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Huffman coding is a lossless data compression algorithm. The idea is to assign variable-length codes to input characters, lengths of the assigned codes are based on the frequencies of corresponding characters. The most frequent character gets the smallest code and the least frequent character gets the largest code.The variable-length codes assigned to input characters are Prefix Codes, means the codes (bit sequences) are assigned in such a way that the code assigned to one character is not the prefix of code assigned to any other character. This is how Huffman Coding makes sure that there is no ambiguity when decoding the generated bitstream.Huffman Coding : <a href="https://www.geeksforgeeks.org/huffman-coding-greedy-algo-3/">https://www.geeksforgeeks.org/huffman-coding-greedy-algo-3/</a>

Huffman Coding

This video is part of the Heap section under GFG SDE Sheet. Given a string S with repeated characters. The task is to rearrange characters in a string such that no two adjacent characters are the same. Note: The string has only lowercase English alphabets and it can have multiple solutions. Return any one of them.Example 1:Input : str = "geeksforgeeks"
Output: 1
Explanation: All the repeated characters of the
given string can be rearranged so that no 
adjacent characters in the string is equal.
Any correct rearrangement will show a output
of 1.Do check out:- Problem: <a href="https://www.geeksforgeeks.org/problems/rearrange-characters4649/1">https://www.geeksforgeeks.org/problems/rearrange-characters4649/1</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/rearrange-characters-string-no-two-adjacent/">https://www.geeksforgeeks.org/rearrange-characters-string-no-two-adjacent/</a>

SDE Sheet - Rearrange characters

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

This video is part of the Heap section under GFG SDE Sheet. Given an input stream of N integers. The task is to insert these numbers into a new stream and find the median of the stream formed by each insertion of X to the new stream.Example 1:Input:
N = 4
X[] = 5,15,1,3
Output:
5
10
5
4
Explanation:Flow in stream : 5, 15, 1, 3 
5 goes to stream --&gt; median 5 (5) 
15 goes to stream --&gt; median 10 (5,15) 
1 goes to stream --&gt; median 5 (5,15,1) 
3 goes to stream --&gt; median 4 (5,15,1 3)&nbsp;Do check out:- Problem: <a href="https://www.geeksforgeeks.org/problems/find-median-in-a-stream-1587115620/1">https://www.geeksforgeeks.org/problems/find-median-in-a-stream-1587115620/1</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/median-of-stream-of-running-integers-using-stl/">https://www.geeksforgeeks.org/median-of-stream-of-running-integers-using-stl/</a>

SDE Sheet - Find median in a stream

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 Heap but also build up problem-solving skills. Given an array arr containing the lengths of the different ropes, we need to connect these ropes to form one rope. The cost to connect two ropes is equal to sum of their lengths. The task is to connect the ropes with minimum cost. &nbsp;Examples:Input: arr[] = [4, 3, 2, 6]
Output: 29
Explanation: We can connect the ropes in following ways.
1) First connect ropes of lengths 2 and 3. Which makes the array [4, 5, 6]. Cost of this operation 2 + 3 = 5. 
2) Now connect ropes of lengths 4 and 5. Which makes the array [9, 6]. Cost of this operation 4 + 5 = 9.
3) Finally connect the two ropes and all ropes have connected. Cost of this operation 9 + 6 =15
Total cost for connecting all ropes is 5 + 9 + 15 = 29. This is the optimized cost for connecting ropes. 
Other ways of connecting ropes would always have same or more cost. For example, if we connect 4 and 6 first (we get three rope of 3, 2 and 10), then connect 10 and 3 (we gettwo rope of 13 and 2). Finally we connect 13 and 2. Total cost in this way is 10 + 13 + 15 = 38.Give the problem a try before going through the video. All the best!!! Problem Link: <a href="https://practice.geeksforgeeks.org/problems/minimum-cost-of-ropes-1587115620/1">https://practice.geeksforgeeks.org/problems/minimum-cost-of-ropes-1587115620/1</a>

PROBLEM OF THE DAY : 11/09/2024 | Minimum Cost of Ropes

This video is part of the Greedy section under GFG SDE Sheet. Given a string S, implement <a href="https://www.geeksforgeeks.org/huffman-coding-greedy-algo-3/">Huffman Encoding</a> and <a href="https://www.geeksforgeeks.org/huffman-decoding/">Decoding</a>.Example 1:Input : abc
Output : abcExample 2:&nbsp;Input : geeksforgeeks
Output : geeksforgeeksDo check out:- Problem: <a href="https://www.geeksforgeeks.org/problems/huffman-decoding-1/1">https://www.geeksforgeeks.org/problems/huffman-decoding-1/1</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/huffman-decoding/">https://www.geeksforgeeks.org/huffman-decoding/</a>

SDE Sheet - Huffman Decoding

<h2>Heap Sort | Comprehensive Guide</h2>Heap Sort is a popular and efficient comparison-based sorting algorithm that uses a binary heap data structure to sort elements. It is known for its efficiency in handling large datasets and provides a time complexity of O(n log n), making it one of the most widely used algorithms for sorting.<h3>What is Heap Sort?</h3>Heap Sort is a sorting algorithm that organizes data by leveraging the properties of a binary heap. A binary heap is a complete binary tree where the elements are arranged either in increasing order (min-heap) or decreasing order (max-heap). Heap sort typically uses a max-heap to repeatedly remove the largest element and place it at the end of the list until the entire list is sorted.<h3>How Heap Sort Works</h3>Heap sort operates in two main phases:Building the Heap:<ul><li>First, the input data is converted into a binary heap structure. This is done using a process called heapify, where each element of the array is rearranged to satisfy the heap property (i.e., for a max-heap, the parent node is greater than its children).</li></ul>Extracting Elements:<ul><li>Once the heap is built, the largest element (root of the max-heap) is removed and swapped with the last element of the heap. The heap is then adjusted (heapified) to maintain the heap structure, and this process is repeated until all elements are sorted.</li></ul><h3>Steps of Heap Sort Algorithm</h3>Build a Max-Heap:<ul><li>Rearrange the elements of the array to form a max-heap. In a max-heap, each parent node is greater than or equal to its child nodes.</li></ul>Swap the Root with the Last Element:<ul><li>After building the max-heap, swap the root element (the largest value) with the last element of the heap.</li></ul>Reduce Heap Size and Heapify:<ul><li>Reduce the heap size by 1 (since the last element is now sorted) and call the heapify function to maintain the max-heap property. Repeat this process until all elements are sorted.</li></ul><h3>Time Complexity of Heap Sort</h3>The time complexity of Heap Sort is O(n log n). Here's why:<ul><li>Building the Heap: It takes O(n) time to build a max-heap from the input array.</li><li>Heapify Process: Heapifying an element takes O(log n) time, and it is performed n times during the extraction phase, resulting in a total of O(n log n) for the sorting phase.</li></ul>Thus, the overall time complexity is O(n log n), making Heap Sort efficient for large datasets.<h3>Space Complexity of Heap Sort</h3>The space complexity of Heap Sort is O(1), as it is an in-place sorting algorithm. This means that Heap Sort does not require any additional memory beyond the input array itself, making it space-efficient.<h3>Applications of Heap Sort</h3>Sorting Large Datasets:<ul><li>Heap Sort is often used for sorting large datasets because of its O(n log n) time complexity and efficient memory usage.</li></ul>Priority Queues:<ul><li>Since a max-heap (or min-heap) is used to implement priority queues, Heap Sort can be utilized to manage and organize priority queues efficiently.</li></ul>Selection Algorithms:<ul><li>Heap Sort is also used in selection algorithms where finding the largest or smallest elements from a list is required.</li></ul><h3>Advantages of Heap Sort</h3>Efficiency:<ul><li>Heap Sort has a time complexity of O(n log n), making it highly efficient for large datasets.</li></ul>In-Place Sorting:<ul><li>Heap Sort is an in-place algorithm, meaning it requires no additional memory beyond the input array.</li></ul>No Worst-Case Degradation:<ul><li>Unlike algorithms like Quick Sort, which can degrade to O(n²) in the worst case, Heap Sort maintains its O(n log n) complexity for all cases.</li></ul><h3>Disadvantages of Heap Sort</h3>Not Stable:<ul><li>Heap Sort is not a stable sorting algorithm, meaning that the relative order of equal elements is not preserved during the sorting process.</li></ul>More Comparisons:<ul><li>Heap Sort generally performs more comparisons compared to Quick Sort or Merge Sort, making it less efficient in some scenarios.</li></ul><h3>Why Learn Heap Sort?</h3>Heap Sort is an important algorithm to learn because of its efficiency, memory usage, and versatility. It’s used in scenarios where sorting large datasets in O(n log n) time is required, and its use of the heap data structure makes it valuable in understanding priority queues and other advanced topics in computer science.Topics Covered:Definition of Heap Sort: What Heap Sort is and how it works.Steps of the Algorithm: Building the heap and extracting elements.Applications: Common uses of Heap Sort in real-world scenarios.For more details and further examples, check out the full article on GeeksforGeeks: <a href="https://www.geeksforgeeks.org/heap-sort/">https://www.geeksforgeeks.org/heap-sort/</a>.

Heap Sort - Data Structures and Algorithms

<h2>Sliding Window Maximum | Maximum of All Subarrays of Size k</h2>In this guide, we’ll explore the sliding window maximum problem, which involves finding the maximum value in every subarray of size k in a given array. This problem is widely used in scenarios like analyzing time series data, optimizing algorithms, and solving computational geometry problems. By the end of this tutorial, you will understand how to solve this problem efficiently using the sliding window technique.<h2>Problem Definition</h2>Given an array of integers and an integer k, the task is to find the maximum of every subarray of size k in the array.<h3>Example:</h3><ul><li>Input: arr = [1, 3, -1, -3, 5, 3, 6, 7], k = 3</li><li>Output: [3, 3, 5, 5, 6, 7]</li></ul>Here, for every subarray of size k, we compute the maximum:<ul><li>Subarray [1, 3, -1] → Max = 3</li><li>Subarray [3, -1, -3] → Max = 3</li><li>Subarray [-1, -3, 5] → Max = 5</li><li>Subarray [-3, 5, 3] → Max = 5</li><li>Subarray [5, 3, 6] → Max = 6</li><li>Subarray [3, 6, 7] → Max = 7</li></ul><h2>Key Points Covered:</h2>Brute-Force Approach:<ul><li>A simple approach is to iterate over all subarrays of size k and compute the maximum value for each.</li><li>Drawback: This method has a time complexity of O(n×k)O(n \times k)O(n×k), where n is the size of the array. For large arrays, this approach becomes inefficient.</li></ul>Optimized Approach Using Deque:<ul><li>The sliding window maximum problem can be solved more efficiently using a deque (double-ended queue). The deque helps maintain the maximum element within the current sliding window in O(n)O(n)O(n) time.</li><li>A deque is used to store indices of array elements, ensuring that the maximum element is always at the front of the deque, while irrelevant elements (those outside the current window) are removed from the deque.</li></ul><h3>Steps to Solve Using Deque:</h3>Initialize an Empty Deque:<ul><li>The deque will store indices of the array elements, ensuring that the maximum of each window can be accessed in constant time.</li></ul>Traverse Through the Array:<ul><li>For each element in the array, perform the following operations:<ul><li>Remove elements from the deque that are no longer within the current window of size k.</li><li>Remove elements from the deque that are smaller than the current element, as they cannot be the maximum for the current window.</li><li>Add the index of the current element to the deque.</li></ul></li></ul>Track Maximum Elements:<ul><li>After processing each window (i.e., once the size of the deque reaches k), the element at the front of the deque is the maximum of the current subarray.</li></ul>Move the Window:<ul><li>Slide the window to the right by one position, and repeat the process for the next window of size k.</li></ul><h3>Example Walkthrough:</h3>Let’s walk through the example arr = [1, 3, -1, -3, 5, 3, 6, 7] with k = 3:Initial Subarray [1, 3, -1]:<ul><li>Max = 3 (indices stored in deque: [1])</li></ul>Next Subarray [3, -1, -3]:<ul><li>Max = 3 (deque maintains [1] after adjusting for window size)</li></ul>Next Subarray [-1, -3, 5]:<ul><li>Max = 5 (deque is updated to store [4] as 5 is greater than the previous elements)</li></ul>Next Subarray [-3, 5, 3]:<ul><li>Max = 5 (deque still maintains index [4])</li></ul>Next Subarray [5, 3, 6]:<ul><li>Max = 6 (deque updated to [6] after comparing and removing smaller elements)</li></ul>Next Subarray [3, 6, 7]:<ul><li>Max = 7 (deque updated to [7])</li></ul>The result is [3, 3, 5, 5, 6, 7].<h3>Time Complexity:</h3>The optimized solution using a deque has a time complexity of O(n)O(n)O(n), where n is the size of the array. This is because each element is added to and removed from the deque at most once. This solution is much more efficient than the brute-force approach.<h3>Applications of Sliding Window Maximum:</h3>Time Series Data Analysis:<ul><li>Sliding window maximum is useful for analyzing trends in time series data, where the goal is to track the maximum values over a specific window of time.</li></ul>Signal Processing:<ul><li>In signal processing, the sliding window maximum helps filter noise by keeping track of the highest signal values over a specific interval.</li></ul>Stock Market Analysis:<ul><li>For analyzing stock prices, sliding window maximum is used to compute the maximum stock price over a given period, such as a week or a month.</li></ul><h2>Why Learn Sliding Window Maximum?</h2>Understanding the sliding window maximum algorithm is crucial for solving problems that require efficient handling of subarrays or subsequences. Mastering this technique is useful for optimizing solutions in competitive programming, data analysis, and real-time processing of large datasets.Topics Included:Brute-Force vs. Optimized Approach: Comparison of brute-force and deque-based solutions for finding maximum values in sliding windows.Efficient Use of Deque: Step-by-step explanation of how the deque is used to maintain the maximum element in the current window.Real-World Applications: Practical scenarios where the sliding window maximum technique can be applied, such as time series analysis and stock market trends.For a detailed guide and further explanations, check out the full article on GeeksforGeeks: <a href="https://www.geeksforgeeks.org/sliding-window-maximum-maximum-of-all-subarrays-of-size-k/">https://www.geeksforgeeks.org/sliding-window-maximum-maximum-of-all-subarrays-of-size-k/</a>.

Sliding Window Maximum (Maximum of all subarrays of size K)

This video is part of the Heap section under GFG SDE Sheet. Given a&nbsp;N&nbsp;x N&nbsp;matrix, where every row and column is sorted in non-decreasing order. Find the kth smallest element in the matrix.Example 1:Input:
N = 4
mat[][] = &nbsp; &nbsp; {{16, 28, 60, 64},
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; {22, 41, 63, 91},
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; {27, 50, 87, 93},
 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; {36, 78, 87, 94 }}
K = 3
Output: 27
Explanation: 27 is the 3rd smallest element. Try it out before watching the implementation of the problem in the video. We recommend watching the video, even if you can solve the problem. You may discover something new. All the best!!!Do check out:- Problem: <a href="https://www.geeksforgeeks.org/problems/kth-element-in-matrix/1">https://www.geeksforgeeks.org/problems/kth-element-in-matrix/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/kth-smallest-element-in-a-row-wise-and-column-wise-sorted-2d-array/"> https://www.geeksforgeeks.org/kth-smallest-element-in-a-row-wise-and-column-wise-sorted-2d-array/</a>

SDE Sheet - Kth Smallest Element in a Row-Column Wise Sorted Matrix

This video is part of the Heap section under GFG SDE Sheet. Given an array of sorted linked lists of different sizes. The task is to merge them in such a way that after merging they will be a single sorted linked list.Examples:Input: arr = [1-&gt;2-&gt;3, 4-&gt;5, 5-&gt;6, 7-&gt;8]
Output: 1-&gt;2-&gt;3-&gt;4-&gt;5-&gt;5-&gt;6-&gt;7-&gt;8
Explanation: The test case has 4 sorted linked 
list of size 3, 2, 2, 2
1st&nbsp; &nbsp; list &nbsp; &nbsp;&nbsp;1 -&gt; 2-&gt; 3
2nd&nbsp; &nbsp;list &nbsp; &nbsp; &nbsp;4-&gt;5
3rd&nbsp; &nbsp; list &nbsp; &nbsp; &nbsp;5-&gt;6
4th&nbsp; &nbsp; list &nbsp; &nbsp; &nbsp;7-&gt;8
The merged list will be 1-&gt;2-&gt;3-&gt;4-&gt;5-&gt;5-&gt;6-&gt;7-&gt;6 Try it out before watching the implementation of the problem in the video. We recommend watching the video, even if you can solve the problem. You may discover something new. All the best!!!Do check out:- Problem: <a href="https://www.geeksforgeeks.org/problems/merge-k-sorted-linked-lists/1">https://www.geeksforgeeks.org/problems/merge-k-sorted-linked-lists/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/merge-k-sorted-linked-lists/">https://www.geeksforgeeks.org/merge-k-sorted-linked-lists/</a>

SDE Sheet - Merge K sorted Linked lists

Explore the process of transforming a Binary Search Tree (BST) into a Max Heap with our detailed tutorial, perfect for computer science students, algorithm enthusiasts, and software developers interested in advanced data structures.In this tutorial, you'll learn:<ul><li>The fundamental differences between BSTs and Max Heaps, focusing on their properties and how they are used differently in data handling and processing applications.</li><li>A systematic approach to convert a BST into a Max Heap. This involves two main steps: performing an in-order traversal to extract the elements in sorted order, and then using this sorted list to construct a Max Heap in a way that maintains the heap property.</li><li>Step-by-step instructions on carrying out each phase of the transformation, starting from tree traversal to the final construction of the heap, ensuring you grasp the complete process and underlying principles.</li><li>Coding demonstrations that show practical implementations of the conversion algorithm. These examples will provide you with a clear understanding of how to code the conversion in various programming languages, reinforcing the theoretical concepts with practical application.</li><li>Best practices and tips for optimizing the conversion process, which are crucial for handling large data sets efficiently and maintaining robust performance in your applications.</li></ul>By the end of this tutorial, you’ll have a thorough understanding of how to effectively convert a BST into a Max Heap, enhancing your ability to work with and manipulate complex data structures.For more comprehensive insights, including detailed code examples and further discussion on the nuances of tree and heap operations, check out our full article at <a href="https://www.geeksforgeeks.org/convert-bst-to-max-heap/">https://www.geeksforgeeks.org/convert-bst-to-max-heap/</a>.This guide aims to enhance your algorithmic thinking and problem-solving skills, preparing you for challenging tasks in software development, competitive programming, and academic research in the field of computer science.

BST to max Heap | DSA Problem

Unlock the secrets of efficient data management with GeeksforGeeks! Dive into the world of binary heaps with our comprehensive guide. From understanding the fundamentals to mastering advanced techniques, this tutorial covers everything you need to know about binary heaps.Here's what you'll discover:<ul><li style="margin-left:0px;">Fundamentals of Binary Heaps: Delve into the basics of binary heaps, including their structure, properties, and common operations such as insertion, deletion, and heapify.</li><li style="margin-left:0px;">Heap Sorting Algorithms: Explore how binary heaps are used in sorting algorithms like heap sort, and learn how to implement these algorithms efficiently.</li><li style="margin-left:0px;">Applications in Data Structures: Understand the practical applications of binary heaps in various data structures and algorithms, such as priority queues, graph algorithms, and more.</li></ul>Whether you're a beginner eager to learn about binary heaps or an experienced programmer looking to enhance your skills, this tutorial has something for everyone.Ready to dive into the world of binary heaps? Explore the ultimate guide on GeeksforGeeks: <a href="https://www.geeksforgeeks.org/binary-heap/">https://www.geeksforgeeks.org/binary-heap/</a>. Let's embark on this enlightening journey together!

Binary Heap Operations | DSA Problem

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