

看了一下大佬的博客

具体分析；

?一个正整数a的位数等于(int)log10(a) + 1
??? 假设A=n!=1*2*3*......*n，那么我们要求的就是
??? (int)log10(A)+1，而：
??? log10(A)
??? =log10(1*2*3*......n)? （根据log10(a*b) = log10(a) + log10(b)有）
??? =log10(1)+log10(2)+log10(3)+......+log10(n)

code：

#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
#define max_v 105
int main()
{
    /*
    一个正整数a的位数等于(int)log10(a) + 1
    假设A=n!=1*2*3*......*n，那么我们要求的就是
    (int)log10(A)+1，而：
    log10(A)
    =log10(1*2*3*......n)  （根据log10(a*b) = log10(a) + log10(b)有）
    =log10(1)+log10(2)+log10(3)+......+log10(n)
        */
    int n,t;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%d",&n);
        double sum=0;
        for(int i=1; i<=n; i++)
        {
            sum+=log10((double)i);
        }
        printf("%dn",(int)sum+1);
    }
    return 0;
}

（编辑：李大同）

【声明】本站内容均来自网络，其相关言论仅代表作者个人观点，不代表本站立场。若无意侵犯到您的权利，请及时与联系站长删除相关内容!