Google Interview: Arrangement of Blocks

Question

You are given N blocks of height 1…N. In how many ways can you arrange these blocks in a row such that when viewed from left you see only L blocks (rest are hidden by taller

Answer 1

Here is my construction solution inspired by @PengOne's ideas.

import itertools

def f(blocks, m):
    n = len(blocks)
    if m > n:
        return []
    if m < 0:
        return []
    if n == m:
        return [sorted(blocks)]
    maximum = max(blocks)
    blocks = list(set(blocks) - set([maximum]))
    results = []
    for k in range(0, n):
        for left_set in itertools.combinations(blocks, k):
            for left in f(left_set, m - 1):
                rights = itertools.permutations(list(set(blocks) - set(left)))
                for right in rights:
                    results.append(list(left) + [maximum] + list(right))
    return results

def b(n, l, r):
    blocks = range(1, n + 1)
    results = []
    maximum = max(blocks)
    blocks = list(set(blocks) - set([maximum]))
    for k in range(0, n):
        for left_set in itertools.combinations(blocks, k):
            for left in f(left_set, l - 1):
                other = list(set(blocks) - set(left))
                rights = f(other, r - 1)
                for right in rights:
                    results.append(list(left) + [maximum] + list(right))
    return results

# Sample
print b(4, 3, 2) # -> [[1, 2, 4, 3], [1, 3, 4, 2], [2, 3, 4, 1]]