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# Algorithms | ||
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## TODO | ||
I would like to include algorithms regarding the following topics: | ||
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| Name | State | Comments | | ||
|:----------------------------------:|-------|-------------------------------------------------------------------------------------- | | ||
| Pseudo-Random generator | S | | | ||
| Hamming code | S | | | ||
| CNF to DNF | S | | | ||
| Quadratic Equation | S | | ||
| Cubic Equation | S | [http://www.sosmath.com/algebra/factor/fac11/fac11.html](http://www.sosmath.com/algebra/factor/fac11/fac11.html) | ||
| Quartic Equation | S | [http://mathworld.wolfram.com/QuarticEquation.html](http://mathworld.wolfram.com/QuarticEquation.html) | ||
|RREF and Guassian Elimination | | ||
|Matrix-Matrix multiplication | | ||
| Determinant of matrix | | ||
| Convert linear mapping to matrix map | | ||
| 2-satisfiability | | ||
| Horner | | ||
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There are many other algorithms I hope to implement in a near future. You can find those lists in each `README.md` file of each section under [`algorithms`](algorithms). What I would also like to include are some _linear programming_ algorithms. | ||
- Linear algebra (Guassian, RREF, Jacobi, determinants, ...) | ||
- Numerical computing (PDE, ODE, Poisson, Social Networks, Graph Partioning, Conjugate Gradient, Page Rank, Horner...) | ||
- Linear programming | ||
- Artificial intelligence (Swarm intelligence, A<sup>*</sup>, Genetic algorithms, ...) | ||
- Geometrical algorithms (Convex hull, ...) | ||
- Generation of random numbers | ||
- Error correction codes | ||
- CNF, DNF, 2-satisfiability | ||
- Equations (quadratic, cubic and quartic equations formulas ...) | ||
- Heuristics to NP-complete problems | ||
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A more exhaustive list of interesting algorithms can be found here: | ||
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- [https://en.wikipedia.org/wiki/List_of_algorithms](https://en.wikipedia.org/wiki/List_of_algorithms) | ||
> [https://en.wikipedia.org/wiki/List_of_algorithms](https://en.wikipedia.org/wiki/List_of_algorithms) |
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# Data Structures | ||
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## TODO | ||
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### PRIORITY | ||
A "good" exhaustive list of data structures which can possibly be implemented can be found here: | ||
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- `TSP` | ||
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- adding the operations: | ||
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- [`longestPrefixOf`](https://github.com/nelson-brochado/algs4/blob/master/src/main/java/edu/princeton/cs/algs4/TST.java) | ||
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- [`keysWithPrefix`](https://github.com/nelson-brochado/algs4/blob/master/src/main/java/edu/princeton/cs/algs4/TST.java) | ||
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- [`keysThatMatch`](https://github.com/nelson-brochado/algs4/blob/master/src/main/java/edu/princeton/cs/algs4/TST.java) | ||
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- Add tests | ||
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- `DSForests` | ||
- Add deletion operation | ||
- Add iterative find-set operation | ||
- Check my solutions to first homework of AnD2 | ||
- Add [print-set operation](http://stackoverflow.com/questions/23055236/union-find-retrieve-all-members-of-a-set-efficiently) | ||
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- `Queue.py` | ||
- Add tests | ||
- Re-implement a MinPriorityQueue | ||
- Add tests for MinPriorityQueue | ||
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- `Graph` | ||
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- Redesign the graph data structure: | ||
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- It should allow the possibility to be represented either as _adjacency list_ or _adjacency matrix_. | ||
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- It should also give the possibility to create either directed or undirected graphs. | ||
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- It should support the common operations efficiently | ||
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- `RBT` | ||
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- Augment RBT to support order statistic trees (OS-RANK and OS-SELECT in O(log n)) | ||
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- Augment RBT to support interval trees | ||
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### NON-PRIORITY | ||
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- Exhaustive list of data structures which can be possibly implemented (if not already): | ||
- [https://en.wikipedia.org/wiki/List_of_data_structures](https://en.wikipedia.org/wiki/List_of_data_structures) | ||
> [https://en.wikipedia.org/wiki/List_of_data_structures](https://en.wikipedia.org/wiki/List_of_data_structures) |
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# Tests | ||
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## TODO | ||
A few algorithms and data structures that I would like to test first: | ||
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All except the ones mentioned in the next section. | ||
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## DONE | ||
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### Algorithms | ||
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#### Crypo | ||
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- caeser cipher | ||
- one time pad | ||
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#### ODE | ||
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- forward Euler method | ||
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#### Sorting | ||
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- bubble sort | ||
- heap sort | ||
- insertion sort | ||
- merge sort | ||
- quick sort | ||
- selection sort | ||
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### Data Structures | ||
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- BST | ||
- BSTNode | ||
- DSForests | ||
- HashTable | ||
- Heap | ||
- MaxHeap | ||
- MinHeap | ||
- MinMaxHeap | ||
- RBT | ||
- Stack | ||
- TST | ||
- Queue | ||
- MinPriorityQueue |