# Algorithms | Sorting | Question 1

What is recurrence for worst case of QuickSort and what is the time complexity in Worst case? (A) Recurrence is T(n) = T(n-2) + O(n) and time complexity is O(n^2) (B) Recurrence is T(n) = T(n-1) + O(n) and time complexity is O(n^2) (C) Recurrence is T(n) = 2T(n/2) + O(n) and time complexity is O(nLogn) (D) Recurrence is T(n) = T(n/10) + T(9n/10) + O(n) and time complexity is O(nLogn)

Explanation: The worst case of QuickSort occurs when the picked pivot is always one of the corner elements in sorted array. In worst case, QuickSort recursively calls one subproblem with size 0 and other subproblem with size (n-1). So recurrence is T(n) = T(n-1) + T(0) + O(n) The above expression can be rewritten as T(n) = T(n-1) + O(n)
 `void` `exchange(``int` `*a, ``int` `*b) ``{ ``  ``int` `temp; ``  ``temp = *a; ``  ``*a   = *b; ``  ``*b   = temp; ``} ``  ` `int` `partition(``int` `arr[], ``int` `si, ``int` `ei) ``{ ``  ``int` `x = arr[ei]; ``  ``int` `i = (si - 1); ``  ``int` `j; ``  ` `  ``for` `(j = si; j <= ei - 1; j++) ``  ``{ ``    ``if``(arr[j] <= x) ``    ``{ ``      ``i++; ``      ``exchange(&arr[i], &arr[j]); ``    ``} ``  ``} ``  ` `  ``exchange (&arr[i + 1], &arr[ei]); ``  ``return` `(i + 1); ``} ``  ` `/* Implementation of Quick Sort ``arr[] --> Array to be sorted ``si  --> Starting index ``ei  --> Ending index ``*/``void` `quickSort(``int` `arr[], ``int` `si, ``int` `ei) ``{ ``  ``int` `pi;    ``/* Partitioning index */``  ``if``(si < ei) ``  ``{ ``    ``pi = partition(arr, si, ei); ``    ``quickSort(arr, si, pi - 1); ``    ``quickSort(arr, pi + 1, ei); ``  ``} ``} `

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