Data structure Merge Sort implementation

Data structure Merge Sort implementation

1. Introduction to Merch Sort BY GROUP 6ix

2. What is Merge Sort? Merge Sort is a popular sorting algorithm that uses a technique called "divide and conquer."that divides the input array into two halves, sorts them, and then merges the sorted halves. Importance in Computer Science Efficiency :Merge Sort has a time complexity of O(n log n), meaning it can handle large amounts of data more quickly. Stability: Merge Sort is a stable sort, which means that it preserves the relative order of equal elements. Divide and Conquer: Merge Sort uses the divide-and-conquer approach, which is a powerful technique in computer science for solving complex problems by breaking them down into simpler subproblems. Foundational Algorithm: Understanding Merge Sort helps in learning about more complex algorithms and concepts in computer science, making it a foundational algorithm for students and professionals alike.

3. How Merge Sort Works: It breaks the problem into smaller parts, solves those smaller parts, and then combines them to get the final sorted list. Divide: Step 1: Take the list and divide it into two halves. If the list has an odd number of elements, one half will have one more element than the other. Conquer: Step 2: Recursively sort each half. This means you keep dividing each half into smaller halves until you have lists that are either empty or have only one element (a single element is already sorted). Combine: Step 3: Merge the sorted halves back together. This involves comparing the smallest elements of each half and arranging them in order, continuing until you have a single sorted list. Here's how it works:

4. Visual Representation: Split into Two Halves : Initial Array: Split Each Half Again Conquer (Sort Each Half) Combine (Merge Sorted Halves)

5. Merge Sort Algorithm Divide and Conquer : Merge Sort follows the divide-and-conquer paradigm. It divides the input array into smaller halves recursively until each subarray contains only one element (base case). Sorting : Once the base case is reached (arrays of size 0 or 1), sorting begins. Each pair of adjacent sorted subarrays is merged into a larger sorted array using the Merge function. Merge Function : The Merge function compares elements from two sorted arrays leftleftleft and rightrightright, ensuring that the merged array remains sorted after each comparison and insertion. Efficiency : Merge Sort has a time complexity of O(nlog⁡n)O(n \log n)O(nlogn) in all cases (worst, average, and best), making it efficient for large datasets. It divides the sorting problem into smaller subproblems and guarantees that each subproblem is solved correctly and efficiently. Stability : Merge Sort is stable, meaning it preserves the relative order of equal elements in the input array.

6. This page is for code and explanation of code

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8. Time and Space Complexity Merge Sort has a time complexity of O(nlog⁡n)O(n \log n)O(nlogn) in all cases (best, average, and worst). This efficiency stems from its divide-and-conquer strategy and how it handles the merging of sorted subarrays during the sorting process: Breakdown of Time Complexity: Divide Step : O(log⁡n) divisions to reach subarrays of size 1. Merge Step: O(n)work per level across O(log⁡n)levels. Combining these factors gives us the O(nlog⁡n)time complexity for Merge Sort in all cases.

9. Complexity Analysis of Merge Sort: Time Complexity: Best Case: O(n log n), When the array is already sorted or nearly sorted. Average Case: O(n log n), When the array is randomly ordered. Worst Case: O(n log n), When the array is sorted in reverse order. Space Complexity: O(n), Additional space is required for the temporary array used during merging. Advantages of Merge Sort: Stability: Merge sort is a stable sorting algorithm, which means it maintains the relative order of equal elements in the input array. Guaranteed worst-case performance: Merge sort has a worst-case time complexity of O(N logN), which means it performs well even on large datasets. Simple to implement: The divide-and-conquer approach is straightforward.

10. Disadvantage of Merge Sort: Space complexity: Merge sort requires additional memory to store the merged sub-arrays during the sorting process. Not in-place: Merge sort is not an in-place sorting algorithm, which means it requires additional memory to store the sorted data. This can be a disadvantage in applications where memory usage is a concern.

11. Comparison to other sorts