codecakes

def countBits(num):
	'''Count number of bits in a positively signed number.'''
	count = 0
	for i in iter(lambda: fn(num), 0):
		num = i
		count += 1
	return count + 1

codecakes

# Slow
sub = lambda astring: [''.join([astring[idx] for idx, each in enumerate("{0:0b}".format(i)) if each == '1']) for i in range(pow(2, len(astring)))]

# Better recursive
def subsequences(chars, n, pt=0, res=''):
	'''Print all subsequences of a string.'''
	# print(pt, n)
	if pt == n:
		print(repr(res))
		return

codecakes

def xorN(n):
	'''Xor of all numbers from 1 to n.'''
	rem = n%4
	if rem ==0:
		return n
	xord = functools.reduce(lambda x,y: x^y, range(1, rem+1))
	return xord if xord < 2 else n+1

codecakes

import math

binaryLen = lambda n: math.floor(math.log2(n)) + 1

def findNextMx(mx, ar , exclude_list):
	'''Find the next max of same bin len as mx.'''
    logmx = binaryLen(mx)
    nextmx = float('-inf')
    for n in ar:
        if n not in exclude_list and n > nextmx:

codecakes

def largestSpan(a_bin, b_bin):
    a_bin_ln = len(a_bin)
    b_bin_ln = len(b_bin)
    max_ij = max(a_bin_ln, b_bin_ln)
    a_bin = a_bin.zfill(max_ij)
    b_bin = b_bin.zfill(max_ij)
    a_bin, b_bin = list(map(int, a_bin)), list(map(int, b_bin))
    maxLen = diff = 0
    start = 0
    cutoff = {}

codecakes

import math

fn = lambda num: math.floor(math.log2(num))

def binary_factorization(num):
	x = fn(num)
	pw = 2**x
	rem = num%pw
	return pw, (fact2(rem) if rem else rem)

codecakes

import functools

@functools.lru_cache(maxsize = 100_000, typed=True)
def maxCut(n, a,b,c):
	if n <0: return -1
	if n == 0: return 0
	res = max([
	maxCut(n-a, a,b,c),
	maxCut(n-b, a,b,c),
	maxCut(n-c, a,b,c)])

codecakes

# See: https://practice.geeksforgeeks.org/problems/power-of-numbers/1/?ref=self

import functools

_MODNUM = 1000000007

# runs fine w/o lru_cache.
functools.lru_cache(maxsize=_MODNUM, typed=True)
def power(N,R):
    if R == 0:

codecakes

def printNos(N, start = 1, result=''):	def powerSet(s, pos = 0, ln = 0, res=None):
    if N == 0:	    '''
        print(result.strip())	    :param s: given string s
        return	    :return: list containing power set of s.
    result += "{0} ".format(start)	    '''
    return printNos(N-1, start+1, result) 

codecakes

# See: https://practice.geeksforgeeks.org/problems/power-set-using-recursion/1/?ref=self

def powerSet(s, pos = 0, ln = 0, res=None):
    '''
    :param s: given string s
    :return: list containing power set of s.
    '''
    res = res or ''
    ln = ln or len(s)
    if pos == ln: