A min-heap is useful when we are interested in the minimum value of a set of numbers. Now, instead of the min, we are interested in the K-th smallest value. a.)  Please design a data structure to allow the following two operations: push (insert a new number) and find_Kmin (return the value of the K-th smallest number without removing it). Both operations should be done in O(log K) time.

Could you help me the following questions? Sara and her friends said they have discovered a way to get O(1) category performance for both insert and remove in a priority queue. Their description of the data structure and algorithms is as follows: They use an array implementation for the priority queue The index of the array represents the rank of an element – e.g. an element whose rank is 50 will be placed at index 49 Each element is the head node to a linked list – if a new element is inserted into the priority queue with the same rank as another element already in the queue, the new element is added to the linked list at its head Example: If an element “X” with rank 25 exists at index 24, and a new element “Y” also has a rank of 25, the linked list at index 24 is “Y” then “X” When remove is performed, the element at the highest index is removed. If there is more than one node at that index, the node at the head of the linked list there is removed Based on this description of the…

Write a function named merge-sort in Scheme that takes a list of integers as input and returns a sorted list. (Hint: Use the merge and split-list methods that you just wrote. You will have to cut-and-paste the code into your answer.) For example, (merge-sort '(5 3 1 2 4)) should return '(1 2 3 4 5) • (every-other '()) should return '()

Please explain    Q#Do the time complexities of a singly linked list differ from the time complexities of the operations (update, insert, lookup, delete) of a doubly-linked list? Group of answer choices a. Yes, the Big-O complexities are different for some of the operations. Adding the additional pointer to the previous node in the doubly linked list makes half of the operations slower.   b. No, the Big-O complexities do not differ. While a Doubly linked list uses an additional pointer of memory, it does not in fact modify the Big-O run-time.   c. Yes, the Big-O complexities are different for all of the operations. Adding the additional pointer to the previous node in the doubly linked list makes all operations slower.