(IN JAVA) In this task, a binomial heap should be implemented. A binomial heap is implemented by an array with its elements being binomial trees: on the first place there is the binomial tree B0 with one element, on the second place there is the binomial tree B1 with two elements, on the third place there is the binomial tree B2 with four elements,. . . Each binomial tree is implemented recursively using the class BinomialNode. In this class there is nothing to implement. Methods in this class are needed for the implementation of the methods in the class BinomialHeap
(IN JAVA) In this task, a binomial heap should be implemented. A binomial heap is implemented by
an array with its elements being binomial trees: on the first place there is the binomial tree
B0 with one element, on the second place there is the binomial tree B1 with two elements,
on the third place there is the binomial tree B2 with four elements,. . . Each binomial tree
is implemented recursively using the class BinomialNode. In this class there is nothing to
implement. Methods in this class are needed for the implementation of the methods in the
class BinomialHeap. More precisely, in the class BinomialHeap you should implement the
following methods:
(i) insert, which takes an integer (a key) and inserts it in the binomial heap. The
method returns true, if the key is successfully inserted and false otherwise. In the
case, if the array should be resized, use the method resizeArray (see below).
(ii) getMin, which returns the minimal key in binomial heap. The implementation will
be also efficient if you iterate through the array. That is to say, you do not need to
store a pointer to minimal key. If the binomial heap is empty, the method should
return the maximal positive integer (Integer.MAX VALUE).
(iii) delMin, which deletes the minimal key from the binomial heap. The method returns
true, if the minimal key is successfully deleted and false otherwise (if the binomial
heap is empty).
(iv) resizeArray, which extends the array. The method is needed, for example, when
you find out that you need an extra place in your array when inserting new element.
Hint: Construct new array which is of double size and rewrite old elements in the
new array.
(v) merge, which merges two binomial trees (of the same size), and returns the merged
binomial tree.
(vi) It might be a good idea to implement a method for merging two binomial heaps – it
can than be used in implementation of insertion and deletion. But it is not necessary.
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