Write a function, longest_path, that takes in an adjacency list for a directed acyclic graph. The function should return the length of the longest path within the graph. A path may start and end at any two nodes. The length of a path is considered the number of edges in the path, not the number of nodes.
graph = {
'a': ['c', 'b'],
'b': ['c'],
'c': []
}
longest_path(graph) # -> 2graph = {
'a': ['c', 'b'],
'b': ['c'],
'c': [],
'q': ['r'],
'r': ['s', 'u', 't'],
's': ['t'],
't': ['u'],
'u': []
}
longest_path(graph) # -> 4graph = {
'h': ['i', 'j', 'k'],
'g': ['h'],
'i': [],
'j': [],
'k': [],
'x': ['y'],
'y': []
}
longest_path(graph) # -> 2graph = {
'a': ['b'],
'b': ['c'],
'c': [],
'e': ['f'],
'f': ['g'],
'g': ['h'],
'h': []
}
longest_path(graph) # -> 3