In theoretical analysis of algorithms, it is common to estimate their complexity in the asymptotic sense, i.e., to estimate the complexity function for arbitrarily large input. The term "analysis of algorithms" was coined by Donald Knuth. Algorithm analysis is an important part of computational complexity theory, which provides theoretical estimation for the required resources of an algorithm to solve a specific computational problem. Most algorithms are designed to work with inputs of arbitrary length. Analysis of algorithms is the determination of the amount of time and space resources required to execute it. Usually, the efficiency or running time of an ... Read More

The graph is a non-linear data-structure, which consists finite number of nodes and a set of edges which are used to connect a pair of nodes. The graphs are used to solve some real-time problems to represent network etc. In different social networks, the graphs are used. In this Section We are going to cover − Bi-Connected Graph Checking Breadth First Search (BFS) for a Graph Bridges in a Graph Check if a given graph is tree or not Connectivity in a directed graph Depth First Search (DFS) for a Graph Detect Cycle in a an Undirected Graph Detect ... Read More

The searching algorithms are used to search or find one or more than one element from a dataset. These type of algorithms are used to find elements from a specific data structures. Searching may be sequential or not. If the data in the dataset are random, then we need to use sequential searching. Otherwise we can use other different techniques to reduce the complexity. In this Section We are going to cover − Binary Search Exponential Search Interpolation Search Jump Search Linear Search Ternary Search

Pattern Searching algorithms are used to find a pattern or substring from another bigger string. There are different algorithms. The main goal to design these type of algorithms to reduce the time complexity. The traditional approach may take lots of time to complete the pattern searching task for a longer text. Here we will see different algorithms to get a better performance of pattern matching. In this Section We are going to cover. Aho-Corasick Algorithm Anagram Pattern Search Bad Character Heuristic Boyer Moore Algorithm Efficient Construction of Finite Automata kasai’s Algorithm Knuth-Morris-Pratt Algorithm Manacher’s Algorithm Naive Pattern Searching Rabin-Karp ... Read More

We have seen different problems in different sections. There are some other problems which are not categorized. In this section we will see some of the random problems. In this Section We are going to cover. Adding base n numbers Babylonian method to find the square root Factorial of a large number Check if a given point lies inside a Polygon Check Perfect Square or Not Check if given four points form a Square Check if two given sets are disjoint? Check if two line segments intersect Check whether a given point lies inside a Triangle Connect n ropes ... Read More

The Backtracking is an algorithmic-technique to solve a problem by an incremental way. It uses recursive approach to solve the problems. We can say that the backtracking is used to find all possible combination to solve an optimization problem. In this Section We are going to cover Hamiltonian Cycle M-Coloring Problem N Queen Problem Rat in Maze Problem Cryptarithmetic Puzzle Subset Sum Problem Sudoku Solving Algorithm Knight-Tour Problem Tug-Of-War Problem Word Break Algorithm Maximum number by swapping problem

Polynomial Time Approximation schemeWe can find some polynomial time solution for NP-Complete problems like 0-1 Knapsack problem or Subset sum problem. These problems are very popular in the real world, so there must be some ways to handle these problems.The Polynomial Time Approximation Scheme (PTAS) is a type to approximate algorithms for optimization problems. For the 0-1 Knapsack problem, there is a Pseudo Polynomial Solution, but when the values are large, the solution is not feasible. Then we need a PTAS solution.Some NP-complete problems like Graph Coloring, K-Center problem etc. they have no known polynomial time solution. PTAS used to approximate ... Read More

Space ComplexitySpace complexity is an amount of memory used by the algorithm (including the input values of the algorithm), to execute it completely and produce the result.We know that to execute an algorithm it must be loaded in the main memory. The memory can be used in different forms:Variables (This includes the constant values and temporary values)Program InstructionExecutionAuxiliary SpaceAuxiliary space is extra space or temporary space used by the algorithms during its execution.Memory Usage during program executionInstruction Space is used to save compiled instruction in the memory.Environmental Stack is used to storing the addresses while a module calls another module ... Read More

Amortize AnalysisThis analysis is used when the occasional operation is very slow, but most of the operations which are executing very frequently are faster. Data structures we need amortized analysis for Hash Tables, Disjoint Sets etc.In the Hash-table, the most of the time the searching time complexity is O(1), but sometimes it executes O(n) operations. When we want to search or insert an element in a hash table for most of the cases it is constant time taking the task, but when a collision occurs, it needs O(n) times operations for collision resolution.Aggregate MethodThe aggregate method is used to find ... Read More

Asymptotic NotationsAsymptotic notations are used to represent the complexities of algorithms for asymptotic analysis. These notations are mathematical tools to represent the complexities. There are three notations that are commonly used.Big Oh NotationBig-Oh (O) notation gives an upper bound for a function f(n) to within a constant factor.We write f(n) = O(g(n)), If there are positive constantsn0  and c such that, to the right of n0 the f(n) always lies on or below c*g(n).O(g(n)) = { f(n) : There exist positive constant c and n0 such that 0 ≤ f(n) ≤ c g(n), for all n ≥ n0}Big Omega NotationBig-Omega ... Read More