Prerequisite – Merge Sort
Merge sort involves recursively splitting the array into 2 parts, sorting and finally merging them. A variant of merge sort is called 3-way merge sort where instead of splitting the array into 2 parts we split it into 3 parts.
Merge sort recursively breaks down the arrays to subarrays of size half. Similarly, 3-way Merge sort breaks down the arrays to subarrays of size one third.
Input : 45, -2, -45, 78, 30, -42, 10, 19 , 73, 93 Output : -45 -42 -2 10 19 30 45 73 78 93 Input : 23, -19 Output : -19 23
After 3 way merge sort: -45 -42 -2 10 19 30 45 73 78 93
Here, we first copy the contents of data array to another array called fArray. Then, sort the array by finding midpoints that divide the array into 3 parts and called sort function on each array respectively. The base case of recursion is when size of array is 1 and it returns from the function. Then merging of arrays starts and finally the sorted array will be in fArray which is copied back to gArray.
Time Complexity: In case of 2-way Merge sort we get the equation: T(n) = 2T(n/2) + O(n)
Similarly, in case of 3-way Merge sort we get the equation: T(n) = 3T(n/3) + O(n)
By solving it using Master method, we get its complexity as O(n log 3n).. Although time complexity looks less compared to 2 way merge sort, the time taken actually may become higher because number of comparisons in merge function go higher. Please refer Why is Binary Search preferred over Ternary Search? for details.
Similar article :
3 way Quick Sort
This article is contributed by Pavan Gopal Rayapati. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: DSA Self Paced. Become industry ready at a student-friendly price.
- Sort elements by frequency | Set 1
- Count Inversions in an array | Set 1 (Using Merge Sort)
- Merge Sort for Linked Lists
- Sort an array of 0s, 1s and 2s
- std::sort() in C++ STL
- Sort a nearly sorted (or K sorted) array
- Sort numbers stored on different machines
- Iterative Quick Sort
- Sort a linked list of 0s, 1s and 2s
- Counting Sort
- Sort elements by frequency | Set 2
- Merge k sorted arrays | Set 1
- Radix Sort
- Sort n numbers in range from 0 to n^2 - 1 in linear time
- Bucket Sort
- Sort an array according to the order defined by another array
- Time complexity of insertion sort when there are O(n) inversions?
- Sort an array in wave form
- Iterative Merge Sort
- Merge Sort for Doubly Linked List
Improved By : CodeSeeker