4 solutions to leetcode 202. Happy Number have almost same performance

Question

I am working on an easy math question Happy number Happy Number - LeetCode

202. Happy Number

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 +たす 92 =わ 82
82 +たす 22 =わ 68
62 +たす 82 =わ 100
12 +たす 02 +たす 02 =わ 1

My solutions

• Solution 1, 28ms 12.1mb

  • string operations

class Solution1:
 def isHappy(self, n):
 s = set()
 while n != 1:
 if n in s: return False
 s.add(n)
 n = sum([int(i) ** 2 for i in str(n)])
 else:
 return True

• Solution 2, 24ms, 12.3mb

class Solution2:
 def isHappy(self, n):
 """
 :type n: int
 :rtype: bool
 """
 s = set()
 while n != 1:
 if n in s: return False
 s.add(n)
 _sum = 0
 while n:
 _sum += (n % 10) ** 2
 n //= 10
 n = _sum
 return n == 1

• Solution 3 the save as solution 2 minor changes (24ms, 12.3mb)

class Solution3:
 def isHappy(self, n):
 """
 :type n: int
 :rtype: bool
 """
 s = set()
 while n:
 if 1 in s:
 return True
 if n in s:
 return False
 s.add(n)
 _sum = 0
 while n:
 _sum += (n%10)**2 #leave unit digit
 n //= 10 #remvoe unit digit 
 n = _sum

• Solution 4 without extra space(24ms, 12.3mb)

class Solution4:
 def isHappy(self, n):
 """
 :type n: int
 :rtype: bool
 """
 while n != 1 and n != 4:
 _sum = 0
 while n :
 _sum += (n % 10) * (n % 10)
 n //= 10
 n = _sum
 return n == 1

TestCase

class MyCase(unittest.TestCase):
 def setUp(self):
 self.solution = Solution3()
 def test_1(self):
 n = 19
 check = self.solution.isHappy(n)
 self.assertTrue(check)

It's interesting that the last 3 solutions shared the same performance, though try best possibility to improve it.

• Oscar Smith: In general, you should never be using a benchmark that takes less than a second. Timings below that are way too variable.

Answer 1

Solution #2:

class Solution2:
 def isHappy(self, n):
 # ...
 while n != 1:
 if n in s: return False
 # ...
 return n == 1

You are looping while n != 1, without any break statements. There is no need to test n == 1 at the return statement at the end. Just return True.

---

Solution #3 returns None if 0 is given as input, instead of returning True or False.

---

Solution #4 becomes an endless loop if 0 is given as input.

Are there any other stopping conditions other that n == 0, n == 1 or n == 4? It isn't clear that all unhappy numbers result in a loop containing the value 4, so the validity of this approach is in question.

Update: Actually Wikipedia provides a clear argument that unhappy numbers will arrive in a loop containing the value 4, so this approach is valid, but should included a comment with a link to that proof.

---

In all your solutions, your loop is testing at least two conditions, such as both n != 1 and n is s. Why not initialize s to contain a 1 (or even just leave it as an empty set), and then only test n in s. No special cases.

def is_happy(n):
 s = { 1 }
 while n not in s:
 s.add(n)
 n = sum(i * i for i in map(int, str(n)))
 return n == 1

Update:

Since Wikipedea has proof that all positive unhappy numbers end in the sequence 4 → 16 → 37 → 58 → 89 → 145 → 42 → 20 → 4 → ..., and happy numbers end in the sequence 1 → 1 → ..., you can create a set of these termination values (including 0 → 0 → ...), and no longer needed to maintain the set of "seen" values. By using all numbers in the unhappy loop, we can terminate the search up to 8 iterations earlier over just checking for n == 1 and n == 4.

def is_happy(num):
 # See https://en.wikipedia.org/wiki/Happy_number#Sequence_behavior
 terminal = { 0, 1, 4, 16, 20, 37, 42, 58, 89, 145 }
 while num not in terminal:
 num = sum(i * i for i in map(int, str(num)))
 return n == 1

---

Finally:

• follow the PEP-8 standards (avoid mixedCase function/method names),
• Stop writing classes!