Just the Facts

本博客介绍了一个算法,用于计算给定范围内(0≤N≤10000)的阶乘的最后非零数字。通过去除末尾的零并仅关注最后四位数字的乘法,实现高效计算。

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Description

The expression N!, read as "N factorial," denotes the product of the first N positive integers, where N is nonnegative. So, for example, 
 N       N! 

 0       1 
 1       1 
 2       2 
 3       6 
 4      24 
 5     120 
10 3628800 

For this problem, you are to write a program that can compute the last non-zero digit of any factorial for (0 <= N <= 10000). For example, if your program is asked to compute the last nonzero digit of 5!, your program should produce "2" because 5! = 120, and 2 is the last nonzero digit of 120.

Input

Input to the program is a series of nonnegative integers not exceeding 10000, each on its own line with no other letters, digits or spaces. For each integer N, you should read the value and compute the last nonzero digit of N!.

Output

For each integer input, the program should print exactly one line of output. Each line of output should contain the value N, right-justified in columns 1 through 5 with leading blanks, not leading zeroes. Columns 6 - 9 must contain " -> " (space hyphen greater space). Column 10 must contain the single last non-zero digit of N!.

Sample Input

1
2
26
125
3125
9999

Sample Output

 1 -> 1
    2 -> 2
   26 -> 4
  125 -> 8
 3125 -> 2
 9999 -> 8

解题思路:

出题人把它归为高精度,真是太坏了!千万别看到阶层就以为是高精度,给的数很吓人,让你求阶层后最右边不为0的数,不会真有人用高精度求了吧。。。。跟高精度八竿子打不着。后面的0乘以任何数都为0,所以不会影响我最后一个不为0的数,唯一担心的是进位问题,由于不会超过10000的阶层,也就是说每次乘的数不会超过10000,我只要每次保证最后一个数不为0,并且取最后4位去乘下一个数就行,无论它怎么进位都影响不到我输出正确答案了。

AC代码:

#include <iostream>
#include <cstdio>
using namespace std;
int main()
{
    int n, ans;
    while(scanf("%d", &n) != EOF)
    {
        ans = 1;
        for(int i = 1; i <= n; i++)
        {
            ans *= i;
            while(ans % 10 == 0)  // 去除末尾的0
                ans /= 10;
            ans %= 10000;  //取最后4位
        }
        printf("%5d -> %d\n", n, ans % 10);  //注意一下输出格式,我PE了一发
    }
    return 0;
}


Compared with homogeneous network-based methods, het- erogeneous network-based treatment is closer to reality, due to the different kinds of entities with various kinds of relations [22– 24]. In recent years, knowledge graph (KG) has been utilized for data integration and federation [11, 17]. It allows the knowledge graph embedding (KGE) model to excel in the link prediction tasks [18, 19]. For example, Dai et al. provided a method using Wasser- stein adversarial autoencoder-based KGE, which can solve the problem of vanishing gradient on the discrete representation and exploit autoencoder to generate high-quality negative samples [20]. The SumGNN model proposed by Yu et al. succeeds in inte- grating external information of KG by combining high-quality fea- tures and multi-channel knowledge of the sub-graph [21]. Lin et al. proposed KGNN to predict DDI only based on triple facts of KG [66]. Although these methods have used KG information, only focusing on the triple facts or simple data fusion can limit performance and inductive capability [69]. Su et al. successively proposed two DDIs prediction methods [55, 56]. The first one is an end-to-end model called KG2ECapsule based on the biomedical knowledge graph (BKG), which can generate high-quality negative samples and make predictions through feature recursively propagating. Another one learns both drug attributes and triple facts based on attention to extract global representation and obtains good performance. However, these methods also have limited ability or ignore the merging of information from multiple perspectives. Apart from the above, the single perspective has many limitations, such as the need to ensure the integrity of related descriptions, just as network-based methods cannot process new nodes [65]. So, the methods only based on network are not inductive, causing limited generalization [69]. However, it can be alleviated by fully using the intrinsic property of the drug seen as local information, such as chemical structure (CS) [40]. And a handful of existing frameworks can effectively integrate multi-information without losing induction [69]. Thus, there is a necessity for us to propose an effective model to fully learn and fuse the local and global infor- mation for improving performance of DDI identification through multiple information complementing.是什么意思
06-11
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