Computer Science is the field where we study about how to solve a problem effectively and efficiently with the aid of computers. The problem could be of any complex ranging from a simple problem of adding two numbers to a problem of making the computer capable of taking decisions on time in real environment, automatically by understanding the situation or environment, as if it is taken by a human ......

The number of (machine) instructions which a program executes during its running time is called its lime complexity in computer science. This number depends primarily on the size of the program's input that is approximately on the number of the strings to be sorted (and their length) and the algorithm used. The time complexity of the program is described by the expression c n2, where c is a consta ......

When there are several different algorithms to solve the same problem, one has to decide which one is best suited for their application. An essential tool for this purpose is the analysis of algorithms. Only after determining the efficiency of various algorithms a decision has to be taken. It is largely a matter of judgment, intuition and experience. There are some basic techniques that are often ......

Searching is a technique of finding whether a given element is present in a list of clement. If the search clement is present in the list the searching technique should return the index where the given searching element is present in the list If the search clement is not present in the list then the searching technique should return NULL indicating that search element is not present in the list. T ......

Solution to a' problem requires a proper sequence of steps with well defined unambiguous actions. To solve a problem using computers, these set of actions need to be transformed into precise instructions
using a suitable computer language. These set of precise instructions is referred as a program.
Developing a program to solve a simple problem is a straight forward task. But developing a progra ......

Solutions to some problems require the associated data to be organized as a linear list of data items in which operations are permitted to take place at only one end of the list. For example, a list of books kept one above another, playing cards, making pancake, storing laundry, wearing bangles, an heap of plates placed one above another in a tray etc. In all these cases, we group things together ......

The linear data structures such as stacks and queues can be realized
using sequential allocation technique i.e. arrays. Since arrays represent contiguous locations in memory,implementing stacks and queues using arrays offers several advantages.

Sparse matrices, which are common in scientific applications, are matrices in which most elements are zero. To save space and running time it is critical to only store the nonzero elements. A standard representation of sparse matrices in sequential languages is to use an array with one element per row each of which contains a linked-list of the nonzero values in that row along with their column nu ......

The divide-and-conquer strategy so successfully used by monarchs and colonizers may also be applied to the development of efficient computer algorithms. In this context, divide and conquer is a technique for designing algorithms that consists of decomposing the instance to be
solved into a number of smaller sub instances of the same problem, solving successively.

Sorting is a process of arranging a set of elements in some order.We can apply the divide-and conquer method to the sorting problem. In this problem we must sort the elements into non decreasing order.

Greedy method is a method of choosing a subset of a data set as the solution set that result in some profit. Consider a problem having the inputs. We are required to obtain a solution which is a series of subsets that satisfy some constraints or conditions. Any subset, which satisfies these constraints, is called a feasible solution. It is required to obtain a feasible solution that maximizes or m ......

The ship may be loaded in stages; one container per stage. At each stage we need to decide which container to load. For this decision we may use the greedy criterion: From the remaining containers, select the one with least weight.

Graph is an important mathematical representation of a physical problem, for example finding optimum shortest path from a city to another city for a traveling sales mall. so as to minimize the cost. A graph can have unconnected node. Further there can be more than one path between two nodes.

Similarly, trees are also non-linear data structures, which are very useful in representing hierarchical relationships among the data items. For example in real life, if we want to express the relationship exists among the members of the family then we use non linear structures like trees. Organizing the data in a hierarchical structure plays a very important role for most of the applications, whi ......

Traversal is the process of visiting all the vertices of the tree in a systematic order. Systematic means that every time the tree is traversed it should yield the same result.This process is not as commonly used
as finding, inserting, and deleting nodes. One reason for this is that traversal is not particularly fast. But traversing a tree has some surprisingly useful applications and is theoreti ......

A binary tree threaded by making all right child pointers that would normally be null point to the in order successor of the node and all left child pointers that would normally be null point to the inorder predecessor of the node, It should be noted that threaded binary tree makes it possible to traverse the values in the binary tree via a linear traversal that is more rapid than a recursive in-o ......

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