UofT-DSI | algorithms_and_data_structures - Assignment 1

[akorade]

What changes are you trying to make? (e.g. Adding or removing code, refactoring existing code, adding reports)

Implemented solutions for all coding problems in assignment_1.ipynb, including 'first_duplicate', 'is_valid_brackets', and 'move_zeros_to_end', with test cases and printed outputs. Added detailed explanations, complexity analysis, and alternative approaches for the 'first_duplicate' problem. Updated kernel metadata.

What did you learn from the changes you have made?

• Implemented optimal O(n) time complexity solution using hash set
• Created 3 additional test cases demonstrating edge cases
• Provided detailed explanations of algorithm logic and correctness
• Analyzed time and space complexity with justifications
• Described alternative brute force approach with trade-off analysis

What did you learn from the changes you have made?

Through this assignment, I learned:

• Hash sets are powerful for lookup operations: Using a set provides O(1) average-case lookups, which is crucial for achieving optimal O(n) time complexity
• Space-time trade-offs: The hash set solution uses O(n) space to achieve O(n) time, whereas a nested loop approach uses O(1) space but requires O(n²) time
• Early termination optimization: Returning immediately upon finding the first duplicate prevents unnecessary iterations
• Importance of order: Processing elements left-to-right ensures we find the FIRST duplicate (by position of second occurrence)
• Algorithm analysis: Breaking down complexity into individual operations helps understand overall performance

Was there another approach you were thinking about making? If so, what approach(es) were you thinking of?

NA

Were there any challenges? If so, what issue(s) did you face? How did you overcome it?

NA

How were these changes tested?

NA

A reference to a related issue in your repository (if applicable)

NA

Checklist

• I can confirm that my changes are working as intended

[github-actions]

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