Algorithms & Data Structures Question

Part 1: In your own words, answer the following:

Investigate how the number of operations grows as the input size (n) increases

Part 2: Identify one algorithm with time complexity O(log n) and one algorithm with time complexity O(n log n)

For each algorithm:

Part 3: Compare O(log n) and O(n log n) in terms of time?

Part 1	O(log n) Explanation	Clearly illustrates logarithmic growth (reducing input size) and correct relation to execution time
Part 1	O(n log n) Explanation	Clearly illustrates combined linear + logarithmic growth and relation to execution time
Part 2	O(log n) Algorithm Description	Clear and correct explanation of how the algorithm works
Part 2	O(log n) Time Complexity Justification	Clearly shows input reduction (e.g., halving) leading to O(log n)
Part 2	O(n log n) Algorithm Description	Clear and correct explanation of how the algorithm works
Part 2	O(n log n) Time Complexity Justification	Clearly identifies where n and log n come from
Part 3	Comparison & Justification	Correctly identifies O(log n) as more efficient with clear explanation based on growth of execution time

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