Complete PreCourse 2 exercises 1 to 5

[MrunaliVaidya98]

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[super30admin]

Let's evaluate each exercise one by one:

Exercise_1.java (Binary Search):

• Correctness: The binary search implementation is correct. It uses the standard iterative approach with proper termination condition (l <= r) and calculates mid correctly to avoid overflow.
• Time Complexity: O(log n) which is optimal for binary search.
• Space Complexity: O(1) since it uses constant extra space.
• Code Quality: The code is clean and readable. The variable names are appropriate. However, the method could be declared as static since it doesn't use any instance variables.
• Edge Cases: Handles cases where the element is not present (returns -1). Also handles the case when the array has one element.

Exercise_2.java (QuickSort):

• Correctness: The partition function uses the standard Lomuto partition scheme which is correct. The sort function recursively sorts the subarrays correctly.
• Time Complexity: Average case O(n log n), worst case O(n²) which is standard for quicksort.
• Space Complexity: O(log n) for the recursion stack in the average case, O(n) in the worst case.
• Code Quality: The code is well-structured. The swap method is correctly implemented. However, the partition function could be more efficient with Hoare's partition scheme which generally requires fewer swaps. Also, the pivot choice (last element) could lead to worst-case performance on sorted arrays. Consider using a randomized pivot.
• Edge Cases: The code should handle arrays with duplicate elements (which it does). Also, the condition in the for loop (j < high) is correct since the pivot is at high.

Exercise_3.java (Linked List Middle Element):

• Correctness: The printMiddle function correctly uses the fast and slow pointer technique to find the middle element. When the fast pointer reaches the end, the slow pointer is at the middle.
• Time Complexity: O(n) which is optimal (one pass).
• Space Complexity: O(1) since only two pointers are used.
• Code Quality: The code is readable. However, the printMiddle method prints the middle element directly instead of returning it, which might not be ideal for reusability. Also, the method name "printMiddle" is appropriate but the output message has a typo ("elemnt" should be "element").
• Edge Cases: Handles even and odd length lists correctly. When the list has one element, fast.next is null so the while loop doesn't run and slow points to the head.

Exercise_4.java (MergeSort):

• Correctness: The merge function correctly merges two sorted subarrays. The sort function recursively divides the array and then merges. The implementation is standard.
• Time Complexity: O(n log n) which is optimal for comparison-based sorting.
• Space Complexity: O(n) for the temporary arrays used in merging.
• Code Quality: The code is well-structured and readable. However, the merge method creates temporary arrays which is standard but could be optimized to avoid creating arrays in every merge call by using a single temporary array. Also, the variable names are clear.
• Edge Cases: Handles arrays of different sizes correctly. The base case (l < r) ensures that arrays of size 1 are already sorted.

Exercise_5.java (Iterative QuickSort):

• Correctness: The partition function is similar to Exercise_2 (Lomuto). The iterative approach uses a stack to simulate recursion. The implementation is correct.
• Time Complexity: Average case O(n log n), worst case O(n²).
• Space Complexity: O(log n) for the stack in the average case, O(n) in the worst case.
• Code Quality: The swap method uses arithmetic to swap without a temporary variable. This can be error-prone for large numbers (due to integer overflow) and is less readable. It's better to use a temporary variable for clarity and safety. The iterative approach is correctly implemented using a stack. However, the stack size is allocated as (h-l+1) which might be inefficient for large arrays. A dynamic stack (like java.util.Stack) could be used instead of an array.
• Edge Cases: The swap method should check for i==j to avoid unnecessary operations (which it does). The partition function handles duplicates correctly.

General Strengths:

• All solutions implement standard algorithms correctly.
• Code is generally readable with appropriate variable names.
• Proper use of algorithms and data structures.

Areas for Improvement:

• In Exercise_2 and Exercise_5, the pivot selection could be improved (e.g., random pivot) to avoid worst-case performance.
• In Exercise_5, the swap method should use a temporary variable for clarity and to avoid potential integer overflow.
• In Exercise_3, the method should return the middle node instead of printing it directly for better reusability.
• In Exercise_4, consider using a single temporary array to reduce memory allocation.

Overall, the solutions are correct and efficient, but minor improvements can be made for robustness and code quality.