# My python code without using extra space

• The idea is pretty simple, the question is essentially the same with "Find the start point of a linked list cycle". I used the fast pointer and slow pointer trick.
Below is my code with some explanation:

``````def fractionToDecimal(self, numerator, denominator):
n = numerator
d = denominator
if n % d == 0:
return str(n//d)
# Deal with negatives
if (abs(n)/n) * (abs(d)/d) < 0:
res = '-'
n = abs(n)
d = abs(d)
else:
res = ''
# Integer part
res = res + str(n//d) + '.'
n = n % d
# Start point of the "list"
frem = n
srem = n
firstTime = True
while frem != 0 and not (firstTime == False and frem == srem):
firstTime = False
srem = (srem * 10) % d
frem = (frem * 10) % d
if frem:
frem = (frem * 10) % d
# The fast pointer encounters a remainder of 0, so no cycle in the "list"
if frem == 0:
res += str((n * 10) // d)
rem = (n * 10) % d
while rem:
res += str((rem * 10) // d)
rem = (rem * 10) % d
return res
else:
# Find the start point of the cycle, meanwhile, generate the non recurring part
srem = n
while frem != srem:
res += str((srem * 10) // d)
srem = (srem * 10) % d
frem = (frem * 10) % d
res += '('
# Generate the recurring part
firstTime = True
while not (firstTime == False and srem == frem):
firstTime = False
res += str((srem * 10) // d)
srem = (srem * 10) % d
res += ')'
return res``````

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