Consider a natural number (or integer number) 58473, the digits of this number are 5, 8, 4, 7, and 3.

Consider a natural number (or integer number) 58473, the digits of this number are 5, 8, 4, 7, and 3. If we need to sum the digits of this number then it is equal to 5 + 8 +4 +7+3 = 27.

There may be many algorithms that can be written to add the digits of integer numbers.

Question No  01:

You are required to design (write) a simple algorithm (Only Pseudo code) that will add (sum) the digits of an integer number.

Question No  02:

You are required to calculate (Step by Step) the worst case time complexity T(n) of the algorithm designed in Question No. 01.

Solution:

Question No. 01:

Here's a simple algorithm in pseudo code to sum the digits of an integer number:

1. Initialize a variable "sum" to 0.

2. Convert the given integer number to a string.

3. Iterate through each character in the string:

   3.1. Convert the character back to an integer.

   3.2. Add the integer value to the "sum" variable.

4. Output the final value of the "sum" variable.

Question No. 02:

To calculate the worst-case time complexity T(n) of the algorithm, let's analyze the steps involved:

Step 1: Initializing a variable "sum" takes constant time, so it can be considered O(1).

Step 2: Converting the given integer number to a string requires converting each digit individually. The number of digits in the worst case scenario would be log10(n). So, this step has a time complexity of O(log n).

Step 3: Iterating through each character in the string requires visiting each digit once. In the worst case scenario, the number of digits would be log10(n). So, this step has a time complexity of O(log n).

Step 3.1: Converting each character back to an integer takes constant time, so it can be considered O(1).

Step 3.2: Adding the integer value to the "sum" variable takes constant time, so it can be considered O(1).

Step 4: Outputting the final value of the "sum" variable takes constant time, so it can be considered O(1).

Considering all the steps, the total worst-case time complexity T(n) of the algorithm is:

T(n) = O(1) + O(log n) + O(log n) + O(1) + O(1) + O(1) = O(log n)

Therefore, the worst-case time complexity of the algorithm is O(log n).