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Data Structure Articles
Page 33 of 164
Check if a cycle between nodes S and T in an Undirected Graph with only S and T repeating
Introduction Graphs are powerful mathematical structures that allow us to model and visualize relationships between various entities. In computer science, graphs find application in a wide range of algorithms and data structures. One common problem with undirected graphs is determining whether a cycle exists between two given nodes. In this article, we embark upon the journey to unravel this mystery and present an elegant solution using C/C++. Determining cycles within an undirected graph is vital in various applications where connectivity matters. Undirected Graphs is determining whether a cycle exists between two given nodes Unweighted bidirectional (or undirected) graphs consist of ...
Read MoreConstruct a Graph from size of components for each node
Introduction Graph theory is a fundamental field in computer science, allowing us to study and visualize relationships between objects or entities. One important aspect of analyzing graphs understands the sizes of components or connected subgraphs within the network. In this article, we will explore how to construct a graph from component size for each node using C++ code. In graph theory, a component refers to any connected subgraph where there exists some path between any two vertices within that subgraph. It helps depict clusters or groups of interconnected nodes within the entire graph structure. A Graph from size of components ...
Read MoreTraverse in lexicographical order using DFS
Introduction Graph traversal could be a principal operation in computer science that includes going by all nodes of a graph. In certain scenarios, it may be fundamental to navigate the graph in the lexicographical order of nodes, which suggests going by the nodes in climbing numerical order. In this article, we'll investigate two distinctive approaches to performing a lexicographical DFS traversal of a graph utilizing the C language. These approaches point to creating the same correct yield while giving elective executions and viewpoints. They offer an establishment for understanding a wide extent of graph-related issues, empowering productive investigation, and analysis ...
Read MoreSmallest set vertices to visit all nodes of the given Graph
Introduction Finding the smallest set of vertices to visit all nodes in a graph could be a crucial issue in graph hypothesis. It has practical applications in different areas, counting network optimization, directing algorithms, and task planning. In this article, we are going investigate three diverse approaches to illuminate this problem: Depth-First Search (DFS), Breadth-First Search (BFS), and Depth-First Traversal with Backtracking. We are going give point by point clarifications, code usage within the C language, and algorithmic steps for each approach. Also, we'll illustrate the utilization of these approaches with a test graph to guarantee that all three strategies ...
Read MoreNumber of ways to reach at starting node after travelling through exactly K edges in a complete graph
Introduction The number of ways to reach the beginning hub after traveling through precisely K edges in a total chart can be calculated utilizing different approaches within the C dialect. One approach is to utilize brute constrain recursion, where we investigate all conceivable ways. Another approach includes energetic programming, where we store and reuse halfway comes about to dodge excess computations. Moreover, a numerical equation exists to specifically compute the number of ways based on the number of hubs and edges. These strategies give effective arrangements to decide the check of ways driving back to the beginning hub in a ...
Read MoreFind first undeleted integer from K to N in given unconnected Graph after Performing Q queries
Introduction Finding the primary undeleted integer from a given extend in a detached graph after performing multiple queries may be a challenging issue in graph theory. In this article, we investigate the errand of distinguishing the primary undeleted numbers and give two approaches to fathom it utilizing C++. Each approach offers a diverse point of view and utilizes distinctive calculations and data structures. The problem includes developing a graph, checking certain nodes as deleted, and after that deciding the primary undeleted numbers inside an indicated extend. The graph represents associations between nodes, and the deleted nodes are those that have ...
Read MorePermutations and Combinations (Concept, Examples, C++ Program)
Permutations and Combinations refer to the arrangements of objects in mathematics. Permutation − In permutation, the order matters. Hence, the arrangement of the objects in a particular order is called a permutation. Permutations are of two types − Permutation with repetition Suppose we have to make a three-digit code. Some possible numbers are 123, 897, 557, 333, 000, and 001. So how many numbers can we make like this? Let us look at it this way− In the once place, we have ten options − 0-9 Similarly, at the tenth and the hundredth place also, we have ten options. 0-9. ...
Read MoreHCF of an array of fractions (or rational numbers)
HCF or the Highest common factor of two or more numbers refers to the highest number which divides them. A rational number is the quotient p/q of two numbers such that q is not equal to 0. Problem Statement Given an array with fractional numbers, find the HCF of the numbers. Example 1 Input [{4, 5}, {10, 12}, {24, 16}, {22, 13}] Output {2, 3120} Explanation The fractional numbers given are: 4/5, 10/12, 24/16 and 22/13 2/3120 is the largest number that divides all of them. Example 2 Input [{18, 20}, {15, 12}, {27, 12}, {20, 6}] ...
Read MoreStella Octangula Number
In mathematics, a Stella Octangula number is a figurate number based on the Stella Octangula, of the form n(2n2 − 1). Stella Octangula numbers which are perfect squares are 1 and 9653449. Problem Statement Given a number n, check whether it is the Stella Octangula number or not. The sequence of Stella Octangula numbers is 0, 1, 14, 51, 124, 245, 426, 679, 1016, 1449, 1990 Example1 Input x = 14 Output Yes Explanation $$\mathrm{For\: n = 2, expression \:n\lgroup 2n^2 – 1\rgroup is\: 14}$$ Example2 Input n = 22 Output No Explanation $$\mathrm{There \:is\: no\: ...
Read MoreNicomachus’ Theorem
According to Nicomachus’ Theorem, the sum of the cubes of the first n integers is equal to the square of the nth triangular number. Or, we can also say − The sum of cubes of first n natural numbers is equal to square of sum of first natural numbers. Putting it algebraically, $$\mathrm{\displaystyle\sum\limits_{i=0}^n i^3=\lgroup \frac{n^2+n}{2}\rgroup^2}$$ Theorem $$1^3 = 1$$ $$2^3 = 3 + 5$$ $$3^3 = 7 + 9 + 11$$ $$4^3 = 13 + 15 + 17 + 19\vdots$$ Generalizing $$n^3 =\lgroup n^2−n+1\rgroup+\lgroup n^2−n+3\rgroup+⋯+\lgroup n^2+n−1\rgroup$$ Proof By Induction For all n Ε Natural ...
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