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)
Answer: (B)
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);
}
} |