/
ProjectEuler_495.py
94 lines (87 loc) · 2.78 KB
/
ProjectEuler_495.py
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from math import sqrt,factorial
from primeUtil import getPrimesUpTo
from iterUtil import tupleRange
from iterUtil import tupleDiff
from sys import argv
import functools
import pdb
# partitionsOf[i] = number of partitions of i
# only first 30 are here since that's all that
# 495 will require (if even that)
partitionsOf = [1, 1, 2, 3, 5,
7, 11, 15, 22, 30,
42, 56, 77, 101, 135,
176, 231, 297, 385, 490,
627, 792, 1002, 1255, 1575,
1958, 2436, 3010, 3718, 4565,
5604]
@functools.lru_cache(maxsize=256)
def factorCardByPrime(n):
if n==0 or n==1: return 0
for prime in getPrimesUpTo(sqrt(n)):
if n%prime==0:
card=factorCardByPrime(n/prime)
if prime not in card:
card[prime]=1
else:
card[prime]+=1
return card
return {int(n): 1}
@functools.lru_cache(maxsize=256)
def factorCardByPrimeFactorial(n):
card={}
for i in range(2,n+1):
c = factorCardByPrime(i)
for prime in c:
if prime not in card:
card[prime]=0
card[prime]+=c[prime]
return card
@functools.lru_cache(maxsize=65536)
def getTuples(cards, notIn, ofLength):
if ofLength==1:
if cards not in notIn:
return 1
return 0
else:
cnt=0
for tup in tupleRange(cards):
if tup not in notIn:
notIn = notIn.union([tup])
cnt += getTuples(tupleDiff(cards,tup), notIn, ofLength-1)
return cnt
def getTupleCount(cards, ofLength):
if ofLength==1:
return 1
if len(cards)==2 and ofLength==2:
if cards[0]==0:
if cards[1]%2==0:
return int(cards[1]/2)
return int((cards[1]+1)/2)
if cards[0]==1:
return cards[1]+1
if cards[0]%2==1:
cards = list(cards)
cards[0] = int(cards[0]/2)
return 2*int(getTupleCount(tuple(cards),ofLength))
if cards[0]%2==0:
cards1 = list(cards)
cards2 = list(cards)
cards1[0] = int(cards[0]/2)
cards2[0] = int(cards[0]/2)-1
return getTupleCount(cards1,ofLength)+getTupleCount(cards2,ofLength)
return 1 + getTupleCount(cards,ofLength-1)
if __name__=="__main__":
print(" ",end="")
for i in range(9):
print(" "+str(i)+" ", end=" ")
print()
setsDone=set()
for i in range(20):
print('{0: =5d} '.format(i), end=" ")
for j in range(9):
tup = (i,j)
#if tuple(sorted(tup)) in setsDone: continue
setsDone.add(tuple(sorted(tup)))
print('{0: =5d}'.format(getTupleCount(tuple(sorted(tup)), 2)), end=" ")
print()