Note for Data Structure using C - DS by pawan kumar

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Introduction to Data Structures and Algorithms Data Structure is a way of collecting and organising data in such a way that we can perform operations on these data in an effective way. Data Structures is about rendering data elements in terms of some relationship, for better organization and storage. For example, we have some data which has, player's name "Virat" and age 26. Here "Virat" is of String data type and 26 is of integer data type. We can organize this data as a record like Player record, which will have both player's name and age in it. Now we can collect and store player's records in a file or database as a data structure. For example: "Dhoni" 30, "Gambhir" 31, "Sehwag" 33 If you are aware of Object Oriented programming concepts, then a class also does the same thing, it collects different type of data under one single entity. The only difference being, data structures provides for techniques to access and manipulate data efficiently. In simple language, Data Structures are structures programmed to store ordered data, so that various operations can be performed on it easily. It represents the knowledge of data to be organized in memory. It should be designed and implemented in such a way that it reduces the complexity and increases the efficiency. Basic types of Data Structures As we have discussed above, anything that can store data can be called as a data structure, hence Integer, Float, Boolean, Char etc, all are data structures. They are known as Primitive Data Structures. Then we also have some complex Data Structures, which are used to store large and connected data. Some example of Abstract Data Structure are :     Linked List Tree Graph Stack, Queue etc. All these data structures allow us to perform different operations on data. We select these data structures based on which type of operation is required. We will look into these data structures in more details in our later lessons.

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The data structures can also be classified on the basis of the following characteristics: Characterstic Description In Linear data structures,the data items are arranged in a linear sequence. Linear Example: Array In Non-Linear data structures,the data items are not in sequence. Example: Non-Linear Tree, Graph In homogeneous data structures,all the elements are of same type. Example: Homogeneous Array NonIn Non-Homogeneous data structure, the elements may or may not be of the Homogeneous same type. Example: Structures Static data structures are those whose sizes and structures associated Static memory locations are fixed, at compile time. Example: Array Dynamic structures are those which expands or shrinks depending upon the Dynamic program need and its execution. Also, their associated memory locations changes. Example: Linked List created using pointers What is an Algorithm ? An algorithm is a finite set of instructions or logic, written in order, to accomplish a certain predefined task. Algorithm is not the complete code or program, it is just the core logic(solution) of a problem, which can be expressed either as an informal high level description as pseudocode or using a flowchart. Every Algorithm must satisfy the following properties: 1. Input- There should be 0 or more inputs supplied externally to the algorithm.

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2. 3. 4. 5. Output- There should be atleast 1 output obtained. Definiteness- Every step of the algorithm should be clear and well defined. Finiteness- The algorithm should have finite number of steps. Correctness- Every step of the algorithm must generate a correct output. An algorithm is said to be efficient and fast, if it takes less time to execute and consumes less memory space. The performance of an algorithm is measured on the basis of following properties : 1. Time Complexity 2. Space Complexity Space Complexity Its the amount of memory space required by the algorithm, during the course of its execution. Space complexity must be taken seriously for multi-user systems and in situations where limited memory is available. An algorithm generally requires space for following components :    Instruction Space: Its the space required to store the executable version of the program. This space is fixed, but varies depending upon the number of lines of code in the program. Data Space: Its the space required to store all the constants and variables(including temporary variables) value. Environment Space: Its the space required to store the environment information needed to resume the suspended function. To learn about Space Complexity in detail, jump to the Space Complexity tutorial. Time Complexity Time Complexity is a way to represent the amount of time required by the program to run till its completion. It's generally a good practice to try to keep the time required minimum, so that our algorithm completes it's execution in the minimum time possible. We will study about Time Complexity in details in later sections. NOTE: Before going deep into data structure, you should have a good knowledge of programming either in C or in C++ or Java or Python etc.

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Asymptotic Notations When it comes to analysing the complexity of any algorithm in terms of time and space, we can never provide an exact number to define the time required and the space required by the algorithm, instead we express it using some standard notations, also known as Asymptotic Notations. When we analyse any algorithm, we generally get a formula to represent the amount of time required for execution or the time required by the computer to run the lines of code of the algorithm, number of memory accesses, number of comparisons, temporary variables occupying memory space etc. This formula often contains unimportant details that don't really tell us anything about the running time. Let us take an example, if some algorithm has a time complexity of T(n) = (n2 + 3n + 4), which is a quadratic equation. For large values of n, the 3n + 4 part will become insignificant compared to the n2 part. For n = 1000, n2 will be 1000000 while 3n + 4 will be 3004. Also, When we compare the execution times of two algorithms the constant coefficients of higher order terms are also neglected. An algorithm that takes a time of 200n2 will be faster than some other algorithm that takes n3 time, for any value of n larger than 200. Since we're only interested in the asymptotic behavior of the growth of the function, the constant factor can be ignored too. What is Asymptotic Behaviour The word Asymptotic means approaching a value or curve arbitrarily closely (i.e., as some sort of limit is taken). Remember studying about Limits in High School, this is the same. The only difference being, here we do not have to find the value of any expression where n is approaching any finite number or infinity, but in case of Asymptotic notations, we use the same model to ignore the constant factors and insignificant parts of an expression, to device a