Merge Sort

Merge sort is a divide-and-conquer algorithm for sorting arrays of elements. The basic idea behind the algorithm is to repeatedly divide the array into smaller sub-arrays until each sub-array contains only one element, and then merge these sub-arrays back together in a way that results in a sorted array. The algorithm is called "merge sort" because it works by merging together the smaller sub-arrays in a way that results in a sorted array.

The first step in the merge sort algorithm is to divide the array into two halves. This is done by finding the midpoint of the array and dividing the array into two sub-arrays, one starting at the first element and the other starting at the midpoint. These two sub-arrays are then sorted using the same merge sort algorithm. This process is repeated recursively until each sub-array contains only one element.

Once all the sub-arrays contain only one element, the next step is to merge them back together in a way that results in a sorted array. This is done by comparing the first elements of each sub-array and taking the smallest element and placing it in a new array. This process is repeated for each element in each sub-array until all elements have been added to the new array. The new array is now a sorted version of the original array.

One of the key features of merge sort is that it is a stable sort, meaning that it preserves the order of equal elements. This makes it a good choice for sorting arrays where there may be duplicate elements or elements that need to maintain a specific order. Additionally, the algorithm has a worst-case time complexity of O(n log n), making it an efficient choice for sorting large arrays.

One of the disadvantages of merge sort is that it requires additional memory to store the sub-arrays and the merged array. This can be a problem for systems with limited memory. However, the algorithm can be implemented in a way that uses an "in-place" merge, meaning that it only uses a single array and doesn't require additional memory.

In conclusion, merge sort is a powerful and efficient sorting algorithm that is well-suited for sorting large arrays. Its divide-and-conquer approach makes it easy to understand and implement, and its stability and time complexity make it a good choice for many sorting tasks. While it requires additional memory compared to some other sorting algorithms, it can be implemented in a way that uses an "in-place" merge to minimize memory usage.

ALGORITHM:

Here's the step-by-step algorithm for the merge sort:

1. Divide the array into two halves: Find the midpoint of the array and divide the array into two sub-arrays, one starting at the first element and the other starting at the midpoint.
2. Recursively sort each half: Recursively call the merge sort on each of the two sub-arrays.
3. Merge the sorted halves: Merge the two sorted sub-arrays back into a single, sorted array by comparing the first elements of each sub-array and taking the smallest element, adding it to the new array, and repeating this process until all elements have been added to the new array.

PSEUDO CODE:

Here is the pseudo-code for the merge sort algorithm:

PYTHON CODE:

Here is the Python code for the merge sort algorithm:

The merge_sort function takes an array as an argument. If the length of the array is less than or equal to 1, it returns the array as is. This serves as the base case for the recursion.

Otherwise, the function divides the array into two halves by finding the midpoint and dividing the array into two sub-arrays. It then calls merge_sort recursively on each of the two sub-arrays. This will continue until the sub-arrays are of length 1.

Once the sub-arrays are sorted, the merge function is called to combine them back into a single, sorted array. The function takes two sorted arrays as input and merges them into a single, sorted array. It does this by comparing the first elements of each array and taking the smallest element, adding it to the new array, and repeating this process until all elements have been added to the new array. The result array is used to store the elements as they are added.

JAVA CODE:

Here is the code and explanation for the merge sort algorithm in Java:

The mergeSort function takes an array as an argument. If the length of the array is greater than 1, it divides the array into two halves by finding the midpoint and dividing the array into two sub-arrays. It then calls mergeSort recursively on each of the two sub-arrays. This will continue until the sub-arrays are of length 1.

Once the sub-arrays are sorted, the merge function is called to combine them back into a single, sorted array. The function takes three arrays as input: the original array, the left half, and the right half. It merges the two halves into the original array by comparing the first elements of each sub-array and taking the smallest element, adding it to the original array, and repeating this process until all elements have been added to the original array. The variables i, j, and k are used to keep track of the current position in each of the arrays.

C CODE:

Here is the code and explanation for the merge sort algorithm in C:

The mergeSort function takes an array, arr, and two indices, l and r, as arguments. If l is less than r, the function divides the array into two halves by finding the midpoint, m, and calling mergeSort recursively on each of the two sub-arrays. This will continue until l is greater than or equal to r.

Once the sub-arrays are sorted, the merge function is called to combine them back into a single, sorted array. The function takes four arguments: the original array, arr, and the indices l, m, and r which represent the left, mid, and right indices of the sub-array. It merges the two halves into the original array by comparing the elements of each sub-array and taking the smallest element, adding it to the original array.

C++ CODE:

Here is the code and explanation for the merge sort algorithm in C++:

The mergeSort function takes an array, arr, and two indices, l and r, as arguments. If l is less than r, the function divides the array into two halves by finding the midpoint, m, and calling mergeSort recursively on each of the two sub-arrays. This will continue until l is greater than or equal to r.

Once the sub-arrays are sorted, the merge function is called to combine them back into a single, sorted array. The function takes four arguments: the original array, arr, and the indices l, m, and r which represent the left, mid, and right indices of the sub-array. It merges the two halves into the original array by comparing the elements of each sub-array.

JAVASCRIPT CODE:

Here is the code and explanation for the merge sort algorithm in JavaScript:

The mergeSort function takes an unsorted array as an argument and returns a sorted array. It uses a recursive approach, dividing the array into smaller sub-arrays until each sub-array only has one element. At that point, it calls the merge function to combine the sub-arrays back into a single, sorted array.

The merge function takes two sorted arrays, left and right, as arguments. It combines the two arrays into a single, sorted array by comparing the elements of each array one by one and inserting the smaller element into the result array.

Once all of the sub-arrays have been merged back into a single, sorted array, the mergeSort function returns that array to the caller.