21位水仙花数

class WaterNum(object):
	"""
	"""
	def __init__(self,N = 21):
		"""
		"""
		self.N			= N
		self.sum		= 0
		self.p_remain	= N
		self.pre_table	= []
		self.max_num	= pow(10,N) - 1
		self.min_num	= pow(10,N - 1)
		self.count		= [-1 for i in range(10)]
		self.filter		= [0 for i in range(10)]

		self.init_pre_table()
		#print('pre_table:\n',self.pre_table)
	
	def init_pre_table(self):
		""" initialize the pre_table
		"""
		for i in range(10):
			powi = pow(i,self.N)
			a = [val * powi for val in range(self.N + 1)]
			self.pre_table.append(a)
	
	def set_filter(self):
		"""
		"""
		k = self.k - 1
		s_str = str(self.sum)
		c = self.p_remain
		#print('c',c,'k',k)
		self.filter = [0 for i in range(10)]
		while self.max_num - self.sum < self.pre_table[k][c]:
			c -= 1
		
		if c == 0:
			return False
		temp_sum = self.sum + self.pre_table[k][c]
		temp_sum_str = str(temp_sum)

		pos = 0
		while pos < len(s_str) and s_str[pos] == temp_sum_str[pos]:
			pos += 1

		sub_str = s_str[:pos]

		for ch in sub_str:
			self.filter[int(ch)] += 1
		#print('sum:',s_str,'temp_sum:',temp_sum_str,'c:',c)
		#print('sub_str:',sub_str)

		return True

	def is_sum_ok(self):
		"""
		"""
		for i in range(self.k,10):
			if self.filter[i] > self.count[i]:
				return False

		return True

	def print_right(self,sum):
		""" test the sum is the value we want
		if yes print it ,if no ,do thing
		"""
		s_str = str(sum)
		count_temp = [0 for i in range(10)]
		for ch in s_str:
			count_temp[int(ch)] += 1
		for i in range(10):
			num_temp = self.count[i]
			# if is -1,turn to 0
			if num_temp < 0:
				num_temp = 0
			if num_temp != count_temp[i]:
				return False
		print('found:',s_str)
		return True

	def trace_back(self):
		"""
		"""
		self.count[self.k] = -1
		self.k += 1
		self.freq = 0

	def search(self):
		"""
		"""
		self.k = 9
		self.freq = 1
		while self.k < 10:
			if self.freq == 0:
				self.freq = 1
				self.count[self.k] += 1
			else:
				if self.freq > self.p_remain:
					self.trace_back()
					continue

				self.count[self.k] = self.freq
			if self.count[self.k] > 0:
				self.p_remain -= self.freq
				temp_sum = self.sum + self.pre_table[self.k][self.freq]
				#print('at 1')
				#print('count',self.count,'temp_sum:',temp_sum,'p_remain',self.p_remain,'k:',self.k)		
				if self.p_remain <= 0 or self.k <= 0:
					self.print_right(temp_sum)
					c = self.count[self.k] - self.freq
					self.sum -= self.pre_table[self.k][c]
					self.p_remain += self.count[self.k]
					self.trace_back()
					#print('at 1-1')
					continue
				else:
					#print('at 1-2')
					if temp_sum > self.max_num:
						c = self.count[self.k] - self.freq
						self.sum -= self.pre_table[self.k][c]
						self.p_remain += self.count[self.k]
						self.trace_back()
						#print('at 1-3')
						continue
					self.sum = temp_sum
				if self.set_filter() == True and self.is_sum_ok() == False:
					#print('at 1-4')
					self.freq = 0
					continue
				else:
					#print('at 1-5')
					self.k -= 1
					self.freq = self.filter[self.k]
					self.count[self.k] = -1
			else:
				#print('at 2')
				#print('count',self.count,'sum:',self.sum,'p_remain',self.p_remain,'k:',self.k)		
				if self.set_filter() == True and self.is_sum_ok() == False:
					self.freq = 0
					#print('at 2-1')
					continue
				self.k -= 1
				self.freq = self.filter[self.k]
				self.count[self.k] = -1
				#print('at 2-2,filter:',self.filter,'freq(',self.k,')',self.freq)

import time

if __name__ == '__main__':
	#time_begin = time.time()
	for i in range(11,39):
		print('found---------------',i,'------------------------')
		time.clock()
		water_num = WaterNum(i)
		water_num.search()
		#time_end = time.time()
		print('use time',int(time.clock()))

found 11 -----------------------------------------------

32164049650

32164049651

40028394225

42678290603

44708635679

49388550606

82693916578

94204591914

use time 0

found 12 -----------------------------------------------

use time 1

found 13 -----------------------------------------------

use time 1

found 14 -----------------------------------------------

28116440335967

use time 3

found 15 -----------------------------------------------

use time 6

found 16 -----------------------------------------------

4338281769391370

4338281769391371

use time 9

found 17 -----------------------------------------------

21897142587612075

35641594208964132

35875699062250035

use time 15

found 18 -----------------------------------------------

use time 23

found 19 -----------------------------------------------

1517841543307505039

3289582984443187032

4498128791164624869

4929273885928088826

use time 35

found 20 -----------------------------------------------

63105425988599693916

use time 51

found 21 -----------------------------------------------

128468643043731391252

449177399146038697307

use time 21

found 22 -----------------------------------------------

use time 54

found 23 -----------------------------------------------

21887696841122916288858

27879694893054074471405

27907865009977052567814

28361281321319229463398

35452590104031691935943

use time 94

found 24 -----------------------------------------------

174088005938065293023722

188451485447897896036875

239313664430041569350093

use time 141

found 25 -----------------------------------------------

832662335985815242605070

832662335985815242605071

1550475334214501539088894

1553242162893771850669378

3706907995955475988644380

3706907995955475988644381

4422095118095899619457938

use time 209

found 26 -----------------------------------------------

use time 305

found 27 -----------------------------------------------

77888878776432530886487094

121204998563613372405438066

121270696006801314328439376

128851796696487777842012787

174650464499531377631639254

177265453171792792366489765

use time 431

found 28 -----------------------------------------------

use time 580

found 29 -----------------------------------------------

4716716265341543230394614213

5022908050052864745436221003

14607640612971980372614873089

19008174136254279995012734740

19008174136254279995012734741

23866716435523975980390369295

use time 748

found 30 -----------------------------------------------

use time 955

found 31 -----------------------------------------------

793545620525277858657607629822

1145037275765491025924292050346

1927890457142960697580636236639

2309092682616190307509695338915

use time 1223

found 32 -----------------------------------------------

17333509997782249308725103962772

use time 1545

found 33 -----------------------------------------------

32186410459473623435614002227248

186709961001538790100634132976990

186709961001538790100634132976991

use time 1937

found 34 -----------------------------------------------

1122763285329372541592822900204593

use time 2416

found 35 -----------------------------------------------

5250083909873201044638631458484846

7673249664848285722449710136138169

12639369517103790328947807201478392

12679937780272278566303885594196922

use time 3041

found 36 -----------------------------------------------

91097771122214850683543503173498149