data structure ppt slide about the basic terminology

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1. Basic Terminologies of Data Structures Unit: Complexity, Arrays, Searching, Sorting & Comparison

2. Introduction to Data Structures Data Structure: Way to organize and store data efficiently. Types: Linear (Arrays, Linked List), Non-linear (Trees, Graphs). Importance: Efficient data handling, faster algorithms.

3. Complexity Analysis Measures efficiency of algorithms. Time Complexity: Growth of execution time with input size. Space Complexity: Growth of memory usage with input size.

4. Asymptotic Notations Big-O (O): Upper bound → Worst-case performance. Big-Omega (Ω): Lower bound → Best-case performance. Big-Theta (Θ): Tight bound → Average-case performance.

5. Arrays & Operations Array: Collection of elements stored in contiguous memory locations. Operations: Traversal, Insertion, Deletion, Updating. Applications: Storing lists, matrices, implementing other DS.

6. Linear Search Checks each element one by one until target is found. Best Case: Ω(1) → element found at first position. Worst Case: O(n) → element at last or not found. C Program Example:

7. Binary Search Efficient searching on sorted arrays. Divide the array into half, check middle element. Best Case: Ω(1), Worst Case: O(log n). C Program Example:

8. Bubble Sort Repeatedly swaps adjacent elements if they are in wrong order. Complexity: Best O(n), Worst O(n^2). C Program Example included.

9. Selection Sort Finds the minimum element and places it at correct position. Complexity: Always O(n^2). Simple but inefficient for large datasets.

10. Insertion Sort Builds sorted array one element at a time. Best: O(n), Worst: O(n^2). Efficient for small datasets.

11. Heap Sort Uses binary heap data structure. Complexity: O(n log n) for all cases. Efficient and widely used.

12. Shell Sort Improved version of Insertion Sort using gaps. Average complexity: O(n^1.5), Worst: O(n^2). Not stable but efficient for medium-sized data.

13. Comparison of Sorting Algorithms Bubble Sort: O(n^2), simple but slow. Selection Sort: O(n^2), better for small datasets. Insertion Sort: O(n^2), good for nearly sorted data. Heap Sort: O(n log n), efficient and consistent. Shell Sort: O(n^1.5), practical improvement over insertion sort.

14. Summary Data Structures form the base of efficient algorithms. Complexity Analysis helps to compare performance. Searching: Linear vs Binary Search. Sorting: Bubble, Selection, Insertion, Heap, Shell. Choice depends on input size, dataset nature & application.