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. b.) In addition to push and find_Kmin, now we also want to support the pop operation to return and remove the K-th smallest element. Please design a data structure to support these three operations, and each operation should take O(log n) time with n being the size of the current set.

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.

What is the difference between stack and heap memory?       Correct choice:  A. Heap memory is allocated manually by the user and is 'long-lived'. You must manually allocate it, whereas memory on the stack will be reclaimed when the memory is out of scope from where it was initialized.   B. Stack memory is allocated manually by the user and is 'long-lived'. You must manually allocate it, whereas memory on the heap will be reclaimed when the memory is out of scope from where it was initialized.

How would you design a stack which, in addition to push and pop, also has a function min which returns the minimum element? Push, pop and min should all operate in O(1) time. Your design (in pseudo code) should include a class Stack and three functions, i.e., push, pop, and min.