2eggs-100floors-cache.py

# Speed up.
cache = {}

def f(n):
    # Speed up.
    if cache.get(n) != None:
        return cache[n]

    if n == 1:
        print('n==1, directly return 1')
        return 1

    p = [] # Storage for temp results.
    for i in range(1, n): # i in [1, n)
        temp = 1 + max(i-1, f(n-i))
        p.append(temp)

    # Speed up.
    cache[n] = min(p)

    return min(p)

print('f(100)', f(100))