Shell Sort

Introduction Shell Sort is an optimization of the insertion sort algorithm, which is an in-place comparison-based sorting algorithm. Insertion sort works by comparing each element of the list with the previous one and inserting it at the appropriate position. However, the insertion sort can be quite slow for larger lists

Sleep Sort (not practical, but an interesting concept)

Introduction to Sleep Sort Sleep sort is a unique and interesting concept in the world of sorting algorithms. As the name suggests, it involves sorting elements by putting them to sleep for a specific duration. Although it is not a practical sorting approach, it provides a great opportunity to explore

Pancake Sort

Introduction to Pancake Sort Pancake sorting is a sorting algorithm that involves sorting a sequence of numbers in ascending order using only one type of operation - flipping. Flipping is a process of reversing the order of a specific number of elements in the sequence, starting from the first element.

Bogo Sort (or Stupid Sort, highly inefficient)

Introduction to Bogo Sort Bogo Sort, also known as Stupid Sort, is a highly inefficient sorting algorithm that works by generating random permutations of its input until it finds one that is sorted. It is intentionally not practical for real-world usage due to its terrible time complexity, which is O(

Bitonic Sort

Introduction to Bitonic Sort Bitonic sort is a parallel, comparison-based sorting algorithm that focuses on converting a random sequence of numbers into a bitonic sequence, which is a sequence that increases and then decreases, or decreases and then increases. In simpler terms, a bitonic sequence is a sequence that has

Cocktail Sort (or Shaker Sort)

Introduction to Cocktail Sort (or Shaker Sort) Cocktail Sort, also known as Shaker Sort or Bidirectional Bubble Sort, is a variation of the famous Bubble Sort algorithm. Like Bubble Sort, Cocktail Sort is a simple comparison-based sorting algorithm meant for small datasets. The primary difference between Bubble Sort and Cocktail

Odd-Even Sort (or Brick Sort)

Introduction Odd-Even Sort, also known as Brick Sort, is a relatively simple comparison-based sorting algorithm. It works by iteratively comparing and swapping adjacent elements in an array or list. The algorithm divides the elements into two groups - odd-indexed and even-indexed elements. It then sorts the odd-indexed elements relative to

Gnome Sort

Introduction to Gnome Sort Gnome Sort, also known as the "stupid sort," is a simple and straightforward sorting algorithm that is based on the concept of a garden gnome sorting flower pots. The gnome moves from left to right, comparing each pair of elements and swapping them if they are

Comb Sort

Introduction to Comb Sort Comb Sort is a simple yet efficient sorting algorithm that improves upon the Bubble Sort algorithm. Bubble Sort compares adjacent elements and swaps them if they are in the wrong order. Comb Sort, on the other hand, uses a gap larger than 1 for comparisons, which

Radix Sort

Introduction to Radix Sort Radix sort is a non-comparative integer sorting algorithm that sorts data with integer keys by grouping keys by the individual digits which share the same significant position and value. Radix sort has been around since the days of punch cards and has been used to sort

Tim Sort

Introduction to Tim Sort Tim Sort is a hybrid sorting algorithm, derived from merge sort and insertion sort, designed to perform well on many kinds of real-world data. It was implemented by Tim Peters in 2002 for use in the Python programming language. The algorithm finds subsequences of the data

Bucket Sort

Introduction to Bucket Sort Bucket Sort is a non-comparison based sorting algorithm that works by distributing the elements of an array into a number of buckets. Each bucket is then sorted individually, either using a different sorting algorithm or applying the bucket sort algorithm recursively. Finally, the sorted values are

Counting Sort

Introduction to Counting Sort Counting sort is a simple and efficient sorting algorithm that sorts a given list of integers by counting the occurrences of each element in the list. It is a non-comparative sorting algorithm, which means it doesn't compare the elements of the list during the sorting process.

Heap Sort

Introduction to Heap Sort Heap Sort is a comparison-based sorting algorithm that uses a binary heap data structure to sort elements. It has an average and worst-case time complexity of O(n log n), making it an efficient sorting algorithm for large data sets. A binary heap is a complete

Quick Sort

Introduction to Quick Sort Quick Sort is a popular sorting algorithm that is both efficient and easy to understand. It is a divide-and-conquer algorithm that works by selecting a 'pivot' element from an array and partitioning the other elements into two groups – those less than the pivot and those greater

Insertion Sort

Introduction Insertion Sort is an easy-to-understand sorting algorithm that can be used to sort a list of elements. It works by dividing the input list into two parts: a sorted part and an unsorted part. At the beginning of the algorithm, the sorted part consists of just one element, and

Selection Sort

Introduction to Selection Sort Selection sort is a simple comparison-based sorting algorithm. The main idea behind the algorithm is to divide the input list into two parts: the sorted part and the unsorted part. Initially, the sorted part is empty, and the unsorted part contains all the elements. The algorithm

Quicksort

Introduction to Quicksort Quicksort is a popular sorting algorithm invented by Tony Hoare in 1960. It is a divide-and-conquer algorithm that works by selecting a "pivot" element from the array, partitioning the other elements into two groups - those less than the pivot and those greater than the pivot -

Bubble Sort

Introduction to Bubble Sort Bubble sort is a simple sorting algorithm that repeatedly steps through the list, compares adjacent elements, and swaps them if they are in the wrong order. The algorithm continues to pass through the list until it makes a pass with no swaps. The name "bubble sort"

Merge Sort

Introduction to Merge Sort Merge Sort is a popular comparison-based sorting algorithm that uses the divide and conquer technique to sort a list of elements. The primary idea behind Merge Sort is to break down a large list into smaller, more manageable lists, sort them individually, and then merge these

Compute the Minimum Weighted Vertex Cover in a Graph

Introduction Compute the Minimum Weighted Vertex Cover (MWVC) in a graph is an optimization problem where we aim to find a set of vertices with the minimum total weight such that every edge in the graph is covered by at least one vertex. This problem has numerous real-world applications, such

Estimate the Maximum Edge Disjoint Paths in a Graph

Introduction Estimating the maximum edge disjoint paths in a graph is an important problem in computer networks, traffic engineering, and other domains. Essentially, it is about finding the maximum number of paths between two nodes in a graph such that no two paths share an edge. This problem has practical

Discover the Largest Complete Subgraph

Introduction: Discover the Largest Complete Subgraph In graph theory, a complete subgraph is a subgraph in which every pair of distinct vertices is connected by a unique edge. Discovering the largest complete subgraph in a given graph is an important problem in many real-world applications, such as network analysis, community

Compute the Maximum Flow-Minimum Cut in a Graph

Introduction In computer science and network theory, computing the maximum flow-minimum cut in a graph is an important optimization problem. This problem involves finding a way to route the maximum amount of flow through a network while also identifying the minimum cut that would separate the network into two disjoint

Detect the Core of a Graph

Introduction to Graph Cores In graph theory, the core of a graph is a subgraph in which every vertex has a degree greater than or equal to a specified value k. In other words, each vertex in the core is connected to at least k other vertices. Detecting the core

Determine the Minimum Cut in a Graph

Introduction Determining the minimum cut in a graph is a classic problem in computer science and graph theory. The minimum cut is the smallest set of edges that, when removed, disconnects the graph into two disjoint subgraphs. This problem has important applications in network design, social network analysis, and other

Calculate the K-Core of a Graph

Introduction to K-Core of a Graph A K-Core of a graph is a subgraph where all vertices have a degree greater than or equal to K. The K-Core decomposition of a graph is a method that helps to identify the connectivity and robustness of a network. This can be useful

Find the Maximum Density Subgraph

1. Explain Find the Maximum Density Subgraph In graph theory, a subgraph is a graph formed from a subset of the vertices and edges of a given graph. The maximum density subgraph (MDS) is a subgraph with the highest density among all subgraphs in the graph. Density of a graph

Find the PageRank of a Web Graph

Introduction: What is PageRank? PageRank is an algorithm used by Google Search to rank the importance of web pages in their search engine results. It was designed by Larry Page and Sergey Brin, the founders of Google, while they were at Stanford University. PageRank works by counting the number and

Calculate the Girth of a Graph

Introduction to Girth of a Graph The girth of a graph is the length of the shortest cycle in the graph. In other words, it is the smallest number of edges that form a closed loop. Calculating the girth of a graph is an important task in graph theory, as

Determine the Wiener Index of a Graph

Introduction to the Wiener Index of a Graph The Wiener Index of a graph is a topological index used in mathematical chemistry to study the molecular structure of chemical compounds. It is defined as the sum of all pairwise shortest path distances between the vertices of the graph. In simpler

Determine the Betweenness Centrality of Nodes in a Graph

Introduction to Betweenness Centrality Betweenness centrality is a measure that helps us understand the importance of nodes within a graph. It is calculated by counting the number of shortest paths between all pairs of nodes that pass through a particular node. Nodes with high betweenness centrality are considered as crucial

Compute the Graph Center and Periphery

Introduction In graph theory, the concepts of graph center and periphery are used to determine the central and peripheral nodes in a network. These measures help us understand the importance of nodes in a network and have various real-world applications like social network analysis, communication networks, transportation networks, and more.

Find the Smallest Cycle Basis in a Graph

Introduction to Smallest Cycle Basis In graph theory, a cycle basis is a set of simple cycles that forms a basis for the cycle space of a given graph. The smallest cycle basis is the one with the minimum total length. Finding the smallest cycle basis in a graph is

Compute the Maximal Matching in a Graph

Introduction to Maximal Matching in a Graph Maximal Matching in a graph is a set of edges such that no two edges share a common vertex and adding any more edges to the set would violate this condition. In other words, it is a set of pairwise non-adjacent edges, which

Calculate the All-Pairs Shortest Paths in a Graph

Introduction Calculating the all-pairs shortest paths in a graph is an essential problem in computer science, with applications in routing, social networks, and data analysis. This problem involves finding the shortest path between every pair of vertices in a graph. In this lesson, we will delve into the Floyd-Warshall algorithm,

Compute the Steiner Tree in a Graph

Introduction to the Steiner Tree Problem The Steiner Tree Problem (STP) is an optimization problem that arises in various fields such as network design, VLSI design, and phylogenetic tree reconstruction. The objective of the problem is to find a minimum-cost tree that spans a given set of terminal vertices in

Identify the Maximum Weighted Independent Set in a Tree

Introduction to Maximum Weighted Independent Set in a Tree In computer science, particularly in graph theory and dynamic programming, the problem of identifying the Maximum Weighted Independent Set (MWIS) in a tree is an important optimization problem. An independent set is a subset of nodes in a graph where no

Determine the Shortest Cycle in a Graph

Introduction In graph theory, finding the shortest cycle in a graph is a common problem. A cycle is a sequence of vertices and edges that starts and ends at the same vertex. It is considered "shortest" when the number of edges in the cycle is minimized. This problem can be

Find the Maximum Cuts in a Graph

Introduction to Maximum Cuts in a Graph Finding the maximum cuts in a graph is an important problem in computer science, especially in network analysis and optimization. The term "cut" refers to dividing a graph into two disjoint sets of vertices, such that all the edges connecting the two sets

Check for Hamiltonian Cycles in a Graph

Introduction A Hamiltonian cycle in a graph is a closed path that visits each vertex of the graph exactly once. The problem of determining whether a given graph contains a Hamiltonian cycle is called the Hamiltonian cycle problem. This problem is of great importance in computer science, particularly in the

Estimate the Minimum Dominating Set in a Graph

Introduction to Minimum Dominating Set in a Graph In graph theory, a dominating set for a graph G is a subset of vertices in G such that every vertex not included in the subset is adjacent to at least one vertex in the subset. The problem of finding the smallest

Determine the Vertex Connectivity of a Graph

Introduction Vertex connectivity of a graph is an important concept in graph theory that helps us understand the resilience of a graph or network. In this blog post, we will be discussing what vertex connectivity is, its real-world applications, and how to determine the vertex connectivity of a graph using

Identify the Maximum k-Connected Subgraph

Introduction In graph theory, the maximum k-connected subgraph problem is an optimization problem that aims to find a subgraph with the maximum number of nodes where each node has a degree of at least k. This problem has various practical applications, such as in the design of reliable communication networks,

Find the Minimum Multiway Cut in a Graph

Introduction The Minimum Multiway Cut (MMC) problem is a classic optimization problem in graph theory that seeks to find the minimum total cost of disconnecting a set of specified terminal nodes from each other. In simpler terms, the aim is to find the minimum number of edges to remove from

Compute the Degree Distribution of a Graph

Introduction to Degree Distribution of a Graph In graph theory, the degree of a vertex is the number of edges connected to it. Degree distribution is a probability distribution of the degrees of vertices in a graph. It is an important measure to analyze various properties of a graph, such

Determine the Eccentricity of Nodes in a Graph

Introduction The eccentricity of a node in a graph is a measure of the maximum distance between that node and any other node in the graph. In simple terms, it tells us the longest path we have to take to reach any other node in the graph from the given

Measure the Closeness Centrality of Nodes in a Graph

Introduction: Closeness Centrality in Graphs Closeness centrality is a measure of how central a node is in a graph. It is computed as the inverse of the average shortest path length to all other nodes in the graph. In other words, a node with high closeness centrality is close to

Find the Longest Common Subsequence of Two Paths

Introduction to Longest Common Subsequence The Longest Common Subsequence (LCS) problem is a classic computer science problem that deals with finding the longest subsequence common to two sequences. A subsequence is a sequence of elements that appears in the same order in both sequences, but not necessarily consecutively. This problem

Compute the Edge Connectivity of a Graph

Introduction to Compute the Edge Connectivity of a Graph Edge connectivity is a measure of the robustness of a graph, or how resistant it is to being disconnected. In other words, it represents the minimum number of edges that must be removed from the graph to disconnect it. Edge connectivity

Verify if a Graph is Bipartite

Introduction to Bipartite Graphs A bipartite graph is a graph whose vertex set can be partitioned into two disjoint sets such that no two vertices within the same set are adjacent. In simple terms, a bipartite graph can be colored with just two colors, and vertices of the same color

Detect Cycles in a Directed Graph

Introduction Detecting cycles in a directed graph is a common problem in computer science that involves identifying whether a graph contains a directed cycle or not. A directed cycle is a sequence of vertices and directed edges in which the last vertex is connected back to the first vertex, forming

Calculate the Maximum Cardinality Bipartite Matching

Introduction to Maximum Cardinality Bipartite Matching Maximum Cardinality Bipartite Matching (MCBM) is a classical combinatorial optimization problem that aims to find the maximum number of pairings between two disjoint sets, such that each element in both sets is paired with at most one element from the other set. In simpler

Construct a Minimum Vertex Cover in a Graph

Introduction A Minimum Vertex Cover (MVC) in a graph is a subset of vertices such that each edge of the graph is incident to at least one vertex in the subset, and the number of vertices in the subset is minimized. In other words, a minimum vertex cover is the

Determine the Chromatic Number of a Graph

Introduction to Chromatic Number of a Graph The chromatic number of a graph is the minimum number of colors needed to color the vertices of the graph in such a way that no two adjacent vertices share the same color. This concept is crucial in graph theory, as it helps

Compute the Maximum Clique in a Graph

Introduction to Maximum Clique Problem The Maximum Clique Problem (MCP) is an NP-hard combinatorial optimization problem in graph theory. It involves finding the largest complete subgraph, or a clique, within a given graph. A clique is a subset of vertices in which every pair of vertices is directly connected by

Find the Maximum Independent Set in a Graph

Introduction to Maximum Independent Set in a Graph In graph theory, an independent set is a set of vertices in a graph such that no two vertices are adjacent. In other words, there are no edges connecting the vertices in the independent set. The problem of finding the maximum independent

Determine Bridges in an Undirected Graph

Introduction Bridges in an undirected graph are edges that, if removed, would increase the number of connected components in the graph. In other words, a bridge is an edge that connects two separate parts of the graph, and its removal would make those parts disconnected. Determining bridges in an undirected

Check for an Eulerian Circuit in a Graph

Introduction to Eulerian Circuits in Graphs An Eulerian circuit is a closed walk in a graph that visits each edge exactly once. In other words, it is a path that starts and ends at the same vertex and covers all the edges of the graph without repeating any edge. Eulerian

Count the Number of Simple Cycles in a Graph

Introduction to Counting the Number of Simple Cycles in a Graph A graph is a mathematical structure representing a set of objects in which some pairs of the objects are connected by links. Graphs are used to model many types of relations and processes in different fields, such as computer

Detect Negative Cycles in a Weighted Graph (Solved)

Introduction In this article, we are going to dive deep into the world of graph theory and understand how to detect negative cycles in a weighted graph. Detecting negative cycles in a graph is a common problem in computer science and has many practical applications in various domains, such as

Identify Articulation Points in an Undirected Graph (Solved)

Introduction: Identify Articulation Points in an Undirected Graph (Solved) Graphs are a versatile data structure that can be used to model various real-world problems, such as social networks, transportation systems, and even electrical circuits. In this article, we will discuss the concept of articulation points in an undirected graph and

Compute the Diameter of a Tree (Solved)

Introduction to Computing the Diameter of a Tree In computer science and graph theory, trees play a crucial role in representing hierarchical relationships between objects. Trees are a special kind of graph that have no cycles and are connected. One of the important properties of a tree is its diameter,

Obtain the Transitive Closure of a Graph (Solved)

Introduction The transitive closure of a graph is a powerful concept that can be used to analyze and solve various problems in computer science. In this blog post, we will first explain what the transitive closure of a graph is and why it's important. Then, we will provide real-world examples

Find the Maximum Flow in a Network (Solved)

Introduction to Maximum Flow in a Network In various real-world scenarios, we often come across the problem of determining the maximum flow that can be achieved through a network of nodes and edges, where each edge has a certain capacity. The maximum flow problem is a classical optimization problem that

Discover the Longest Path in a Directed Acyclic Graph (Solved)

Introduction to the Longest Path Problem The longest path problem is the problem of finding a simple path of maximum length in a given directed acyclic graph (DAG). In other words, it is the problem of finding the longest sequence of nodes such that each node is followed by its

Calculate the Minimum Spanning Tree of a Graph (Solved)

Introduction to the Minimum Spanning Tree A Minimum Spanning Tree (MST) is a tree that spans all the vertices in a connected, undirected graph and has the minimum possible total edge weight. In other words, it is a tree that connects all the nodes in a graph such that the

Identify the Strongly Connected Components in a Directed Graph (Solved)

Introduction to Strongly Connected Components in a Directed Graph In computer science, a directed graph is a graph that is made up of a set of vertices and a set of directed edges (also known as "arcs"). In a directed graph, each edge has an initial vertex, called its "tail"

Determine the Connected Components in a Graph (Solved)

Introduction Connected components in a graph are the subgraphs in which all the vertices are connected to each other by at least one path. In this lesson, we will learn how to determine the connected components in a graph. Understanding connected components is essential for various real-world applications, such as

Compute the Shortest Path between Two Nodes (Solved)

Introduction In computer science, one of the fundamental problems is finding the shortest path between two nodes in a graph. The shortest path problem is applicable in various real-world scenarios such as navigation systems, network routing, traffic optimization, and social network analysis. In this tutorial, we will discuss the shortest