# Question

Write an algorithm to determine if a number is “happy”.

A happy number is a number defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are happy numbers.

# Set Solution

Use a set to store intermediate results to capture loops.

```
class Solution(object):
def isHappy(self, n):
"""
:type n: int
:rtype: bool
"""
intermediate = set()
while True:
nextN = self.squareDigits(n)
if nextN == 1:
return True
elif nextN == n:
return False
elif nextN in intermediate:
return False
n = nextN
intermediate.add(nextN)
def squareDigits(self, n):
res = 0
for digit in str(n):
digit = int(digit)
res += digit * digit
return res
```

# Floyd Cycle Detection Solution

```
class Solution(object):
def isHappy(self, n):
"""
:type n: int
:rtype: bool
"""
slow, fast = n, n
while True:
slow = self.squareDigits(slow)
fast = self.squareDigits(fast)
fast = self.squareDigits(fast)
if slow == 1:
return True
if slow == fast:
return False
def squareDigits(self, n):
res = 0
for digit in str(n):
digit = int(digit)
res += digit * digit
return res
```