Introduction to Data Structures and Algorithms (DSA)
Data Structures and Algorithms (DSA) are fundamental concepts in computer science. They provide systematic approaches to solving computational problems efficiently. Data structures are about organizing and storing data in memory, while algorithms define the step-by-step procedure to perform tasks such as sorting, searching, or manipulating the data.
Sorting Algorithms
Sorting algorithms are used to arrange elements of a dataset in a particular order, such as ascending or descending. Various sorting techniques exist, each with unique properties, pros, and cons. Below are links to explore sorting algorithms in this application:
Runtime Comparison of Sorting Algorithms
The table below shows the runtime of various sorting algorithms implemented in C++, Python, and JavaScript. Execution time may vary depending on the dataset size and the environment.
| Algorithm | C++ (ms) | Python (ms) | JavaScript (ms) |
|---|---|---|---|
| Bubble Sort | 15 | 25 | 20 |
| Selection Sort | 2 | 4 | 3 |
| Insertion Sort | 10 | 15 | 12 |
| Quick Sort | 1 | 2 | 1.5 |
| Binary Search | 1 | 1.5 | 1.2 |
| Simple Constraint | |||
| Chain Constraint | |||
| Fabrik Constraint |
Understanding Time and Space Complexity
Time Complexity refers to the amount of time an algorithm takes to complete as a function of the input size. Space Complexity measures the amount of memory required by an algorithm during its execution. Both metrics are crucial to evaluate the efficiency of an algorithm.
Time and Space Complexity of Sorting Algorithms
| Algorithm | Best Case (Time) | Average Case (Time) | Worst Case (Time) | Space Complexity |
|---|---|---|---|---|
| Bubble Sort | O(n) | O(n^2) | O(n^2) | O(1) |
| Selection Sort | O(n^2) | O(n^2) | O(n^2) | O(1) |
| Insertion Sort | O(n) | O(n^2) | O(n^2) | O(1) |
| Quick Sort | O(n log n) | O(n log n) | O(n^2) | O(log n) |
| Binary Search | O(1) | O(log n) | O(log n) | O(1) |
| Simple Constraint | ||||
| Chain Constraint | ||||
| Fabrik Constraint |