import random

class Node:
    def __init__(self, x):
        self.x = x
        self.left = None
        self.right = None

def insert(root, x):
    # TODO: inserați x în arbore
    pass

def search_path_length(root, x):
    # TODO: calculați lungimea drumului până la x
    pass

def average_search_path(n):
    """Construiește un BST dintr-o permutare aleatoare și măsoară media."""
    perm = list(range(1, n + 1))
    random.shuffle(perm)

    root = None
    for x in perm:
        root = insert(root, x)

    lengths = [search_path_length(root, x) for x in perm]
    return sum(lengths) / n

def experiment(trials=2000, n=100):
    total = 0
    for _ in range(trials):
        total += average_search_path(n)
    return total / trials

for n in [10, 20, 50, 100, 200, 500, 1000]:
    avg = experiment(trials=1000, n=n)
    print(f"n = {n} → lungime medie ≈ {avg:.3f}")