hdu 4927 Series 1 高精度

最新推荐文章于 2021-03-08 10:39:05 发布

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本文介绍了一种基于数学序列求导的算法实现，该算法通过计算序列的高阶差分来找出序列的最后一项，并提供了一个使用Java实现的具体示例。

Series 1

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 262144/262144 K (Java/Others)
Total Submission(s): 885 Accepted Submission(s): 331

Problem Description

Let A be an integral series {A ₁, A ₂, . . . , A _n}.

The zero-order series of A is A itself.

The first-order series of A is {B ₁, B ₂, . . . , B _n-1},where B _i = A _i+1 - A _i.

The ith-order series of A is the first-order series of its (i - 1)th-order series (2<=i<=n - 1).

Obviously, the (n - 1)th-order series of A is a single integer. Given A, figure out that integer.

Input

The input consists of several test cases. The first line of input gives the number of test cases T (T<=10).

For each test case:
The first line contains a single integer n(1<=n<=3000), which denotes the length of series A.
The second line consists of n integers, describing A ₁, A ₂, . . . , A _n. (0<=A _i<=10 ⁵)

Output

For each test case, output the required integer in a line.

Sample Input

Sample Output

  
   0
-5

Author

BUPT

Source

2014 Multi-University Training Contest 6

就是大数，会了java没什么难的

import java.util.*;
import java.math.*;
public class Main {
	static int n;
	static BigInteger[] a = new BigInteger[4100];
	static BigInteger c,ans,p;
	
	
	public static void slove() {
		
		ans=BigInteger.valueOf(0);
		c=BigInteger.valueOf(1);
		for(int i=0;i<n;i++)
		{
			if((i&1) != 0) p=BigInteger.valueOf(-1);
			else p=BigInteger.valueOf(1);
			ans=ans.add(c.multiply(p).multiply(a[n-i]));
			c=c.multiply(BigInteger.valueOf(n-i-1)).divide(BigInteger.valueOf(i+1));
		}
		System.out.println(ans);
	}
	
	
    public static void main(String[] args) {

		 
        Scanner cin = new Scanner(System.in);
        int T;
        T=cin.nextInt();
        for(int tt=0;tt<T;tt++){

            n=cin.nextInt();
            for(int i=1;i<=n;i++)
            {
            	a[i]=cin.nextBigInteger();
            }
            slove();
        }
        cin.close();
    }
	
}