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What are Divide and Conquer algorithms?

The name 'Algorithm' refers to the sequence of instruction that must be followed to clarify a problem. The logical description of the instructions which may be executed to perform an essential function. Algorithms are usually generated independent of primary languages , i. The time complexity of an algorithm denoted the total time needed by the program to run to completion.

The name 'Algorithm' refers to the sequence of instruction that must be followed to clarify a problem. The logical description of the instructions which may be executed to perform an essential function. Algorithms are usually generated independent of primary languages , i.

The time complexity of an algorithm denoted the total time needed by the program to run to completion. It is generally expressed by using the big O notation. In bubble sort technique the list is split into two sub-lists sorted and unsorted.

The smallest component is bubbled from unsorted sub-list. After moving the smallest component, the imaginary wall moves one element ahead. The bubble sort was initially written to bubble up the highest item in the list. This technique is simple to understand but time-consuming. In this type, two successive components are compared, and swapping is done.

Thus, step-by-step entire array items are checked, given a list of 'n' elements the bubble sort needed up to n-1 passes to sort the record. In selection sort, the list is split into two sub-lists sorted and unsorted. These two lists are split by an imaginary wall.

We find the smallest item from unsorted sub-list and swap it to the starting. And the wall moves one item ahead, as the sorted file is increases and an unsorted file is decreased. Assume that we have a file on n elements. By applying a selection sort, the first item is compared with all remaining n-1 elements. The smallest item is placed at the first location. Again, the second item is compared with the remaining n-1 elements.

At the time of the comparison, the smaller item is swapped with a bigger item. Similarly, the entire array is checked for smallest component, and then swapping is done accordingly. Here we need n-1 passes or repetition to rearrange the data completely. Quicksort is based on division. It is also called a partition exchange sorting. The basic concept of quick sort method is to pick one item from an array and rearranges the remaining item around it.

This element split the main list into two sublists. This chosen item is known as a pivot. Once the pivot is selected, then it shifts all the components less than pivot to the left of value pivot, and all the items higher than the pivot are shifted to the right side.

This process of choosing pivot and division the list is tested recursively until sub-lists consisting of only one element. An NP-Complete problem is a problem in NP that is as difficult as any other trouble in this class because any other dispute in NP can be decreased to it in Polynomial-time. Time Efficiency measured by estimate the number of times the essential algorithms functions are executed.

Space Efficiency is measured by calculating the number of additional memory units consumed by the algorithm. The order of algorithm is standard documentation of an algorithm that has been developed to represent a task that bound the estimated time for algorithms.

The order of an algorithm is a method of defining its efficiency. It is commonly referred to as O-notation. Brute Force is a straightforward method for solving problem, usually directly based on the problem's statement and descriptions of the concepts involved.

Finiteness- If we trace out the instructions of an algorithm, then for all step the algorithm complete after a finite number of steps. The basic concept of merge sort has split the list into two smaller sub-lists of relatively equal size. Recursively repeat this method until only one item is left in the sub-list.

After this, various sorted sub-lists are combined to form a sorted parent list. This method goes on recursively till the original sorted list arrived. Linear search method is also called a sequential search technique. The linear search is a technique of searching an item in a list in sequence. Binary search is higher than the linear search. However, it cannot be tested on the unsorted data structure.

The binary search is based on the method divide-and-conquer. The binary search begins by testing the data in the middle component of the array. This determines an object is whether in the first half or second half. If the object is in the first half, we do not need to check the second half and if it is in the second half no need to check in first half.

Similarly, we repeat this procedure until we find an object in the list or not found from the list. Here we need three variables to identify first, last, and middle elements. Both the selection and bubble sorts exchange items. But insertion sort does not exchange items. In insertion sort, the item is inserted at an appropriate place similar to card insertion. Here the list is split into two parts sorted and unsorted sub-lists.

In each pass, the first component of unsorted sublist is picked up and moved into the sorted sublist by inserting it in a relevant position. Suppose we have 'n' items, we need n-1 passes to sort the items. Given the problem with inputs, we recover a subset that appeases come constraints. Any subset that satisfies these constraints is known as a feasible solution. A feasible solution, which either maximizes or minimizes a given purpose method is known as an optimal solution.

Suppose we have a huge information set stored in an array. The amount of time needed to lookup an item in the array is either O log n or O n based on whether the array is sorted or not.

If the array is sorted, then a procedure such as a binary search can be used to search the array. Otherwise, the array must be searched linearly. Either method may not be desirable if we need to process a very high data set.

Therefore we discuss a new procedure called hashing that allows us to update and fetch any entry in constant time O 1. The constant time or O 1 performance defines the amount of time to operate does not depend on data size n.

Encryption is the step of converting plaintext into a secret code format called " Cliphertext ". To convert the content, the algorithm uses a string of bits referred to as " keys " for estimation. The larger the key, the higher the number of potential patterns for generating the ciphertext. Most encryption algorithm use codes fixed blocks of input that have a length of about 64 to bits, while some uses stream technique.

DP is another method for problems with optimal substructure: An optimal solution to a problem include optimal solutions to subproblems.

This doesn't necessarily define that every optimal solution to a subproblem will contribute to the primary solution. For divide and conquer top-down , the subproblems are independent, so we can resolve them in any order.

For the greedy technique bottom-up , we can always choose the "right" subproblem by a greedy choice. In dynamic programming , we solve many subproblems and save the results: not all of them will contribute to solving the bigger problem.

Because of optimal substructure, we can be sure that at least some of the subproblems will be useful. It is convenient to order the elements of a given instance in descending order by their value-to-weight ratios.

Then the first element gives the best payoff per weight unit, and the last one gives the worst payoff per weight unit. Warshall's algorithm is a function of dynamic programming procedure, which is used to find the transitive closure of a directed graph.

A greedy technique for an optimization problem always makes the option which look best at the moment and add it to the current subsolution. A spanning tree for a linked graph is a tree whose vertex set is the same as the vertex set of the given graph, and whose edge set is a subgroup of the edge set of the given graph. Weight of a spanning tree w T is the total of weights of all edges in T. The Minimum spanning tree MST is a spanning tree with the smallest feasible weight.

This is a greedy method. A greedy method chooses some local optimum i. Take a graph with 'n' vertices, keep on adding the shortest least cost edge, while avoiding the generation of cycles, until n - 1 edges have been added. Frequently two or more edges may have the same rate.

The order in which the edges are decided, in this method, does not matter. Different Minimum spanning tree may result, but they will all have the same total price, which will always be the minimum cost.

A sorting network is a numerical model of a network of wires and comparator modules that is used to sort a series of numbers. Each comparator connects two wires and sorts the values by outputting the smaller value to one wire, and the higher to the other. The main difference between sorting networks and comparison sorting algorithms is that with a sorting network, the series of comparisons is set in advance, regardless of the result of previous comparisons.

This independence of comparison series is useful for parallel execution of the methods. Floyd's algorithm is a function, which is used to find all the pairs shortest paths problem. Floyd's algorithm is relevant to both directed and undirected weighted graph, but they do not include a cycle of a negative length. Prim's algorithm is a greedy and efficient technique, which is used to find the minimum spanning the tree of a weighted linked graph.

Dijkstra's algorithm solves the single-source shortest path method of finding shortest paths from a given vertex the source , to another vertex of a weighted graph or digraph.

300+ TOP Data Structures and Algorithms Multiple Choice Questions and Answers

Coding interviews are comprised mainly of data structure and algorithm-based questions as well as some of the logical questions such as, How do you swap two integers without using a temporary variable? There are a lot of computer science graduates and programmers applying for programming, coding, and software development roles at startups like Uber and Netflix. Once you have gone through these questions, you should feel confident enough to attend any telephonic or face-to-face interviews. Without any further ado, here is my list of some of the most frequently asked coding interview questions from programming job interviews :. An array is the most fundamental data structure, which stores elements at a contiguous memory location.

Download PDF 1 Explain what is an algorithm in computing? An algorithm is a well-defined computational procedure that take some value as input and generate some value as output. Quick Sort algorithm has the ability to sort list or queries quickly. It is based on the principle of partition exchange sort or Divide and conquer. This type of algorithm occupies less space, and it segregates the list into three main parts Elements less than the Pivot element Pivot element Elements greater than the Pivot element 3 Explain what is time complexity of Algorithm?

50+ Data Structure and Algorithms Interview Questions for Programmers

Coding is simply the translation of your solution concept into a computer language that implements the solution. This book is a software engineer's notes on problem solving. Ideally suited as practice material for coding interviews. This started out as a collection of interview questions and solutions that suthor accumulated over the years.