In 3 to 5 sentences, What does it mean for a set to be closed over an operation?

Define a recursive function named trim; it takes as its arguments a linked list (the head node of it) and a non-negative integer representing the index of an element in the list. The function mutates the linked list such that all elements that occur after the index is removed. Additionally, the function returns a linked list of all the elements that were moved. If the index value exceeds the length of the linked list, it should raise an IndexError. For example, if we defined a list as l1 = LN(1, LN(2, LN 3))) , calling the function would return the linked list LN(2, LN(3)), and the mutated l1 would become LN(1). You must use recursion. def trim(l: LN, index: int) -> LN:

Program in C

Towers of Hanoi. There is a story about Buddhist monks who are playing this puzzle with 64 stone disks. The story claims that when the monks finish moving the disks from one post to a second via the third post, time will end. Eschatology (concerns about the end of time) and theology will be left to those better qualified; our interest is limited to the recur- sive solution to the problem.   A stack of n disks of decreasing size is placed on one of three posts. The task is to move the disks one at a time from the first post to the second. To do this, any disk can be moved from any post to any other post, subject to the rule that you can never place a larger disk over a smaller disk. The (spare) third post is provided to make the solution possible. Your task is using c++ write a recursive function that describes instructions for a solution to this problem. We don’t have graphics available, so you should output a sequence of instructions that will solve the problem.   Hint: If you could…