`` Complete the following tasks:

1. Implement the binomial queue. Implement a hash-table of the keys that are already in the priority queue. So, for any pair (key, pointer), where pointer is the pointer of the the node that holds key in the priority queue, hash on the key, and store the pair (key, pointer) in your hash table.

2. Count and print out the total number of comparisons and assignments executed for the insertions of all the N elements into the binomial queue.

3. Test the deleteMin() operation by applying a sequence of 10 deleteMin() and by printing out the result.

4. Test the function find() as follows: Prompt the user to input a string key. Execute the private function find(key). If find returns a pointer to a node that indeed holds key printout that find() was successful. Otherwise, printout that find() did not find the key.

5. You are ready to implement now the remove and decreaseKey operations. Keep in mind that remove is a simple extension of decreaseKey: first decrease the key of the target so that it percolates to the top (i.e., becomes the minimum key), then simply call deleteMin. Note that percolating up involves accessing (and possibly moving) the parent node. You may modify the given code so that each node keeps a pointer to its parent.

6. Test your implementation by applying a sequence of remove(key) operations, and verify their correctness. For instance after remove(key), find(key) should return “not found”. Prompt the user 5 times to input a key. Execute the remove(key)operation and verify (by printing whether the removal was successful or not).