Quick Sort is a popular and efficient sorting algorithm used to sort arrays and lists. It works by dividing the unsorted list into two sub-lists: elements less than a chosen pivot element and elements greater than the pivot. The pivot is then placed in its final position in the sorted array. The sub-lists are then sorted recursively until the entire list is sorted. Quick sort is known for its average-case linear time complexity and its ability to sort large datasets quickly. However, like all sorting algorithms, quick sorting has its worst-case scenarios. Let us know What are the ‘Worst Case Of Quick Sort’.
Worst Case Of Quick Sort
In quick sort, the basic idea is to partition the data into two sub-arrays, with elements less than a pivot in one sub-array and elements greater than the pivot in the other sub-array. The pivot is chosen such that, after the partition, the length of the two sub-arrays is roughly equal. This process is then repeated recursively on each sub-array until the sub-arrays are reduced to their base case, which is an array with a single element.
The worst-case scenario for quicksort occurs when the pivot is chosen poorly. If the pivot is always chosen as the largest or smallest element in the array, then the partition will always result in one sub-array with all elements and the other sub-array with no elements. This will lead to a skewed tree, with a height of n-1, where n is the number of elements in the array. This means that quicksort will take O(n^2) time to sort the data, making it slower than other sorting algorithms such as bubble sort or selection sort.
To avoid the worst-case scenario, it is important to choose a pivot that is close to the middle of the data. This will result in roughly equal partitions and a balanced tree, with a height of log(n). In practice, randomization is used to choose the pivot, which helps to avoid the worst-case scenario.
Few worst-case scenarios of quick sort
1. Unsorted or reversed input: QuickSort’s performance is worst when the input is already sorted or in reverse order, as it results in skewed partitioning. In such cases, the pivot is always the first or the last element, leading to a time complexity of O(n^2). This is because on each iteration, only one element is sorted and the size of the unsorted sub-array remains n-1, leading to n-1 iterations.
2. Pivot Selection: Poor pivot selection, such as always selecting the first or last element, can result in skewed partitioning and poor performance. For example, if the pivot is always the first element, and the input is sorted in reverse order, the pivot will always be the largest element, and all elements to the right of it will be larger. This leads to an inefficient partitioning where only one element is sorted in each iteration.
3. Already Partitioned Input: If the input is already partially partitioned, QuickSort may perform poorly as it would not result in any meaningful partitioning. This is because in each iteration, the pivot would always be the same element, and the sub-arrays would remain the same size, leading to a time complexity of O(n^2).
4. Small Sub-Arrays: QuickSort is not efficient for small sub-arrays, as the overhead of recursive calls can outweigh the benefits of sorting. In such cases, it may be more efficient to switch to another sorting algorithm, such as Insertion Sort, for sorting small sub-arrays.
5. Repetitive or Identical Values: If the input array has a high degree of repetition or identical values, QuickSort may perform poorly, as it may result in sked partitioning. This is because the pivot would always be one of the repeated values, leading to an inefficient partitioning where only one element is sorted in each iteration.
6. Input with few unique values: QuickSort is not efficient for inputs with a limited number of unique values. This is because the pivot would always be one of the unique values, leading to an inefficient partitioning where only one element is sorted in each iteration.
7. Input with many duplicates: Large amounts of duplicates can cause QuickSort to perform poorly, as it may result in a sked partitioning. This is because the pivot would always be one of the duplicates, leading to an inefficient partitioning where only one element is sorted in each iteration.
8. Input with nearly sorted elements: If the input array is nearly sorted, QuickSort’s performance would be poor as it would not result in meaningful partitioning. This is because the pivot would always be one of the nearly sorted elements, leading to an inefficient partitioning where only one element is sorted in each iteration.
9. Input with a sorted sub-array and a reversed sub-array: In this case, QuickSort would result in a sked partitioning and may not perform efficiently. This is because the pivot would always be one of the elements in the sorted sub-array, leading to an inefficient partitioning where only one element is sorted in each iteration.
10. Input with a sorted sub-array and an unsorted sub-array: If the input array has a sorted subarray and an unsorted subarray, QuickSort may perform poorly, as it would not result in meaningful partitioning. This is because the pivot would always be one of the elements in the sorted sub-array, leading to an inefficient partitioning where only one element is sorted in each iteration.
11. Constant pivot: When the pivot selected is always the same, QuickSort performs poorly.
12. A sorted sub-array followed by an unsorted sub-array of size n-1: In this case, the pivot would always be the last element, leading to a time complexity of O(n^2).
13. A sorted sub-array followed by an unsorted subarray of size 1: In this case, the pivot would always be the middle element, leading to a time complexity of O(n^2).
14. An unsorted sub-array followed by a sorted sub-array of size n-1: In this case, the pivot would always be the first element, leading to a time complexity of O(n^2).
15. An unsorted sub-array followed by a sorted subarray of size 1: In this case, the pivot would always be the middle element, leading to a time complexity of O(n^2)
Conclusion
In conclusion, while quick sort is a fast and efficient sorting algorithm, it is important to be aware of its worst-case scenarios and take steps to avoid them. Choosing a good pivot is key to avoiding the worst-case scenario and ensuring that quick sort performs at its best.
