Question

State the order of magnitude in Big-O notation (assuming there are N elements), and explain your answer in detail for the following operations.

2. Sorting an array using quick sort.

Answer 1

Answer 2:

Sorting an array using quicksort will take

means that to sort an array of size N, quicksort will not perform worse than the order of . Although, it may sort the array in order of time.

• Quicksort in worst case takes time to sort an array and this may happen when the array is already sorted either in ascending or descending order. When the array is already sorted the partition procedure will always pick the smallest or largest element as the pivot. The recurrence relation we get in this case is:
  
  T(N) = T(1) + T(N - 1) + (N)
  
  which on solving gives
  
  
• Quicksort in the best case takes time to sort an array and this may happen when the partitioning procedure always picks median as the pivot. The recurrence relation we get in this case is:
  
  T(N) = 2T(N / 2) +  (N)
  
  which on solving gives

On analysing worst-case and best case it is safe to state that quicksort will take time to sort an array of N elements.

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