Description
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.
Example1
{5,6,3,9,-1}
1
Returns: {1, -3, 6, -10 }
Example2
{5,6,3,9,-1}
2
Returns: {-4, 9, -16}
Example3
{5,6,3,9,-1}
4
Returns: {-38}
Example4
{4,4,4,4,4,4,4,4}
3
{0, 0, 0, 0, 0}
Solution
Computing a sequence of derivatives is a recursion.
1) Finding the basic cases
- Whether given n is 0, return origin integer array if yes. Otherwise, start recursive
2) Finding the recursive relationship
- When recursing, the calculated derivative sequence is passed in each time, and n-1
public class DerivativeSequence {
public static int[] derSeq(int[] a, int n) {
if (n == 0) {
return a;
}
return derSeq(getSeq(a), n - 1);
}
public static int[] getSeq(int[] a) {
int[] res = new int[a.length - 1];
for (int i = 0; i < a.length - 1; i++) {
res[i] = a[i + 1] - a[i];
}
return res;
}
}
Time Complexity
O(n)
