Problem Description
Given an integer num, repeatedly add all its digits until the result has only one digit, and return it.
Key Insights
- The process of adding digits can be continued until a single digit is obtained.
- This can be efficiently calculated using the properties of numbers in mod 9.
- The result can be quickly derived using a mathematical formula without loops or recursion.
Space and Time Complexity
Time Complexity: O(1)
Space Complexity: O(1)
Solution
To solve the problem of repeatedly adding the digits of a number until only one digit remains, we can utilize the concept of digital roots. The digital root can be found using the formula: 1 + (num - 1) % 9, which effectively reduces the number to a single digit in constant time. This approach avoids the need for iterative or recursive summation.