Using the Vector1D interface, implement an immutable class called PrecisionVector1D that uses an array of doubles internally while exposing elements as integers. This interface is used to represent a vector of numbers: (1, 2, 11), (23, 23, 52, 31), (), etc. It is designed to store decimals until needed. For example, the first vector from the last sentence could be multiplied by 1.1 to yield an internal representation of (1.1, 2.2, 12.1) which would be displayed as (1, 2, 12). When converting from double to int, you may use your choice of rounding schemes (up or down; casting). Do not use the builtin Java functionality for cloning or duplicating arrays. public interface Vector1D {
//returns the i'th element of the vector. assume the index is valid.
public int getElement(int i);
//returns the number of elements in the vector
public int getLength();
//returns the vector as a string of integers (e. g., "(1, 3, 4)")
public String getString();
//returns the sum of all elements of the vector.
public double getSum();