Which of the following algorithm design approach is used in Quick sort…

Answer: Quicksort uses the divide and conquer approach.

How it applies:

• Choose a pivot and partition the array into elements less than the pivot and elements greater than the pivot.

• Recursively apply the same process to the left and right partitions.

• After recursion finishes, the entire array is sorted (no separate merge step is required).

Why the other approaches do not apply (brief):

• Dynamic programming: requires overlapping subproblems and memoization; quicksort divides into independent subproblems instead.

• Backtracking: explores and abandons partial solutions under constraints; quicksort does not perform such search.

• Greedy approach: makes locally optimal choices to build a solution; quicksort's partition-and-recurse pattern is not a greedy construction.

Complexity and characteristics:

• Average time complexity: O(n log n).

• Worst-case time complexity: O(n^2) (can be avoided with good pivot choice such as randomized pivot or median-of-three).

• Space: typically O(log n) average due to recursion (in-place partitioning), though worst-case recursion depth can be O(n).

• Stability: standard quicksort is not stable.