The Problem

Solution using Hash Map:

This problem is asking to find out if the given number is happy or not.

How we define if the number is happy or not, will copy-paste from the problem statement itself as the process is so clear:

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.

I hope it is clear! so we take the number and we keep replacing the number with the sum of the squares of it is digits until we end up with 1 so it is happy if it keeps looping and giving numbers already found before so it is not happy.

Example:

number = 19

• Let's do it step by step: we sum the squares of its digits and assign it back to the same number variable: > number = 1² + 9² = 1 + 81 = 82

is it equal to 1 or did we saw it before no so continue

number = 8² + 2² = 64 + 4 = 68

Not equal to 1 and didn't saw it before, continue

number = 6² + 8² = 36 + 64 = 100

Not equal to 1 and didn't saw it before, continue

number = 1² + 0² + 0² = 36 + 64 = 1

Oooh, this is equal to 1 so we are done and number 19 is a happy number.

Try this number (58) with yourself and see if it is happy or not so you can understand the procedure very-well.

Pseudocode:

From above we can see we need a loop to keep going and sum the number digits every-time when we going to stop when we find a number that we already saw before, even if it is 1 if we try it again like in the above example:

number = 1 = 1² = 1

Which we already saw before so we stop looping and return our answer.

Will use hash-map to store the numbers we get why hash-map not a list because look-up in hash-map is just O(1) but in a list is O(n)

1. define seen_numbers = {}
2. loop number not in seen_numbers
3.     seen_numbers.append(number)
4.     number = sum(digit^2 for digit in number)
5. return number is equal to 1

Complexity:

• Time complexity: as we sum in each iteration the digits and we keep looping until we find a cycle so we can say our time will be O(log(n)).

• Space complexity we have to store almost every number we find until we hit a cycle so it will be almost the same as the time so it will be O(log(n))

  • Solution in Python to understand more

I hope this helps any feedback will be appreciated :).