Precourse-2 Solution

[Simranb10]

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[super30admin]

Exercise_1 (Binary Search):

• Correctness: The binary search implementation is correct. It properly handles the standard binary search logic with l <= r loop condition, correct calculation of mid-point avoiding integer overflow (l + (r - l) / 2), and appropriate updates to search boundaries.
• Time Complexity: O(log n) - correct.
• Space Complexity: O(1) - correct (no extra space used).
• Code Quality: Clean and readable implementation with good comments. The code follows the standard iterative binary search pattern.

Exercise_2 (QuickSort):

• Correctness: The QuickSort implementation is correct. The partition function uses the standard Lomuto partition scheme with the last element as pivot, correctly placing elements less than pivot to the left and returning the pivot's final position. The recursive sorting logic is properly implemented.
• Time Complexity: O(n log n) average case, O(n²) worst case - correct.
• Space Complexity: O(log n) for recursion stack in average case - correct.
• Code Quality: Well-structured with clear separation of swap, partition, and sort functions. Could benefit from more inline comments explaining the partition logic.

Exercise_3 (Linked List - Middle Element):

• Correctness: The solution correctly uses the fast and slow pointer technique to find the middle element in a single pass. Edge cases are handled properly (when list has 0, 1, or 2 elements, the loop simply doesn't execute or exits appropriately).
• Time Complexity: O(n) - correct.
• Space Complexity: O(1) - correct.
• Code Quality: Clean implementation. The main method demonstrates good testing by building the list incrementally and printing the middle after each insertion.

Exercise_4 (MergeSort):

• Correctness: The MergeSort implementation is correct. The merge function properly merges two sorted subarrays, and the recursive sort function correctly divides the array until single elements, then merges them back in sorted order.
• Time Complexity: O(n log n) - correct.
• Space Complexity: O(n) - correct (auxiliary arrays created during merge).
• Code Quality: Well-organized with clear separation of merge and sort functions. The code is readable and follows the standard merge sort algorithm.

Exercise_5 (Iterative QuickSort):

• Correctness: The iterative QuickSort implementation is correct. It successfully replaces recursion with an explicit stack data structure, correctly partitioning and sorting subarrays. The swap function uses arithmetic operations to swap without a temporary variable (though this approach can overflow with large integers).
• Time Complexity: O(n log n) average case, O(n²) worst case - correct.
• Space Complexity: O(n) for the stack - correct.
• Code Quality: Good use of stack data structure to eliminate recursion. The partition logic is identical to Exercise_2, showing good code reuse awareness. The swap without temp variable is clever but could be simplified for clarity.

Overall Assessment:
All five exercises demonstrate solid understanding of fundamental algorithms and data structures. The implementations are correct, efficient, and follow good coding practices. The student shows proficiency in:

• Algorithm implementation (Binary Search, QuickSort, MergeSort)
• Data structure manipulation (Linked List)
• Time and space complexity analysis
• Using appropriate data structures to solve problems (stack for iterative QuickSort)

Areas for Minor Improvement:

1. Exercise_5: The swap without temp variable using arithmetic operations could potentially cause integer overflow. Using a traditional temp variable is safer and more readable.
2. All exercises could benefit from more comprehensive edge case testing.
3. Consider adding input validation (e.g., null checks, empty array checks).