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   Problem Statement  

 Problem Statement for DerivativeSequence

Problem Statement

    

Given a sequence of K elements, we can calculate its difference sequence by taking the difference between each pair of adjacent elements. For instance, the difference sequence of {5,6,3,9,-1} is {6-5,3-6,9-3,-1-9} = {1,-3,6,-10}. Formally, the difference sequence of the sequence a1, a2, ... , ak is b1, b2, ... , bk-1, where bi = ai+1 - ai.

The derivative sequence of order N of a sequence A is the result of iteratively applying the above process N times. For example, if A = {5,6,3,9,-1}, the derivative sequence of order 2 is: {5,6,3,9,-1} -> {1,-3,6,-10} -> {-3-1,6-(-3),-10-6} = {-4,9,-16}.

You will be given a sequence a as a int[] and the order n. Return a int[] representing the derivative sequence of order n of a.

 

Definition

    
Class:DerivativeSequence
Method:derSeq
Parameters:int[], int
Returns:int[]
Method signature:int[] derSeq(int[] a, int n)
(be sure your method is public)
    
 

Notes

-The derivative sequence of order 0 is the original sequence. See example 4 for further clarification.
 

Constraints

-a will contain between 1 and 20 elements, inclusive.
-Each element of a will be between -100 and 100, inclusive.
-n will be between 0 and K-1, inclusive, where K is the number of elements in a.
 

Examples

0)
    
{5,6,3,9,-1}
1
Returns: {1, -3, 6, -10 }
The first example given in the problem statement.
1)
    
{5,6,3,9,-1}
2
Returns: {-4, 9, -16 }
The second example given in the problem statement.
2)
    
{5,6,3,9,-1}
4
Returns: {-38 }
3)
    
{4,4,4,4,4,4,4,4}
3
Returns: {0, 0, 0, 0, 0 }
After 1 step, they all become 0.
4)
    
{-100,100}
0
Returns: {-100, 100 }

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This problem was used for:
       Single Round Match 322 Round 1 - Division II, Level One