A matrix is a two-dimensional data structure made up of rows and columns set out like a grid of squares. Grids, multidimensional arrays, and tabular data are frequently represented using it. Problem Statement We are given a matrix of dimensions and the task is to check whether each row of the matrix consists of every number from 1 to n. The order of the numbers in the row do not matter. Return true if this statement holds true else return false. For Example Input: mtx = [[1, 2, 3], [3, 2, 1], [2, 1, 3]] Output: True ... Read More

A grid is basically a matrix having some particular elements in it representing some features of that grid. Problem Statement Now, in this problem, we are given a grid of size m*n, which have its elements as 0’s, 1’s, and 2’s only. Every digit represents something, like 1 represents the position of the person, 2 represents a cell with fire and 0 represents an empty cell. Our job is to count the minimum moves required to come out of a grid safely. A grid will be the input given to us by the user. Let us see how we should ... Read More

A binary string is a string that only has two characters, usually the numbers 0 and 1, and it represents a series of binary digits. Problem Statement Now, in this problem, we are given a binary string comprising zeros and ones. We have two conditions to keep in mind while solving the problem. First, one digit can delete another digit that is a ‘1’ can delete a ‘0’ and vice versa. Secondly, if at any moment the entire string consists of only 0’s and 1’s then the corresponding digit is printed. Here, a binary string will be the input given ... Read More

Recently, graph-based representations have gained enormous popularity for simulating real-world data. Cliques are a key issue in graph theory that is used to solve numerous mathematical issues and create graphs. Cliques are extensively researched in the field of computer science, with the clique problem assessing if a clique having a certain size within a graph is NP-complete.  Yet, in spite of all complexities, there has been research into several techniques for finding cliques. What Are Cliques? In all undirected graphs G = (N, E), a clique, is a "subset of the nodes", so that all pairs of distinct nodes is ... Read More

How Do Graphs Work? A group of things that are connected is referred to as a graph. They may represent anything at all, from based on merely mathematical ideas, to real-life objects, events and occurrences. For instance, a graph represents a list of individuals with a family connection. Similarly, a network of metropolitan areas is linked together by roadways. Typically, we describe the elements of the network as nodes or vertices, while the links among them are referred to as edges or arcs. Pic 1 − Visual Representation of a Graph with Nodes and Edges Unweighted Graph: What Is ... Read More

Even with limitless time, algorithms are unable to resolve all computer problems. The answer to NP-complete problems remains unknown. It's worth noting that when single NP-complete issue is able to be answered in polynomial time, then all others may be resolved as well. Dense Subgraph A dense subgraph is one that has numerous edges for each vertex in the theory of graphs and computer science. Clique A clique constitutes a subsection of a graph in which every vertex is linked to every other vertex, making the "subgraph" a full graph.  "Maximal Clique Problem" aims for locating the largest clique in ... Read More

There is no solution to "NP-complete" problems. So far, there hasn't been a polynomial time method developed for any NP-complete problem, nor has anyone shown that there isn't one. There is an intriguing fact about NP-complete problems: if one manages to be resolved under polynomial time, all are within reach. In this post, we'll prove that a problem comprising an independent set and clique is NP-Complete. Clique A clique refers to a "subgraph" of a graph in which every node is connected to one another, implying that the subsection is a complete graph. NP-Class The NP in the NP class ... Read More

The travelling salesman problem is a popular topic in AI and operational research. Since its first articulation, a plethora of publications have been written providing various solutions to this problem. Furthermore, a slew of novel formulations has been presented by associated practitioners in an attempt to broaden the application of the fundamental TSP. Travelling Salesman Problem: Definition Formally defined, the travelling salesman problem (TSP) is as follows - Discover the shortest way that covers each city "precisely once and returns to the initial city" when provided with a collection of cities and distances between each city. More On The Problem ... Read More

Even with infinite time, there are some computing issues that algorithms cannot resolve. NP-complete problems are those whose solution is unknown. It's intriguing to note that if one NP-complete question can be resolved in polynomial time, subsequently, all others can be resolved. In this study, we will define a sparse graph, discuss several complexity classes, independent sets, and demonstrate that sparse graphs are NP-complete. What Is A Sparse Graph? A sparse graph is one with a limited number of edges. The total number of edges in this situation is significantly fewer than there could be or the highest possible number ... Read More

Graph coloring is a subset of graph labelling in graph theory. The use of colors stems from coloring the nations on a map, wherein each face is colored. There are several real-world applications for graph coloring, as well as issues of theory. Apart from the traditional forms of problems, other constraints can be imposed on the graph, the manner a color is given, or even the color itself. It has even gained widespread appeal in the shape of the renowned numerical puzzle Sudoku. Graph coloring remains an active area of study. What Is Vertex Coloring? The assignment of colors or ... Read More