Discrete mathematics in Python

dmfc.py

def digits(n):
	result = []
	l = 0	
	while n > 0:
		d = n % 10
		result.insert(0, d)
		n = n // 10
		l += 1
	return (l, result)

def digitalroot(n, trace=False):
	if trace:		
		tr = []
	l, n = digits(n)
	while l > 1:
		s = sum(n)
		if trace:
			tr.insert(0, s)
		l, n = digits(s)
	if trace:
		return (n, tr)
	return n

def perfectsquare(n):
	return sum(map(lambda x: pow(x, 2), range(1, n+1)))

def ismonotonic(n, increasing=True):
	fncmp = lambda a, b: a < b if increasing else a > b
	prev = n[0]
	for i in n[1:]:
		if not fncmp(prev, i):
			return False
		prev = i
	return True

def strhaspairs(s, pairs):
	lv, rv = pairs
	lpn, rpn = 0, 0
	for c in s:
		if c == lv:
			lpn += 1
		elif c == rv:
			rpn += 1
	return lpn == rpn

def wordcount(s):
	count = 0
	ws = 0x20
	ca, cz  = 0x41, 0x5a
	cA, cZ = ca+0x20, cz+0x20
	i, l = 0, len(s) - 1
	wb = False
	while i <= l:
		if ord(s[i]) == ws and wb == True:
			wb = False
			count += 1
		elif (ord(s[i]) >= ca and ord(s[i]) <= cz) or (ord(s[i]) >= cA and ord(s[i]) <= cZ):
			wb = True
		i += 1
	else:
		if wb:
			count += 1
	return count

def xorswap(a, b):
	a ^= b
	b ^= a
	a ^= b
	return (a, b)

def simple_swap(n):
	for i in range(len(n)-1):
		if n[0] > n[i+1]:
			a, b = n[i], n[i+1]
			n[i], n[i+1] = xorswap(a, b)
	return n

def collatz_conjecture(n):
	result = []
	while n != 1:
		if n&0x1 == 0:
			n = n // 2
			result.append(n)
		else:
			n = 3*n+1
			result.append(n)
	return result

def tobinary(n):
	result = []
	while n != 0 :
		d = n % 2
		n = n // 2
		result.insert(0, d)
		
	return result