This is a collection of implementations that we developed for the Algorithms course in the sophomore year of my BS in computer science at UDC (Spain) even though the focus of the course was theoretical. Each project is a collection of implementations and empirical studies of different versions of the algorithms. We checked the running times of an upper bound, a lower bound and a tight bound as n grows. They are the following:
- Fibonacci
- Maximum Subarray
- Prim's algorithm
- QuickSort and InsertionSort
This table is one of the cases, where t(n)/h(n) tends to infinity, t(n)/g(n) to a constant and t(n)/f(n) to 0 correspondingly.
h(n) = pow(n,1.8) g(n) = pow (n,2) f(n) = pow(n,2.2)
| n | t(n) | t(n)/h(n) | t(n)/g(n) | t(n)/f(n) |
|---|---|---|---|---|
| 500 | 1361.00 | 0.065389 | 0.005444 | 0.001571 |
| 1000 | 5439.00 | 0.086202 | 0.005439 | 0.001366 |
| 2000 | 10693.00 | 0.055905 | 0.002673 | 0.000585 |
| 4000 | 38106.00 | 0.065720 | 0.002382 | 0.000453 |
| 8000 | 152505.00 | 0.086764 | 0.002383 | 0.000395 |
| 16000 | 606014.00 | 0.113734 | 0.002367 | 0.000342 |
| 32000 | 2430785.00 | 0.150490 | 0.002374 | 0.000298 |
Contact Daniel Ruiz Perez for requests, bug reports and good jokes.
The software in this repository is available under the GNU General Public License, version 3. See the LICENSE file for more information.
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