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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.
Example:
Input: 19
Output: true
Explanation:
12 + 92 = 82
82 + 22 = 68
62 + 82 = 100
12 + 02 + 02 = 1
Once you know how to pull individual digits out of a number, these are relatively straight forward. You just need to keep track of your in-progress sums vs. total sums and the total sums you’ve previously seen for loop detection.
To get a digit, you just mod the number by its base (10
, assuming its base 10
). Then you divide the original number by its base and continue. An unrolled look for the number 19
would look like:
x = 19
x % 10 # => 9
x //= 10 # (x => 1)
x % 10 # => 1
x //= 10 # (x => 0)
I don’t think I missed any this time.
There’s possibly a way to detect loops without using a set (mathematical) to decrease memory usage but I don’t know of it.
class Solution:
def isHappy(self, n: int) -> bool:
seen = set()
curr = n
prev = n
while prev != 1:
if prev in seen:
break
seen.add(prev)
curr = prev
prev = 0
while curr:
digit = curr % 10
curr //= 10
prev += digit ** 2
return prev == 1
Runtime: 36 ms, faster than 30.40% of Python3 online submissions for Happy Number.
Memory Usage: 13.9 MB, less than 5.26% of Python3 online submissions for Happy Number.