GCC（阶乘和求余，很重要）

小灰灰 2022-08-07 15:58 135阅读 0赞

# GCC #

**Time Limit: 1000/1000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others)  
Total Submission(s): 4162    Accepted Submission(s): 1365**

Problem Description

The GNU Compiler Collection (usually shortened to GCC) is a compiler system produced by the GNU Project supporting various programming languages. But it doesn’t contains the math operator “!”.  
In mathematics the symbol represents the factorial operation. The expression n! means "the product of the integers from 1 to n". For example, 4! (read four factorial) is 4 × 3 × 2 × 1 = 24. (0! is defined as 1, which is a neutral element in multiplication, not multiplied by anything.)  
We want you to help us with this formation: (0! + 1! + 2! + 3! + 4! + ... + n!)%m

Input

The first line consists of an integer T, indicating the number of test cases.  
Each test on a single consists of two integer n and m.

Output

Output the answer of (0! + 1! + 2! + 3! + 4! + ... + n!)%m.  
  
Constrains  
0 < T <= 20  
0 <= n < 10^100 (without leading zero)  
0 < m < 1000000

Sample Input

1
    10 861017

Sample Output

593846

Source

[2009 Asia Wuhan Regional Contest Online][]

阶乘和求余，见过快速幂求余，见过阶乘求余，没见过阶乘和求

余，公式我也看不懂！就知道前面，如果stl>=7就说明n是一个非

常 大的数的一个因子，当这个数大于n时，其余数为0！所 以要求

n以及n以下的阶乘和

#include<cstdio>
    #include<cstring>
    #include<string>
    #include<iostream>
    using namespace std;
    int main()
    {
        long long ans,sum,f;
        int t,stl,n,i;
        char c[500];
        cin>>t;
        while(t--)
        {
            cin>>c>>n;
            stl=strlen(c);
            if(stl>=7)
            {
                ans=n;
            }
            else
            {
                ans=0;
                for(i=0;i<stl;i++)
                {
                    ans=ans*10+(c[i]-'0');
                }
            }
            for(f=i=1,sum=0;i<=ans;i++)
            {
                f=f*i%n;
                sum=(sum+f)%n;
            }
            sum=(sum+1)%n;
            cout<<sum<<endl;
        }
    }

[2009 Asia Wuhan Regional Contest Online]: http://acm.hdu.edu.cn/search.php?field=problem&key=2009+Asia+Wuhan+Regional+Contest+Online&source=1&searchmode=source