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

AlgorithmAn algorithm is a finite set of instructions, those if followed, accomplishes a particular task. It is not language specific, we can use any language and symbols to represent instructions.The criteria of an algorithmInput: Zero or more inputs are externally supplied to the algorithm.Output: At least one output is produced by an algorithm.Definiteness: Each instruction is clear and unambiguous.Finiteness: In an algorithm, it will be terminated after a finite number of steps for all different cases.Effectiveness: Each instruction must be very basic, so the purpose of those instructions must be very clear to us.Analysis of algorithmsAlgorithm analysis is an important part ... Read More

This algorithm is used to print the array elements in a spiral way. At first starting from the first row, print the whole content and then follow the last column to print, then the last row and so on, thus it prints the elements in spiral fashion. The time complexity of this algorithm is O(MN), M is the number of rows and N is the number of columns.Input and OutputInput: The matrix:  1   2   3   4   5   6  7   8   9  10  11  12 13  14  15  16  17  18 Output: Contents of ... Read More