Alternating Digit Sum

Problem Description

You are given a positive integer n. Each digit of n has a sign according to the following rules:

• The most significant digit is assigned a positive sign.
• Each other digit has an opposite sign to its adjacent digits.

Return the sum of all digits with their corresponding sign.

Key Insights

• The most significant digit contributes positively to the sum.
• Each subsequent digit alternates in sign.
• The position of each digit can be determined by its index from left to right.
• The alternating pattern can be simply derived from the index of each digit.

Space and Time Complexity

Time Complexity: O(log(n)), since we are processing each digit of the number. Space Complexity: O(1), because we are using a constant amount of space irrespective of the input size.

Solution

To solve the problem, we can follow these steps:

1. Convert the number n into a string to easily access each digit.
2. Initialize a variable to hold the sum.
3. Iterate through each digit, using its index to determine the sign (positive for even indices, negative for odd indices).
4. Convert each digit back to an integer and add or subtract it from the sum based on its sign.
5. Return the final sum.

In terms of data structures, we primarily use a string for digit access, and a simple integer for the accumulated sum.

Code Solutions