[IMP] PreCourse-2

[amitmittal117]

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[super30admin]

Let's evaluate each exercise one by one:

Exercise_1.py (Binary Search):

• Correctness: The code sorts the array at the beginning, which is not standard for binary search since binary search requires the array to be sorted. The problem likely expects the array to already be sorted. Sorting the array changes the indices, so the returned index may not correspond to the original array. This is incorrect.
• Time Complexity: The sort operation adds O(n log n) time, which is worse than the expected O(log n) for binary search.
• Space Complexity: O(1) is correct for the iterative binary search, but the sort might use additional space (O(n) for Timsort in worst case).
• Code Quality: The code is readable and well-structured, but the sorting step is a critical flaw.
• Improvement: Remove the arr.sort() line. Assume the input array is already sorted.

Exercise_2.py (QuickSort):

• Correctness: The implementation of QuickSort using Lomuto partition scheme is correct.
• Time Complexity: O(n log n) on average, O(n^2) in worst case (if the pivot is chosen poorly). However, the pivot is always the last element, which may lead to worst-case behavior on already sorted arrays.
• Space Complexity: O(log n) for the recursive call stack in the average case, but O(n) in the worst case.
• Code Quality: The code is clean and follows the standard approach. However, adding comments to explain the partition function and the recursive steps would improve readability.
• Improvement: Consider using a random pivot to avoid worst-case scenarios. Also, add comments to explain the code.

Exercise_3.py (Find Middle of Linked List):

• Correctness: The solution correctly uses the two-pointer (slow and fast) technique to find the middle node. It works for both even and odd lengths (for even, it returns the second middle node, which is standard).
• Time Complexity: O(n) is correct.
• Space Complexity: O(1) is correct.
• Code Quality: The code is clear and concise. The LinkedList class and methods are well-defined.
• Improvement: The push method is inefficient (O(n)) for each insertion. For a linked list, it's better to insert at the head for O(1) time. However, since the problem is about finding the middle, it doesn't affect the core functionality. But for general use, consider adding at the head.

Exercise_4.py (MergeSort):

• Correctness: The recursive MergeSort implementation is correct. It divides the array into halves, sorts them recursively, and then merges.
• Time Complexity: O(n log n) is correct.
• Space Complexity: O(n) for the merging step is correct. However, the recursive calls use O(log n) stack space, but the dominant space is O(n) for the temporary arrays.
• Code Quality: The code is well-structured. The function names are clear. However, the function combine might be better named merge to match the algorithm.
• Improvement: Consider implementing an in-place merge to reduce space usage, but the current approach is standard. Also, the driver code prints the sorted array correctly.

Exercise_5.py (Iterative QuickSort):

• Correctness: The iterative QuickSort using a stack to simulate recursion is implemented correctly. The partition function is the same as in Exercise_2.
• Time Complexity: Same as recursive QuickSort: O(n log n) on average, O(n^2) in worst case.
• Space Complexity: The stack uses O(n) space in the worst case, which is the same as the recursive version. However, iterative version can be optimized to use O(log n) space by always pushing the smaller subarray first.
• Code Quality: The code is readable. However, the stack implementation uses a fixed-size array which might be inefficient in terms of memory. Using a dynamic list (like Python list) would be more flexible.
• Improvement: Instead of a fixed-size array, use a list and append/pop. Also, consider choosing a random pivot to avoid worst-case behavior.

Overall, the student demonstrates good understanding of algorithms, but there are critical issues in Exercise_1 (sorting in binary search) and minor improvements possible in others.