Done Precourse-2

[pranjay01]

No description provided.

[super30admin]

Let's evaluate each exercise one by one:

Exercise_1.py (Binary Search):

• Correctness: The implementation of binary search is correct. It correctly handles the search by adjusting the low and high pointers.
• Time Complexity: O(log n) as stated, which is optimal for binary search.
• Space Complexity: O(1) as stated, since it uses iterative approach without recursion.
• Code Quality: The code is clean and readable. However, the parameters are named 'l' and 'r' which are not very descriptive. It would be better to use 'low' and 'high' consistently (the function uses 'low' and 'high' internally, but the parameters are 'l' and 'r').
• Efficiency: The implementation is efficient. No changes needed.

Exercise_2.py (QuickSort):

• Correctness: The partition function has an issue. The pivot is chosen as the last element (which is standard), but the partition logic is incorrect. The typical Lomuto partition uses a loop that swaps elements when they are less than or equal to the pivot. However, in this code, the inner loop always increments j, and swaps with i only when the condition is met. This is actually correct for Lomuto partition, but note that the pivot element is at the end and the function returns the index i. However, the quickSort function calls partition with partition(arr,0,high) which ignores the low parameter. This is a bug because the partition should be done from low to high, not from 0 to high. Also, the recursive calls use low and pivot-1 and pivot+1 and high, which is correct, but the initial call to partition should be within the current segment.

• Time Complexity: Average case O(n log n), but worst case O(n^2) if the pivot is chosen poorly. However, the partition function is called with the last element as pivot, which may lead to worst-case behavior on 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 has comments that explain the approach, which is good. However, the partition function should use the low and high parameters correctly. Also, the variable names are acceptable.

• Improvement: The partition function should be called with partition(arr, low, high) and the partition function should use low and high correctly. Currently, the partition function ignores the low parameter and always starts from index 0? Actually, in the provided code, the partition function does not use the low parameter at all. It sets j = low and i = low-1, which is correct, but the call in quickSort uses partition(arr,0,high) which should be partition(arr, low, high). Also, the pivot is chosen as arr[high], which is correct.

  Correction for partition call: In quickSort, it should be pivot = partition(arr, low, high).

Exercise_3.py (Find Middle of Linked List):

• Correctness: The solution uses an array to store the nodes. This works, but it does not use the linked list structure as intended. The problem is likely to test traversing the linked list with two pointers (slow and fast) to find the middle without storing all elements.
• Time Complexity: O(n) for push and O(1) for printMiddle, which is good but not the typical way.
• Space Complexity: O(n) for storing the array, which is extra space that is not necessary.
• Code Quality: The code is simple, but it misses the point of the exercise. The linked list should be traversed without storing all nodes in an array.
• Improvement: Implement the two-pointer technique (slow and fast pointers) to find the middle without extra space.

Exercise_4.py (MergeSort):

• Correctness: The implementation is correct. It recursively divides the array and then merges the sorted halves.
• Time Complexity: O(n log n) as expected.
• Space Complexity: O(n) for the temporary arrays in the merge step. This is standard for top-down merge sort.
• Code Quality: The code is well-structured. However, the function signature uses right=None and then sets it to len(arr)-1. This is acceptable, but it might be better to have a wrapper function. The merge function creates two temporary arrays, which is fine.
• Efficiency: The merge function could be optimized to avoid creating temporary arrays by using a single temporary array for the entire process, but the current approach is acceptable.

Exercise_5.py (Iterative QuickSort):

• Correctness: The partition function is the same as in Exercise_2, which is correct for Lomuto partition. However, the iterative implementation uses a stack to simulate recursion. The stack is initialized as stack = [0] * len(arr) which creates a list of zeros of length n, and then appends l and h. This is inefficient because the stack might need to hold up to O(n) elements, but the initial allocation is unnecessary. Instead, you can initialize an empty stack and push the initial values.
• Time Complexity: Same as recursive QuickSort: O(n log n) average, O(n^2) worst-case.
• Space Complexity: The stack can use O(n) space in the worst case.
• Code Quality: The code is readable. However, the stack implementation could be improved by not pre-allocating with zeros. Also, the partition function should be called with the current segment (low and high) and it is correct in this case.
• Improvement: Initialize the stack as stack = [] and then push the initial values. Also, the partition function is called with low and high correctly.

Overall, the student has a good understanding of the algorithms, but there are some issues in Exercise_2 (QuickSort) and Exercise_3 (Linked List) that need to be fixed. The other exercises are mostly correct.