One of the famous divide-and-conquer sorting algorithms is Quick Sort Algorithm. There are many sorting algorithms available for different purposes. It is a recursive algorithm. It picks a pivot element and sorts the array by placing the pivot element at its correct position in the array. The pivot element can be selected in a random way, or usually, the pivot element is taken as the first or last element of the array.
We will learn about the quick sort in this article with the help of an example. You need to stay with us till the end of the article to know more about the quick sort in detail.
What Is A Quick Sort Algorithm?
Quicksort Algorithm is a highly effective and widely employed sorting algorithm renowned for its speed and effectiveness. It operates on the principle of divide and conquer. It breaks unsorted arrays into smaller sub-arrays, sorts them individually, and then merges them to achieve a fully sorted result.
The key to the efficiency of the quick sort algorithm lies in its clever partitioning strategy, where it chooses a pivot element, and elements in the array are rearranged such that elements smaller than the pivot are on one side, and elements greater than the pivot are on the other. The number of comparisons and swaps required to sort the entire dataset is significantly decreased by applying this procedure recursively to the sub-arrays.
Quicksort has a time complexity of O(n logn) and is one of the fastest sorting algorithms available. However, its worst time complexity may increase O(n^2) if the pivot has continuously unbalanced partitions.
Because of its speed and adaptability, Quicksort is frequently preferred in applications where effective sorting is crucial, such as database management systems, programming languages, and many real-time scenarios.
Quick Sort Algorithm
Let us know the algorithm for applying quick sort to an array.
| Quick Sort Algorithm |
|
Analysis Of Quick Sort Algorithm
Quick sort is a very efficient and widely used sorting algorithm due to its adaptive nature. Let us know by checking the analysis of the quick sort algorithm based on various criteria.
1. Efficiency
The time complexity of quick sorting is much lower and often faster than many sorting algorithms, especially in large datasets. The average time complexity for the quick sort algorithm is O(n logn), which makes it one of the most efficient and ready-to-use sorting algorithms.
2. Divide and Conquer Approach
Quick Sort adapts the divide and conquer strategy in its implementation. It does so by dividing the dataset into smaller subarrays and then sorting them individually. It then combines them to obtain the final result. This recursive approach makes this sorting algorithm efficient.
3. In-Place Sorting
It is an in-place sorting algorithm, so it does not require any extra space for sorting. It sorts the elements within the existing array to make it more efficient.
4. Unstable Sorting
Quick Sort sufferers from unstable sorting as it can not always retain the position of two equal keys, and their relative order may change. However, we can make it stable using adaptive changes.
5. Random Pivot Selection
Pivot elements can be selected randomly, and there is no limitation on choosing the first or last element. Selecting pivot elements randomly helps increase the algorithm’s efficiency and decreases the risk of poor performance in the worst case.
6. Average-Case Time Complexity
The average-case time complexity of Quick Sort is O(n log n), which is faster than most sorting algorithms. In practice, it often performs better than merge and heap sort. However, the worst time complexity sometimes reaches O(n^2) when the pivot element is incorrectly chosen datasets or when sorting is a critical component of a larger algorithm or application.
Example Of Quick Sort Algorithm
Let us understand the quick sort algorithm in more detail with the help of an example. Let us take an array having five elements 5,2,3,6, and 9. Now, we will check step by step how we can implement the quick sort algorithm to sort the array.
Step 1:
Let us choose a pivot element. We will choose last element 6 as the pivot element.
| 5 | 2 | 9 | 3 | 6 |
Step 2:
- Now, you need to create two pointers, left and right, which initially point to the first element of the array.
- Now, move the left pointer to the right until you find an element greater than or equal to the pivot element.
- Also, move the right pointer to the left by decrementing it by one until you encounter an element greater or equal to the pivot element in the array.
- Now, swap the elements at the left and right pointers if the element at left is greater than the pivot and the element at right is less.
Step 3:
- You need to continue the process until the left pointer and right pointer do not cross each other.
- At this point, all the elements less than the pivot element are to the left of the pivot, and all the elements greater than it is to the right.
- After completing the pass, the array may look like this.
| 5 | 2 | 3 | 6 | 9 |
Step 4:
Now, you must recursively sort the subarrays to the pivot element’s left and right subarrays.
Left subarray
In the left subarray, follow the same process and choose the last element, 3, as the pivot element.
| 5 | 2 | 3 |
After sorting the left subarray, the left subarray will look like this. All elements smaller than the pivot elements are on the left side and the elements greater than it are on the right side.
| 2 | 3 | 5 |
Now, again recursively sort the left part and right part subarrays.
Right Subarray:
We will sort the right subarray similarly, but we only have a single element in this example. Single elements are always sorted; hence we do not need to sort them.
Step 5:
After sorting all the subarrays, we can combine them to get the final sorted array.
| 2 | 3 | 5 | 6 | 9 |
Advantages Of Quick Sort Algorithm
- It is an in-place algorithm and does not require any extra space for its execution.
- It is one of the most efficient algorithms, with an average time complexity of O(N log N).
- It is a divide-and-conquer approach in which the larger array is broken into smaller ones and then joined at last.
Disadvantages Of Quick Sort Algorithm
- If the pivot element is not chosen properly, then the worst case time complexity may rise to O (n^2).
- It is not a stable algorithm.
Quick Sort Time And Space Complexity
Let us now check the time and space complexity of the quick sort algorithm.
| Quick Sort Algorithm | |
| Aspect | Complexity |
| Time Complexity | |
| Best Case | O (n log n) |
| Average Case | O (n log n) |
| Worst Case | O(n^2) |
| Space Complexity | |
| Space Complexity | O(log n) |
Recommended Reads
- Examples of algorithms used in real-life
- Best website to learn code
- Artificial Intelligence Is changing the World
- How to Become a full Stack Developer
Quick Sort Algorithm FAQs
Why is Quick Sort regarded as an effective sorting algorithm?
Quick Sort is a divide-and-conquer sorting algorithm known for its speed and efficiency. Choosing a pivot element and recursively dividing an array into smaller sub-arrays allows it to sort an array efficiently. It is one of the fastest sorting algorithms available and is regarded as efficient due to its average-case time complexity of O(n log n).
How does Quick Sort handle worst-case scenarios when time complexity exceeds square time?
In the worst-case scenario, the time complexity of quick sort can rise to O (n^2). To handle this rise in time complexity, you must choose the pivot element properly, as it arises due to unbalanced partitions inside the array. You can choose the pivot randomly to reduce the possibility of such imbalance in the partitions.
Is Quick Sort an in-place sorting algorithm, and why is in-place sorting important?
Yes, Quick Sort is an in-place sorting algorithm. It does not require any extra memory to sort the elements. It sorts the array in the existing array.
Is Quick Sort a stable algorithm or unstable?
Quick sort is an unstable algorithm as it can not always retain the original position of the equal elements inside the array after sorting.
