Add Binomial Heap

[czgdp1807]

Description of the problem

Example of the problem

References/Other comments

https://en.wikipedia.org/wiki/Binomial_heap

[czgdp1807]

After studying https://en.wikipedia.org/wiki/Binomial_heap I have reached to the following API and class structure to support binomail heaps,

BinomialTreeNode
BinomialTreeNode will represent the nodes in the binomial trees which are a part of heaps. They will subclass the TreeNode. The following will be the data members,

1. parent - The reference to the parent of the current node.
2. key - The key of the current node.
3. children - The list of children. The list will contain the references to other nodes representing it's children. It will be supported by DynamicOneDimensionalArray.
4. data - The data to be stored at the current node.
   The above class will go to https://github.com/codezonediitj/pydatastructs/blob/master/pydatastructs/utils/misc_util.py

BinomialTree

This will represent the theoretical concept of binomial trees.
The following will be the data members of this class,

1. root - The root node of the tree. It will be of the type, BinomialTreeNode.
2. order - The order of the tree as defined on Wikipedia page.

The following will be the methods of this class,

1. add_sub_tree(self, other_tree) - This will add other_tree as the a child of the current tree.
2. is_empty - It will return True if the current tree is empty.

The above class will go to https://github.com/codezonediitj/pydatastructs/tree/master/pydatastructs/miscellaneous_data_structures

Binomial Heap

This will represent the binomial heap.
The following data members will be supported by this class,

1. root_list - This will contain the binomial trees sorted by order. It will be supported by DynamicOneDimensionalArray.

The following will be the methods supported by the class,

1. merge_tree(self, tree1, tree2) - This will merge tree1 and tree2.
2. merge(self, other_heap) - This will merge other_heap and self. It will update the self.root_list with contents of the new heap.
3. insert(key, data) - It will insert a new BinomialTreeNode object into the heap.
4. find_minimum() - It will find the node with the minimum key in the heap.
5. delete_minimum() - It will delete the node with the minimum key in the heap.
6. decrease_key(self, node) - It will decrease the key of the node and will change the structure of the heap. accordingly.
7. delete(self, node) - It will delete the node from the heap.

The above class will go to, https://github.com/codezonediitj/pydatastructs/blob/master/pydatastructs/trees/heaps.py

It is just a rough idea of how the API will look like. Changes might happen during coding them out.