Write a function to count the number of nodes in a singly linked list. Discuss the approach and complexity of your solution.

Using the function provided, write a function that decides whether two lists are "identical". That is, if cycling by any number N makes the lists identical, the function should return True, otherwise, it should return False. for example identical([1,2,3,4,5], [5,4,1,2,3,]) should give True and identical([1,2,3,4,5,6], [1,2,3,5,4]) should give False.

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:

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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 write a function PythQuad(n) in python that generates a list of pythagorean quadruples (x,y,z,w) such that x <= y <= z <= w < n. Please do not use a triply nested loop, use the properties of a pythagorean quadruple to write the function.

Java Programming language Please help me with this. Thanks in advance.

Implement a function to insert a node at the end of a doubly linked list. Explain the steps involved and analyze the time complexity of your implementation.