Course Code Selection Problem Summary

1. Problem Overview:

   • I was tasked with processing course enrollment data to manage student choices and detect inversion counts for course selections.
   • The goal was to ensure the data handling was robust, accounting for various edge cases.

2. Approach:

   • I decided to implement two separate programs to solve the problem:
     • Linear Approach: A straightforward method to process the data, iterating through the course selections.
     • Divide-and-Conquer Method: A more efficient algorithm to handle larger datasets, leveraging the divide-and-conquer strategy.

3. Data Structure:

   • I planned to copy data from CSV files into a temporary 2D array for processing.
   • I would check for negative values, blank fields, and out-of-range values during the data processing.

4. Edge Cases Handling:

   • I suggested using -1 as a placeholder for blank fields, which would lead to an output of 'N/A' if included in the data.
   • I identified specific edge cases to test, including:
     • Normal data inputs.
     • Duplicate entries.
     • Negative values (considered invalid).
     • Missing data (using -1 as a placeholder).
     • Out-of-range values (course codes outside the valid range of 1001 to 1005).
     • Empty files.

5. Output Requirements:

   • I intended to create an output CSV file displaying 'N/A' for inversion counts in cases of negatives or other edge cases.
   • Additionally, I planned to print results in a console format using an unordered map to track inversion counts.
   • The output format would summarize counts of students with invalid choices, zero inversions, one inversion, etc.

6. Implementation Goals:

   • Ensure the code could handle all 100 student data effectively and count inversions accurately.
   • Cap inversion counts appropriately, with an understanding that a completely reverse-sorted array should yield a maximum of four inversions.

7. Testing and Validation:

   • I planned to rigorously test the implementation with various cases to ensure accuracy and robustness in handling the enrollment data.

Integeer multiplication problem

1. Integer Multiplication Program:

   • I created a program to multiply large integers using a divide-and-conquer approach, specifically the Karatsuba algorithm.
   • I adjusted the program to handle large integers by using string representation to avoid overflow issues, as C++'s int and long long types can only handle numbers up to certain limits.

2. Test Cases:

   • I provided a comprehensive set of test cases for the multiplication program, covering:
     • Normal Cases (1-4): Both numbers positive, different lengths, and even lengths.
     • Negative Cases (5-7): Various combinations of positive and negative numbers.
     • Zero Cases (8-10): Handling scenarios involving zero.
   • The final list of test cases included:

     std::vector<std::pair<long long, long long>> testCases = {
         {1, 9},
         {1234567890, 1286608618},
         {12345678, 87},
         {100872863, 292842910},
         {-1234, 53212678},
         {123321234, -5678},
         {-1234567890, -9087654321},
         {0, 5231231678},
         {1232131134, 0},
         {0, 0}
     };

3. Program Adjustments:

   • I modified the program to remove unnecessary cin usage since I was providing all test cases in a vector.
   • We discussed potential arithmetic overflow and the need to convert numbers to strings for large integer multiplication.

4. Debugging Results:

   • I encountered unexpected results from the program, indicating arithmetic overflow with large numbers.
   • After analysis, I confirmed that the logic was correctly implemented, and we transitioned to using string multiplication to support larger integers appropriately.

5. Final Program:

   • The final program used strings for multiplication, correctly handled both positive and negative cases, and printed results for all test cases directly.

6. Course Problem Discussion:

   • I shared that I was working on a course problem involving processing course enrollment data.
   • The solution involved using both linear and divide-and-conquer methods to handle the data.
   • I planned to implement edge case handling, such as negative values, blank fields, and out-of-range values.
   • The requirement was to create an output CSV file to track inversion counts and display results in a specific format.

7. Outcomes:

   • The integer multiplication program successfully handled large integers and was verified against a calculator for correctness.
   • My approach to the course problem was structured and allowed for testing various edge cases to ensure robustness.