A directed graph can be implemented as a list, whose elements are pairs of nodes. Assume the nodes are integers. In Haskell, you can define a graph as follows:

type Node = Int type Edge = (Node, Node) type Graph = [Edge] type Path = [Node] g :: Graph g = [ (1, 2), (1, 3), (2, 3), (2, 4), (3, 4) ] h :: Graph h = [ (1, 2), (1, 3), (2, 1), (3, 2), (4, 4) ]

a) Write a function named nodes to get the list of nodes of a graph. For example, nodes g => [1, 2, 3, 4] . b) Write a function named adjacent that takes a node N and a graph G and returns a list of all nodes that are connected to N such that N is the source. For example, adjacent 2 g => [3, 4], adjacent 4 g => [] , adjacent 4 h => [4]. c) Write a function named detach that takes a node N and a graph G and returns the graph formed by removing N from G. For example, detach 3 g => [(1, 2), (2, 4)]. d) Write a function named paths that accepts two nodes V1 and V2 (and a graph G) and returns a list of all possible cycle-free paths from V1 to V2. For example, paths 2 2 g => [[2]], paths 3 2 g => [], paths 1 4 g => [[1, 2, 3, 4], [1, 2, 4], [1, 3, 4]]. Hint: use the functions adjacent and detach above

Write the code in Haskell