问题
I recently met a algorithm question in open.kattis.com. The question's link is https://open.kattis.com/problems/listgame2. Basically, it is a question ask the players to factorize a integer X (10^3 <= X <= 10^15) to get as many distinct positive integers (Y1,...,Yk) as possible such that (Y1+1)(Y2+1)⋯(Yk+1) = X.
I already came up with a solution using Python3, which does pass several test cases but failed one of them:MyStatus
My code is:
def minFactor(n, start):
maxFactor = round(n**0.5)
for i in range(start, maxFactor+1):
if n % i == 0:
return i
return n
def distinctFactors(n):
curMaxFactor = 1
factors = []
while n > 1:
curMaxFactor = minFactor(n, curMaxFactor+1)
n //= curMaxFactor
factors.append(curMaxFactor)
# This is for the situation where the given number is the square of a prime number
# For example, when the input is 4, the returned factors would be [2,2] instead of [4]
# The if statement below are used to fix this flaw
# And since the question only requires the length of the result, deleting the last factor when repeat do works in my opinion
if factors[-1] in factors[:-1]:
del factors[-1]
return factors
num = int(input())
print(len(distinctFactors(num)))
Specifically, my idea inside the above code is quite simple. For example, when the given input is 36, I run the minFactor function to find that the minimum factor of 36 is 2 (1 is ignored in this case). Then, I get 18 by doing 36/2 and invoke minFactor(18,3) since 2 is no more distinct so I start to find the minimum factor of 18 by 3. And it is 3 clearly, so I get 6 by doing 18/3 in function distinctFactors and invoke minFactor(6,4), since 4 is smaller than sqrt(6) or 6**0.5 so 6 itself will be returned and I finally get the list factors as [2,3,6], which is correct.
I have scrutinised my code and algorithm for hours but I still cannot figure out why I failed the test case, could anyone help me with my dilemma??? Waiting for reply.
回答1:
Consider the number 2**6.11**5
.
Your algorithm will find 5 factors:
2
2**2
2**3
11
11**2
(11**2 this will be discarded as it is a repeat)
A 6 length answer is:
2
2**2
11
11**2
2*11
2**2*11
来源:https://stackoverflow.com/questions/46654759/algorithm-factorize-a-integer-x-to-get-as-many-distinct-positive-integersy1