Cut rectangle in minimum number of squares

Question

I\'m trying to solve the following problem:

A rectangular paper sheet of M*N is to be cut down into squares such that:

1. The paper i

Answer 1

Here is a greedy impl. As @David mentioned it is not optimal and is completely wrong some cases so dynamic approach is the best (with caching).

def greedy(m, n):
    if m == n:
        return 1
    if m < n:
        m, n = n, m
    cuts = 0

    while n:
        cuts += m/n
        m, n = n, m % n
    return cuts

print greedy(2, 7)

Here is DP attempt in python import sys

def cache(f):
    db = {}

    def wrap(*args):
        key = str(args)
        if key not in db:
            db[key] = f(*args)
        return db[key]
    return wrap


@cache
def squares(m, n):
    if m == n:
        return 1
    xcuts = sys.maxint
    ycuts = sys.maxint
    x, y = 1, 1
    while x * 2 <= n:
        xcuts = min(xcuts, squares(m, x) + squares(m, n - x))
        x += 1
    while y * 2 <= m:
        ycuts = min(ycuts, squares(y, n) + squares(m - y, n))
        y += 1
    return min(xcuts, ycuts)