What Is the Merge Sort in Data Structure?
Merge sort is one of the most efficient sorting algorithms used in computer science. It falls under the category of comparison-based sorting algorithms and is known for its superior performance.
In this article, we will explore what merge sort is and how it works.
Understanding Merge Sort
Merge sort follows the divide-and-conquer approach to sort a given list or array of elements. The algorithm divides the input into smaller subproblems, solves them individually, and then merges the sorted subarrays to obtain a final sorted result.
The Steps Involved in Merge Sort:
- Divide: The given list is divided into two halves recursively until each subproblem contains only one element. This process continues until we have n subproblems, where n is the total number of elements in the input list.
- Conquer: The individual subproblems are solved by applying merge sort recursively on each half.
- Merge: The sorted halves are merged back together to obtain a final sorted result.
How Does Merge Sort Work?
To understand how merge sort works, let’s consider an example. Suppose we have an unsorted array [7, 2, 4, 1, 5]. The steps involved in merge sort can be explained as follows:
- Divide: The array is divided into two halves: [7, 2] and [4, 1, 5].
- Conquer: Recursively apply merge sort on each half:
- [7] is already sorted (base case).
- [2] is already sorted (base case).
- [4, 1, 5] is divided into [4] and [1, 5].
- [4] is already sorted (base case).
- [1, 5] is divided into [1] and [5].
- [1] is already sorted (base case).
- [5] is already sorted (base case).
- Merge: Merge the sorted halves back together:
- Merge [7] and [2]: [2, 7].
- Merge [4] and [1, 5]: [1, 4, 5].
- Efficiency: Merge sort has a time complexity of O(n log n), making it highly efficient for large datasets.
- Stability: Merge sort maintains the relative order of elements with equal keys during the sorting process.
- Predictability: Merge sort always takes the same amount of time to sort an array of elements regardless of their initial order. This makes it a reliable choice for sorting.
- Scalability: Merge sort can handle large datasets without consuming excessive memory as it sorts the elements in a balanced manner.
Finally, merge the two merged halves: [2, 7], [1, 4, 5]. The final sorted array is [1, 2, 4, 5, 7].
Advantages of Merge Sort:
Merge sort has several advantages:
Conclusion
Merge sort is a powerful sorting algorithm that efficiently sorts arrays or lists of elements. It follows the divide-and-conquer approach and ensures stable and predictable sorting results.
Its time complexity of O(n log n) makes it an excellent choice for sorting large datasets. Understanding how merge sort works is essential for any developer striving for efficient data manipulation and organization.