def init(alist, num1, num2):
	dplist = alist
	for i in range(num1 + 1):
		dplist.append([])
	for i in range(num1 + 1):
		for j in range(num2 + 1):
			dplist[i].append(0)
	for i in range(1, num1 + 1):
		dplist[i][0] = i
	for j in range(1, num2 + 1):
		dplist[0][j] = j

def dp(alist, list1, list2):
	num1 = len(list1)
	num2 = len(list2)


	for i in range(1, num1 + 1):
		for j in range(1, num2 + 1):
			if list1[i - 1] != list2[j - 1]:
				alist[i][j] = min(alist[i][j - 1], 
						  alist[i - 1][j - 1], 
						  alist[i - 1][j]) + 1
			else:
				alist[i][j] = min(alist[i][j - 1], 
						  alist[i - 1][j - 1], 
						  alist[i - 1][j])


	for i in range(0, num1 + 1):
		for j in range(0, num2 + 1):
			if j == num2:
				print alist[i][j]
			else: print alist[i][j], '  ',		
	return alist[num1][num2]

def levenshtein(str1, str2):
	alist = []
	list1 = [i for i in str1]
	list2 = [i for i in str2]
	num1 = len(list1)
	num2 = len(list2)
	if num1 == 0:
		return num2
	if num2 == 0:
		return num1
	init(alist,num1, num2)
	return dp(alist, list1, list2)


if __name__ == '__main__':
        print levenshtein('sitting', 'kitten')