Happy Number
A happy number is defined by repeatedly replacing it with the sum of squares of its digits until it either reaches 1 (happy) or loops endlessly (not happy).
Return True if n is a happy number.
Example:
19
True
- We start with the input number 19 and calculate the sum of squares of its digits: 12+92=1+81=82
- Then, we repeat the process with 82: 82+22=64+4=68
- Next, we calculate the sum of squares of the digits of 68: 62+82=36+64=100
- Finally, we continue this process: 12+02+02=1, which is 1, so the number 19 is happy, and we return True
Constraints:
- 1 <= n <= 2^31 - 1
Background Knowledge
The concept of a happy number is a mathematical idea where a number is repeatedly replaced by the sum of the squares of its digits. This process is repeated until the number either reaches 1, in which case it is considered a happy number, or it loops endlessly, indicating that it is not a happy number. To understand this problem, it's essential to be familiar with basic mathematical operations, such as squaring numbers and summing them up.
In the context of Hash Maps & Sets, this problem involves keeping track of the numbers that have been seen so far to detect loops. A hash set is an unordered collection of unique elements, which can be used to store the numbers that have been encountered during the process. This allows for efficient lookups to check if a number has been seen before, helping to identify loops.
The key mathematical concept here is the idea of a cycle or a loop. If a number is not happy, it will eventually enter a cycle where it repeats the same sequence of numbers. Detecting this cycle is crucial to determining whether a number is happy or not. This involves understanding how to use a hash set to keep track of seen numbers and how to calculate the sum of squares of digits.
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