Input : (1, 5), (3, 2) (1, 2) (5, 4) (6, 4)
We need to sort key-value pairs in the increasing order of keys of first digit
There are two possible solution for the two pairs where the key is same i.e. (1, 5) and (1, 2) as shown below:
OUTPUT1: (1, 5), (1, 2), (3, 2), (5, 4), (6, 4)
OUTPUT2: (1, 2), (1, 5), (3, 2), (5, 4), (6, 4)
A stable algorithm produces first output. You can see that (1, 5) comes before (1, 2) in the sorted order, which was the original order i.e. in the given input, (1, 5) comes before (1, 2).
Second output can only be produced by an unstable algorithm. You can see that in the second output, the (1, 2) comes before (1, 5) which was not the case in the original input.
Some sorting algorithms are stable by nature like Insertion sort, Merge Sort, Bubble Sort, etc. And some sorting algorithms are not, like Heap Sort, Quick Sort, etc.
QuickSort is an unstable algorithm because we do swapping of elements according to pivot’s position (without considering their original positions).
How to make QuickSort stable?
Quicksort can be stable but it typically isn’t implemented that way. Making it stable either requires order N storage (as in a naive implementation) or a bit of extra logic for an in-place version.
In below implementation, we use extra space. The idea is to make two separate lists:
1) First list contains items smaller than pivot.
2) Second list contains items greater than pivot.
[1, 5, 7, 8, 9, 10]
In above code, we have intentionally used middle element as pivot to demonstrate how to consider position as part of comparison. Code simplifies a lot if we use last element as pivot. In case of last element, we can always push equal elements in the smaller list.
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
- Stable Selection Sort
- Stable sort for descending order
- Position of an element after stable sort
- Why quicksort is better than mergesort ?
- C++ Program for QuickSort
- Python Program for QuickSort
- Dual pivot Quicksort
- QuickSort using Random Pivoting
- Java Program for QuickSort
- QuickSort on Doubly Linked List
- QuickSort on Singly Linked List
- 3-Way QuickSort (Dutch National Flag)
- When does the worst case of Quicksort occur?
- Generic Implementation of QuickSort Algorithm in C
- Hoare's vs Lomuto partition scheme in QuickSort
- Comparisons involved in Modified Quicksort Using Merge Sort Tree
- Can QuickSort be implemented in O(nLogn) worst case time complexity?
- QuickSort Tail Call Optimization (Reducing worst case space to Log n )
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.
Improved By : AgamKashyap