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Given a linked list of 0s, 1s and 2s, sort it.Examples:Input: 1 -&gt; 1 -&gt; 2 -&gt; 0 -&gt; 2 -&gt; 0 -&gt; 1 -&gt; NULL&nbsp; Output: 0 -&gt; 0 -&gt; 1 -&gt; 1 -&gt; 1 -&gt; 2 -&gt; 2 -&gt; NULL Input: 1 -&gt; 1 -&gt; 2 -&gt; 1 -&gt; 0 -&gt; NULL&nbsp; Output: 0 -&gt; 1 -&gt; 1 -&gt; 1 -&gt; 2 -&gt; NULL&nbsp; Following steps can be used to sort the given linked list.Traverse the list and count the number of 0s, 1s, and 2s. Let the counts be n1, n2, and n3 respectively. Traverse the list again, fill the first n1 nodes with 0, then n2 nodes with 1, and finally n3 nodes with 2.Sort a linked list of 0s, 1s and 2s : <a href="https://www.geeksforgeeks.org/sort-a-linked-list-of-0s-1s-or-2s/">https://www.geeksforgeeks.org/sort-a-linked-list-of-0s-1s-or-2s/</a>

Sort a linked list of 0s, 1s and 2s

Counting sort is a sorting technique based on keys between a specific range. It works by counting the number of objects having distinct key values (kind of hashing). Then do some arithmetic to calculate the position of each object in the output sequence.&nbsp;Counting sort makes assumptions about the data, for example, it assumes that values are going to be in the range of 0 to 10 or 10 – 99 etc, Some other assumptions counting sort makes are input data will be all real numbers. Like other algorithms this sorting algorithm is not a comparison-based algorithm, it hashes the value in a temporary count array and uses them for sorting. It uses a temporary array making it a non In Place algorithm.Counting Sort : <a href="https://www.geeksforgeeks.org/counting-sort/">https://www.geeksforgeeks.org/counting-sort/</a>

Counting Sort

Welcome to the daily solving of our PROBLEM OF THE DAY with Yash Dwivedi We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of Arrays but also build up problem-solving skills. Given an array arr[], where each element is at most k away from its target position, you need to sort the array optimally.Note:&nbsp; &nbsp;<ol><li>The given Array can be Circular.</li><li>You need to change the given array arr[] in place.</li></ol>Examples:Input: arr[] = [6, 5, 3, 2, 8, 10, 9], k = 3 Output: [2, 3, 5, 6, 8, 9, 10] Explanation: The sorted array will be 2 3 5 6 8 9 10Give the problem a try before going through the video. All the best!!! Problem Link: <a href="https://www.geeksforgeeks.org/problems/nearly-sorted-1587115620/1">https://www.geeksforgeeks.org/problems/nearly-sorted-1587115620/1</a>

PROBLEM OF THE DAY : 14/11/2024 | Nearly Sorted

Welcome to the daily solving of our PROBLEM OF THE DAY with Yash Dwivedi We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of Arrays but also build up problem-solving skills. Given an array&nbsp;arr[], find all possible indices [i, j, k] of triplets [arr[i], arr[j], arr[k]] in the array whose sum is equal to zero. Return indices of triplets in any order and all the returned triplets indices should also be internally sorted, i.e., for any triplet indices [i, j, k], the condition i &lt; j &lt; k should hold.Note: Try to solve this using the O(n2) approach.Examples:Input: arr[] = [0, -1, 2, -3, 1]
Output: [[0, 1, 4], [2, 3, 4]]
Explanation: Triplets with sum 0 are: arr[0] + arr[1] + arr[4] = 0 + (-1) + 1 = 0
arr[2] + arr[3] + arr[4] = 2 + (-3) + 1 = 0Give the problem a try before going through the video. All the best!!! Problem Link: <a href="https://www.geeksforgeeks.org/problems/find-all-triplets-with-zero-sum/1">https://www.geeksforgeeks.org/problems/find-all-triplets-with-zero-sum/1</a>

PROBLEM OF THE DAY : 04/11/2024 | Find All Triplets with Zero Sum

Welcome to the daily solving of our PROBLEM OF THE DAY with Kunal Jain We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of Arrays but also build up problem-solving skills. Given an array&nbsp;arr[][]&nbsp;such that&nbsp;arr[i][0]&nbsp;is the&nbsp;starting time&nbsp;of ith meeting and arr[i][1]&nbsp;is the&nbsp;ending time&nbsp;of ith meeting, the task is to check if it is possible for a person to attend all the meetings such that he can attend only one meeting at a particular time.Note: A person can attend a meeting if its starting time is greater than or equal to the previous meeting's ending time.Examples:Input: arr[][] = [[1, 4], [10, 15], [7, 10]] Output: true Explanation: Since all the meetings are held at different times, it is possible to attend all the meetings.Give the problem a try before going through the video. All the best!!! Problem Link: <a href="https://www.geeksforgeeks.org/problems/attend-all-meetings/1">https://www.geeksforgeeks.org/problems/attend-all-meetings/1</a>

PROBLEM OF THE DAY : 12/11/2024 | Meeting Rooms

Welcome to the daily solving of our PROBLEM OF THE DAY with Kunal Jain We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of Arrays but also build up problem-solving skills. Given an array arr[ ], your task is to find the minimum number of increment operations required to make all the elements of the array unique. i.e.- no value in the array should occur more than once. In one operation, a value can be incremented by 1 only.Examples :Input: arr[] = [1, 2, 2]
Output: 1
Explanation: If we increase arr[2] by 1 then the resulting array becomes {1, 2, 3} and has all unique values.Hence, the answer is 1 in this case.Give the problem a try before going through the video. All the best!!! Problem Link:<a href=" https://www.geeksforgeeks.org/problems/union-of-two-sorted-arrays-with-distinct-elements/1"> https://www.geeksforgeeks.org/problems/make-array-elements-unique--170645/1</a>

PROBLEM OF THE DAY : 11/11/2024 | Make Array Elements Unique

Welcome to the daily solving of our PROBLEM OF THE DAY with Geetesh Yadav We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of Arrays but also build up problem-solving skills. Given an array arr[] such that each element is in the range [0 - 9], find the minimum possible sum of two numbers formed using the elements of the array. All digits in the given array must be used to form the two numbers. Return a string without leading zeroes.Examples :Input: arr[] = [6, 8, 4, 5, 2, 3]
Output: 604
Explanation: The minimum sum is formed by numbers 358 and 246. &nbsp;Give the problem a try before going through the video. All the best!!! Problem Link: <a href="https://www.geeksforgeeks.org/problems/minimum-sum4058/1">https://www.geeksforgeeks.org/problems/minimum-sum4058/1</a>

PROBLEM OF THE DAY : 09/11/2024 | Minimum Sum

This video is part of the Heap section under GFG SDE Sheet. Given an array of size N. The task is to sort the array elements by completing functions heapify() and buildHeap() which are used to implement Heap Sort.Example 1:Input:
N = 5
arr[] = {4,1,3,9,7}
Output:
1 3 4 7 9
Explanation:
After sorting elements
using heap sort, elements will be
in order as 1,3,4,7,9.Do check out:- Problem: <a href="https://www.geeksforgeeks.org/problems/heap-sort/1">https://www.geeksforgeeks.org/problems/heap-sort/1</a> SDE Sheet Link: <a href="https://www.geeksforgeeks.org/sde-sheet-a-complete-guide-for-sde-preparation/">https://www.geeksforgeeks.org/sde-sheet-a-complete-guide-for-sde-preparation/</a> Article Link: <a href="https://www.geeksforgeeks.org/heap-sort/">https://www.geeksforgeeks.org/heap-sort/</a>

SDE Sheet - Heap Sort

Welcome to the daily solving of our PROBLEM OF THE DAY with Kunal Jain We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of Arrays but also build up problem-solving skills. Given an array arr[ ] of positive elements. Consider the array as a circular array, meaning the element after the last element is the first element of the array. The task is to find the maximum sum of the absolute differences between consecutive elements with shuffling of array elements allowed i.e. shuffle the array elements and make [a1..an] such order that&nbsp; |a1&nbsp;– a2| + |a2&nbsp;– a3| + …… + |an-1&nbsp;–&nbsp;an| + |an&nbsp;– a1| is maximized.Examples:Input: arr[] = [4, 2, 1, 8]
Output: 18
Explanation: After Shuffling, we get [1, 8, 2, 4]. Sum of absolute difference between consecutive elements after rearrangement = |1 - 8| + |8 - 2| + |2 - 4| + |4 - 1| = 7 + 6 + 2 + 3 = 18. &nbsp;Give the problem a try before going through the video. All the best!!! Problem Link:<a href=" https://www.geeksforgeeks.org/problems/remove-duplicates-in-small-prime-array/1"> </a><a href="https://practice.geeksforgeeks.org/problems/swap-and-maximize5859/1">https://practice.geeksforgeeks.org/problems/swap-and-maximize5859/1</a>

PROBLEM OF THE DAY : 01/11/2024 | Swap and Maximize

Welcome to the daily solving of our PROBLEM OF THE DAY with Ayush Tripathi We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of Arrays but also build up problem-solving skills. Given an array arr of&nbsp;distinct integers. Rearrange the array in such a way that the first element is the largest and the second element is the smallest, the third element is the second largest and the fourth element is the second smallest, and so on.Examples:Input: arr[] = [7, 1, 2, 3, 4, 5, 6]
Output: [7, 1, 6, 2, 5, 3, 4]
Explanation: The first element is first maximum and second element is first minimum and so on. &nbsp;Give the problem a try before going through the video. All the best!!! Problem Link: <a href="https://practice.geeksforgeeks.org/problems/alternative-sorting1311/1">https://practice.geeksforgeeks.org/problems/alternative-sorting1311/1</a>

PROBLEM OF THE DAY : 25/10/2024 | Alternative Sorting

<h2>Insertion Sort Algorithm | Comprehensive Guide</h2>Insertion Sort is a simple and intuitive sorting algorithm that builds the final sorted array one item at a time. It is much like the process of sorting playing cards in your hands, where you take one card at a time and insert it into its correct position among the previously sorted cards. Insertion Sort is often used for small datasets and is efficient when the array is nearly sorted.<h3>What is Insertion Sort?</h3>Insertion Sort works by dividing the array into a sorted and an unsorted part. Initially, the first element is considered sorted, and the rest of the array is unsorted. The algorithm takes each element from the unsorted part and places it into its correct position within the sorted part. This process continues until the entire array is sorted.<h3>Key Steps in Insertion Sort</h3>Start with the First Element:<ul><li>The first element is considered sorted by default.</li></ul>Pick the Next Element:<ul><li>Take the next element from the unsorted portion of the array and compare it with elements in the sorted portion.</li></ul>Shift Elements:<ul><li>Shift elements in the sorted portion to the right to make space for the new element.</li></ul>Insert the Element:<ul><li>Insert the picked element into its correct position in the sorted part.</li></ul>Repeat:<ul><li>Repeat the process for all elements in the unsorted portion.</li></ul><h3>Example of Insertion Sort</h3>Let’s sort the array: [12, 11, 13, 5, 6]<ol><li>Start with 12 (the first element) as the sorted part.</li><li>Pick 11 and compare it with 12. Since 11 is smaller, insert 11 before 12.<ul><li>Array after insertion: [11, 12, 13, 5, 6]</li></ul></li><li>Pick 13 and compare it with 12. Since 13 is larger, leave it in place.<ul><li>Array remains: [11, 12, 13, 5, 6]</li></ul></li><li>Pick 5 and compare it with the sorted part [11, 12, 13]. Shift elements to the right and insert 5.<ul><li>Array after insertion: [5, 11, 12, 13, 6]</li></ul></li><li>Pick 6 and insert it into its correct position in the sorted part [5, 11, 12, 13].<ul><li>Final sorted array: [5, 6, 11, 12, 13]</li></ul></li></ol><h3>Pseudocode for Insertion Sort</h3>pythonCopy codedef insertion_sort(arr):
 &nbsp; &nbsp;# Traverse from 1 to len(arr)
 &nbsp; &nbsp;for i in range(1, len(arr)):
 &nbsp; &nbsp; &nbsp; &nbsp;key = arr[i]
 &nbsp; &nbsp; &nbsp; &nbsp;j = i - 1
 &nbsp; &nbsp; &nbsp; &nbsp;# Move elements of arr[0..i-1], that are greater than key,
 &nbsp; &nbsp; &nbsp; &nbsp;# to one position ahead of their current position
 &nbsp; &nbsp; &nbsp; &nbsp;while j &gt;= 0 and key &lt; arr[j]:
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;arr[j + 1] = arr[j]
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;j -= 1
 &nbsp; &nbsp; &nbsp; &nbsp;arr[j + 1] = key
<h3>Key Points:</h3><ul><li>Outer Loop: Moves from the second element to the last element.</li><li>Inner Loop: Shifts elements of the sorted part to the right to insert the new element in its correct position.</li></ul><h3>Time Complexity of Insertion Sort</h3><ul><li>Best Case: O(n), which occurs when the array is already sorted.</li><li>Worst Case: O(n²), when the array is sorted in reverse order.</li><li>Average Case: O(n²), which occurs when the array elements are randomly ordered.</li></ul>Insertion Sort is efficient for small arrays and arrays that are nearly sorted.<h3>Space Complexity:</h3><ul><li>The space complexity is O(1) because Insertion Sort is an in-place sorting algorithm, meaning it does not require additional memory for sorting the array.</li></ul><h3>Advantages of Insertion Sort</h3>Simple and Easy to Implement:<ul><li>Insertion Sort has a simple algorithm that is easy to implement and understand, making it a great introduction to sorting algorithms.</li></ul>Efficient for Small or Nearly Sorted Arrays:<ul><li>Insertion Sort works well for small datasets or nearly sorted arrays, where it can outperform more complex algorithms like QuickSort.</li></ul>In-Place Sorting:<ul><li>Insertion Sort sorts the array without needing extra space, making it memory-efficient.</li></ul>Stable Sorting Algorithm:<ul><li>Insertion Sort is a stable algorithm, meaning it maintains the relative order of elements with equal values.</li></ul><h3>Disadvantages of Insertion Sort</h3>Inefficient for Large Arrays:<ul><li>Insertion Sort has a time complexity of O(n²) in the worst and average cases, making it inefficient for large datasets compared to algorithms like QuickSort or Merge Sort.</li></ul>Shifting Elements:<ul><li>In cases where many elements need to be shifted, Insertion Sort can be slow.</li></ul><h3>Applications of Insertion Sort</h3>Small Data Sets:<ul><li>Insertion Sort is ideal for small datasets due to its simplicity and low overhead.</li></ul>Nearly Sorted Arrays:<ul><li>Insertion Sort performs well when the input is nearly sorted, as its time complexity is linear in the best case.</li></ul>Online Sorting:<ul><li>In situations where elements are continuously being added, Insertion Sort can be used to keep a running list sorted. For example, inserting new records into a database in sorted order.</li></ul><h3>Why Learn Insertion Sort?</h3>Learning Insertion Sort provides a solid foundation in sorting algorithms. While it may not be the most efficient for large datasets, it introduces key concepts like in-place sorting and stable sorting algorithms. Understanding Insertion Sort also prepares you for learning more advanced algorithms such as QuickSort and Merge Sort. Additionally, for small or nearly sorted data, Insertion Sort can often be a very practical and simple solution.Topics Covered:Definition of Insertion Sort: Understanding how the algorithm works by inserting elements into the correct position.Steps of the Algorithm: Iterating through the array and shifting elements to sort them.Time and Space Complexity: Analysis of Insertion Sort's performance in different cases.Applications: Practical uses of Insertion Sort for small or nearly sorted datasets.For more details and further examples, check out the full article on GeeksforGeeks: <a href="https://www.geeksforgeeks.org/insertion-sort-algorithm/">https://www.geeksforgeeks.org/insertion-sort-algorithm/</a>.

Insertion Sort Algorithm

<h2>Merge Sort Algorithm | Comprehensive Guide</h2>Merge Sort is a widely-used sorting algorithm that follows the divide and conquer approach to sort elements. It works by recursively dividing the array into smaller subarrays, sorting those subarrays, and then merging them back together to produce the final sorted array. Merge Sort is known for its efficiency and stability, making it an ideal choice for sorting large datasets.<h3>What is Merge Sort?</h3>Merge Sort is a recursive algorithm that splits an array into two halves, sorts each half, and then merges the two sorted halves together to form a fully sorted array. It consistently achieves a time complexity of O(n log n), making it one of the most efficient sorting algorithms for large datasets.<h3>Key Steps in Merge Sort</h3><ol><li>Divide:<ul><li>Divide the unsorted array into two roughly equal halves.</li></ul></li><li>Conquer:<ul><li>Recursively sort each half using the same divide-and-conquer strategy until you reach arrays of size 1 (which are inherently sorted).</li></ul></li><li>Merge:<ul><li>Merge the two sorted halves back together to form a single sorted array.</li></ul></li></ol><h3>Example of Merge Sort</h3>Let’s take an example array: [38, 27, 43, 3, 9, 82, 10]<ol><li>Divide:<ul><li>Split the array into two halves:<ul><li>Left half: [38, 27, 43]</li><li>Right half: [3, 9, 82, 10]</li></ul></li></ul></li><li>Recursively Divide:<ul><li>Divide each half further until each subarray contains a single element:<ul><li>[38, 27, 43] becomes [38], [27], [43]</li><li>[3, 9, 82, 10] becomes [3], [9], [82], [10]</li></ul></li></ul></li><li>Merge:<ul><li>Merge the subarrays back together:<ul><li>Merge [38] and [27] to form [27, 38].</li><li>Merge [27, 38] and [43] to form [27, 38, 43].</li><li>Merge [3] and [9] to form [3, 9].</li><li>Merge [82] and [10] to form [10, 82].</li><li>Merge [3, 9] and [10, 82] to form [3, 9, 10, 82].</li></ul></li></ul></li><li>Final Merge:<ul><li>Finally, merge [27, 38, 43] and [3, 9, 10, 82] to get the fully sorted array: [3, 9, 10, 27, 38, 43, 82]</li></ul></li></ol><h3>Pseudocode for Merge Sort</h3>pythonCopy codedef merge_sort(arr):
 &nbsp; &nbsp;if len(arr) &gt; 1:
 &nbsp; &nbsp; &nbsp; &nbsp;# Finding the mid of the array
 &nbsp; &nbsp; &nbsp; &nbsp;mid = len(arr) // 2

 &nbsp; &nbsp; &nbsp; &nbsp;# Dividing the array into two halves
 &nbsp; &nbsp; &nbsp; &nbsp;left_half = arr[:mid]
 &nbsp; &nbsp; &nbsp; &nbsp;right_half = arr[mid:]

 &nbsp; &nbsp; &nbsp; &nbsp;# Sorting the first half
 &nbsp; &nbsp; &nbsp; &nbsp;merge_sort(left_half)

 &nbsp; &nbsp; &nbsp; &nbsp;# Sorting the second half
 &nbsp; &nbsp; &nbsp; &nbsp;merge_sort(right_half)

 &nbsp; &nbsp; &nbsp; &nbsp;# Initializing pointers for left_half, right_half and main array
 &nbsp; &nbsp; &nbsp; &nbsp;i = j = k = 0

 &nbsp; &nbsp; &nbsp; &nbsp;# Merging the arrays
 &nbsp; &nbsp; &nbsp; &nbsp;while i &lt; len(left_half) and j &lt; len(right_half):
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;if left_half[i] &lt; right_half[j]:
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;arr[k] = left_half[i]
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;i += 1
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;else:
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;arr[k] = right_half[j]
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;j += 1
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;k += 1

 &nbsp; &nbsp; &nbsp; &nbsp;# Check if any element is left in left_half
 &nbsp; &nbsp; &nbsp; &nbsp;while i &lt; len(left_half):
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;arr[k] = left_half[i]
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;i += 1
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;k += 1

 &nbsp; &nbsp; &nbsp; &nbsp;# Check if any element is left in right_half
 &nbsp; &nbsp; &nbsp; &nbsp;while j &lt; len(right_half):
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;arr[k] = right_half[j]
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;j += 1
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;k += 1
<h3>Key Points:</h3><ul><li>Base Case: The recursion ends when the array is reduced to a single element.</li><li>Merging Process: The merge function combines two sorted subarrays into a single sorted array.</li></ul><h3>Time Complexity of Merge Sort</h3><ul><li>Best Case: O(n log n), since the array is always divided into halves, and merging takes linear time.</li><li>Worst Case: O(n log n), even in the worst case, Merge Sort consistently divides and merges in logarithmic time.</li><li>Average Case: O(n log n), making it efficient across a wide variety of cases.</li></ul><h3>Space Complexity:</h3><ul><li>Merge Sort requires O(n) extra space for the temporary arrays used in merging, as it doesn't sort the array in place. This can be a drawback compared to some other sorting algorithms like QuickSort, which operates in-place.</li></ul><h3>Advantages of Merge Sort</h3><ol><li>Stable Sorting:<ul><li>Merge Sort is a stable sorting algorithm, meaning that it maintains the relative order of equal elements in the original array.</li></ul></li><li>Predictable Time Complexity:<ul><li>Merge Sort consistently operates with O(n log n) time complexity, making it a reliable choice for large datasets.</li></ul></li><li>Works Well with Large Data:<ul><li>Due to its efficiency and stability, Merge Sort is often used for sorting large datasets, especially when dealing with linked lists or external data storage (e.g., sorting data that doesn’t fit into memory).</li></ul></li></ol><h3>Disadvantages of Merge Sort</h3>Requires Extra Space:<ul><li>One of the major drawbacks of Merge Sort is its space complexity. It requires additional memory for temporary arrays, which makes it less space-efficient compared to algorithms like QuickSort.</li></ul>In-Place Sorting:<ul><li>Merge Sort is not an in-place sorting algorithm, meaning it doesn’t rearrange elements within the same array but uses additional memory to perform sorting.</li></ul><h3>Applications of Merge Sort</h3>External Sorting:<ul><li>Merge Sort is often used in external sorting algorithms, where data is too large to fit into memory and must be sorted using disk storage.</li></ul>Linked Lists:<ul><li>Merge Sort is particularly efficient for sorting linked lists because it does not require random access to elements, unlike arrays.</li></ul>Stable Sorts:<ul><li>Merge Sort is useful when stability is a concern. In some applications (e.g., database sorting), it is important to maintain the relative order of elements with equal keys.</li></ul><h3>Why Learn Merge Sort?</h3>Learning Merge Sort helps you understand the fundamentals of divide-and-conquer algorithms. Merge Sort is not only one of the most efficient comparison-based sorting algorithms but also lays the foundation for understanding other algorithms and optimizations in computer science. It is widely used in practice, especially in environments where stability and guaranteed performance are important, such as in databases and large-scale data processing.Topics Covered:Definition of Merge Sort: Understanding the divide-and-conquer approach to sorting.Steps in Merge Sort: Dividing the array, recursively sorting, and merging subarrays.Time and Space Complexity: Analysis of Merge Sort’s performance in different cases.Applications: Practical uses of Merge Sort in external sorting, linked lists, and large datasets.For more details and further examples, check out the full article on GeeksforGeeks: <a href="https://www.geeksforgeeks.org/merge-sort/">https://www.geeksforgeeks.org/merge-sort/</a>.

Merge Sort Algorithm

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