Discrete Mathematics Repeat Maximizing the Heap The process of maximizing the heap and removing vertices continues until the heap has one vertex. The following results of the remaining steps for...

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Discrete Mathematics

Repeat Maximizing the Heap The process of maximizing the heap and removing vertices continues until the heap has one vertex.

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Algorithm	Best Case	Worst Case
Selection	O(n²)	O(n²)
Bubble	O(n)	O(n²)
Heap	O(n log n)	O(n log n)

Selection Sort:

Time Complexity: O(n²) in both best and worst as there are two nested loops, so number of comparisons performed are equal in both best and worst case.

Bubble Sort:

Worst and Average Case Time Complexity: O(n*n). Worst case occurs when array is reverse sorted.

Best Case Time Complexity: O(n). Best case occurs when array is already sorted.

Heap Sort:

Time Complexity: Time complexity of "Repeat Maximizing the Heap" operation given above is O(log n). Time complexity of creating and building heap is O(n) and thus overall time complexity of Heap Sort is O(n log n) in both best and worst case.

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