Count Nodes With the Highest Score.py

class Solution:
    def countHighestScoreNodes(self, parents: List[int]) -> int:
        graph = collections.defaultdict(list)
        for node, parent in enumerate(parents):  # build graph
            graph[parent].append(node)
        n = len(parents)                         # total number of nodes
        d = collections.Counter()
        def count_nodes(node):                   # number of children node + self
            p, s = 1, 0                          # p: product, s: sum
            for child in graph[node]:            # for each child (only 2 at maximum)
                res = count_nodes(child)         # get its nodes count
                p *= res                         # take the product
                s += res                         # take the sum
            p *= max(1, n - 1 - s)               # times up-branch (number of nodes other than left, right children ans itself)
            d[p] += 1                            # count the product
            return s + 1                         # return number of children node + 1 (self)
        count_nodes(0)                           # starting from root (0)
        return d[max(d.keys())]                  # return max count