python

[Dvnc94]

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[super30admin]

1. Celebrity Problem:

   • Correctness: The solution appears correct for finding a celebrity in a group of people using the knows() API. It first identifies a potential candidate and then verifies if this candidate is indeed a celebrity.
   • Time Complexity: O(n) as correctly noted, since it performs two passes through the list of people.
   • Space Complexity: O(1) as correctly noted, using only a constant amount of extra space.
   • Code Quality: The code is clean and straightforward. However, adding comments explaining the logic would improve readability.
   • Efficiency: The solution is already optimal for this problem.

2. Water in Village Problem:

   • Correctness: The solution correctly implements Kruskal's algorithm with Union-Find (Disjoint Set Union) to solve the minimum spanning tree problem, including the virtual node for wells.
   • Time Complexity: O(E log E) as correctly noted, due to the sorting step. The Union-Find operations are nearly constant time with path compression.
   • Space Complexity: O(n) for the parent array, which is necessary for the Union-Find structure. The student noted O(1), which is incorrect.
   • Code Quality: The code is well-structured. The use of helper functions (find and union) is good practice. Adding comments would enhance understanding.
   • Efficiency: The solution is efficient, but noting the space complexity correctly is important.

General Feedback:

• Both solutions are well-implemented and follow standard approaches for their respective problems.
• The student should ensure accurate space complexity analysis, especially for data structures like the parent array in Union-Find.
• Adding comments to explain the logic, especially for complex parts like the Union-Find operations, would improve code readability and maintainability.
• Edge cases (like n=0 or n=1) should be considered, though they might be handled implicitly in these solutions.