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‎README.md

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@@ -5,7 +5,22 @@ Algorithms and Data Structures implemented in Java
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This is a collection of algorithms and data structures which I've implement over the years in my academic and professional life. The code isn't overly-optimized but is written to be correct and readable. The algorithms and data structures are well tested and, unless noted, are believe to be 100% correct.
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* Created by Justin Wetherell
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=======
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## Table of Contents
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- [Data Structures](#data-structures)
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- [Mathematics](#mathematics)
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- [Numbers](#numbers)
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- [Graphs](#graphs)
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- [Search](#search)
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- [Sequences](#sequences)
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- [Sorts](#sorts)
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- [String Functions](#string-functions)
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## * Created by Justin Wetherell
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* For questions use: http://groups.google.com/forum/#!forum/java-algorithms-implementation
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* Google: http://code.google.com/p/java-algorithms-implementation
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* Github: http://github.com/phishman3579/java-algorithms-implementation
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# What's been implemented:
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## Data Structures
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* AVL Tree
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* B-Tree
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* Binary Heap [backed by an array or a tree]
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+ chebyshev
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+ euclidean
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* Division
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=======
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* [AVL Tree](src/com/jwetherell/algorithms/data_structures/AVLTree.java)
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* [B-Tree](src/com/jwetherell/algorithms/data_structures/BTree.java)
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* [Binary Heap (backed by an array or a tree)](src/com/jwetherell/algorithms/data_structures/BinaryHeap.java)
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* [Binary Search Tree](src/com/jwetherell/algorithms/data_structures/BinarySearchTree.java)
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* [Compact Suffix Trie (backed by a Patricia Trie)](src/com/jwetherell/algorithms/data_structures/CompactSuffixTrie.java)
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* [Disjoint Set](src/com/jwetherell/algorithms/data_structures/DisjointSet.java)
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* [Fenwick Tree {Binary Indexed Tree (BIT)}](src/com/jwetherell/algorithms/data_structures/FenwickTree.java)
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* [Graph](src/com/jwetherell/algorithms/data_structures/Graph.java)
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+ Undirected
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+ Directed (Digraph)
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* [Hash Array Mapped Trie (HAMT)](src/com/jwetherell/algorithms/data_structures/HashArrayMappedTrie.java)
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* [Hash Map (associative array)](src/com/jwetherell/algorithms/data_structures/HashMap.java)
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* [Interval Tree](src/com/jwetherell/algorithms/data_structures/IntervalTree.java)
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* [Implicit Key Treap]((src/com/jwetherell/algorithms/data_structures/ImplicitKeyTreap.java))
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* [KD Tree (k-dimensional tree or k-d tree)](src/com/jwetherell/algorithms/data_structures/KDTree.java)
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* [List [backed by an array or a linked list]]((src/com/jwetherell/algorithms/data_structures/List.java))
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* [Matrix](src/com/jwetherell/algorithms/data_structures/Matrix.java)
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* [Patricia Trie](src/com/jwetherell/algorithms/data_structures/PatriciaTrie.java)
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* [Quad-Tree (Point-Region or MX-CIF)](src/com/jwetherell/algorithms/data_structures/QuadTree.java)
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* [Queue [backed by an array or a linked list]](src/com/jwetherell/algorithms/data_structures/Queue.java)
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* [Radix Trie (associative array) [backed by a Patricia Trie]](src/com/jwetherell/algorithms/data_structures/RadixTree.java)
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* [Red-Black Tree](src/com/jwetherell/algorithms/data_structures/RedBlackTree.java)
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* [Segment Tree](src/com/jwetherell/algorithms/data_structures/SegmentTree.java)
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* [Skip List](src/com/jwetherell/algorithms/data_structures/SkipList.java)
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* [Splay Tree](src/com/jwetherell/algorithms/data_structures/SplayTree.java)
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* [Stack [backed by an array or a linked list]](src/com/jwetherell/algorithms/data_structures/Stack.java)
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* [Suffix Tree (Ukkonen's algorithm)](src/com/jwetherell/algorithms/data_structures/SuffixTree.java)
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* [Suffix Trie [backed by a Trie]](src/com/jwetherell/algorithms/data_structures/SufficTrie.java)
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* [Treap](src/com/jwetherell/algorithms/data_structures/Treap.java)
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* [Tree Map (associative array) [backed by an AVL Tree]](src/com/jwetherell/algorithms/data_structures/TreeMap.java)
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* [Trie](src/com/jwetherell/algorithms/data_structures/Trie.java)
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* [Trie Map (associative array) [backed by a Trie]](src/com/jwetherell/algorithms/data_structures/TrieMap.java)
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## Mathematics
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* [Distance](src/com/jwetherell/algorithms/mathematics/Distance.java)
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+ chebyshev
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+ euclidean
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* [Division](src/com/jwetherell/algorithms/mathematics/Division.java)
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+ using a loop
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+ using recursion
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+ using shifts and multiplication
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+ using only shifts
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+ using logarithm
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* Multiplication
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=======
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* [Multiplication](src/com/jwetherell/algorithms/mathematics/Multiplication.java)
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+ using a loop
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+ using recursion
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+ using only shifts
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+ using logarithms
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+ using FFT
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* Primes
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+ is prime
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+ strings
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+ numbers
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* Modular arithmetic
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=======
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+ [Fast Fourier Transform](src/com/jwetherell/algorithms/mathematics/FastFourierTransform.java)
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* [Primes](src/com/jwetherell/algorithms/mathematics/Primes.java)
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+ is prime
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+ prime factorization
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+ sieve of eratosthenes
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+ [Co-Primes (relatively prime, mutually prime)](src/com/jwetherell/algorithms/mathematics/Coprimes.java)
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+ [Greatest Common Divisor](src/com/jwetherell/algorithms/mathematics/GreatestCommonDivisor.java)
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- using Euclid's algorithm
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- using recursion
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* [Permutations](src/com/jwetherell/algorithms/mathematics/Permutations.java)
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+ strings
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+ numbers
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* [Modular arithmetic](src/com/jwetherell/algorithms/mathematics/Modular.java)
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+ add
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+ subtract
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+ multiply
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+ divide
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+ power
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## Numbers
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* Integers
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=======
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* [Knapsack](src/com/jwetherell/algorithms/mathematics/Knapsack.java)
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* [Ramer Douglas Peucker](src/com/jwetherell/algorithms/mathematics/RamerDouglasPeucker.java)
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## Numbers
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* [Integers](src/com/jwetherell/algorithms/numbers/Integers.java)
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+ to binary String
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- using divide and modulus
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- using right shift and modulus
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- using logarithm
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- using bits
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+ to English (e.g. 1 would return "one")
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* Longs
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=======
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* [Longs](src/com/jwetherell/algorithms/numbers/Longs.java)
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+ to binary String
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- using divide and modulus
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- using right shift and modulus
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- using BigDecimal
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* Complex
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=======
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* [Complex](src/com/jwetherell/algorithms/numbers/Complex.java)
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+ addition
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+ subtraction
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+ multiplication
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## Graphs
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* Find shortest path(s) in a Graph from a starting Vertex
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- Dijkstra's algorithm (non-negative weight graphs)
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- Bellman-Ford algorithm (negative and positive weight graphs)
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* Find minimum spanning tree
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* Find longest increasing subsequence (dynamic programming)
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* Find number of times a subsequence occurs in a sequence (dynamic programming)
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* Find i-th element in a Fibonacci sequence
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=======
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- [Dijkstra's algorithm (non-negative weight graphs)](src/com/jwetherell/algorithms/graph/Dijkstra.java)
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- [Bellman-Ford algorithm (negative and positive weight graphs)](src/com/jwetherell/algorithms/graph/BellmanFord.java)
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* Find minimum spanning tree
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- [Prim's (undirected graphs)](src/com/jwetherell/algorithms/graph/Prim.java)
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- [Kruskal's (undirected graphs)](src/com/jwetherell/algorithms/graph/Kruskal.java)
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* Find all pairs shortest path
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- [Johnsons's algorithm (negative and positive weight graphs)](src/com/jwetherell/algorithms/graph/Johnsons.java)
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- [Floyd-Warshall (negative and positive weight graphs)](src/com/jwetherell/algorithms/graph/FloydWarshall.java)
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* [Cycle detection](src/com/jwetherell/algorithms/graph/CycleDetection.java)
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- Depth first search while keeping track of visited Verticies
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- [Connected Components](src/com/jwetherell/algorithms/graph/ConnectedComponents.java)
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* [Topological sort](src/com/jwetherell/algorithms/graph/TopologicalSort.java)
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* [A* path finding algorithm](src/com/jwetherell/algorithms/graph/AStar.java)
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* Maximum flow
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- [Push-Relabel](src/com/jwetherell/algorithms/graph/PushRelabel.java)
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* Graph Traversal
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- [Depth First Traversal](src/com/jwetherell/algorithms/graph/DepthFirstTravesal.java)
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* [Edmonds Karp](src/com/jwetherell/algorithms/graph/EdmondsKarp.java)
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## Search
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* Get index of value in array
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+ [Linear](src/com/jwetherell/algorithms/Sequences/LinearSearch.java)
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+ [Quickselect](src/com/jwetherell/algorithms/Sequences/QuickSelect.java)
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+ [Binary [sorted array input only]](src/com/jwetherell/algorithms/Sequences/BinarySearch.java)
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+ [Lower bound [sorted array input only]](src/com/jwetherell/algorithms/Sequences/LpperBound.java)
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+ [Upper bound [sorted array input only]](src/com/jwetherell/algorithms/Sequences/UpperBound.java)
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+ Optimized binary (binary until a threashold then linear) [sorted array input only]
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+ [Interpolation [sorted array input only]](src/com/jwetherell/algorithms/Sequences/InterpolationSearch.java)
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## Sequences
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* [Find longest common subsequence (dynamic programming)](src/com/jwetherell/algorithms/Sequences/LongestCommonSubsequence.java)
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* [Find longest increasing subsequence (dynamic programming)](src/com/jwetherell/algorithms/Sequences/LongestIncreasingSubsequence.java)
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* [Find number of times a subsequence occurs in a sequence (dynamic programming)](src/com/jwetherell/algorithms/Sequences/SubsequenceCounter.java)
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* [Find i-th element in a Fibonacci sequence](src/com/jwetherell/algorithms/Sequences/FibonacciSequence.java)
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+ using a loop
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+ using recursion
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+ using matrix multiplication
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+ using Binet's formula
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* Find total of all elements in a sequence
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+ using a loop
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+ using Triangular numbers
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* Shell's Sort
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## String Functions
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=======
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* [Find total of all elements in a sequence(Arithmetic Progression)](src/com/jwetherell/algorithms/Sequences/ArithmeticProgression.java)
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+ using a loop
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+ using Triangular numbers
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* [Largest sum of contiguous subarray (Kadane's algorithm)](src/com/jwetherell/algorithms/Sequences/LargestSumContiguousSubarray.java)
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* [Longest palin­dromic sub­se­quence (dynamic programming)](src/com/jwetherell/algorithms/Sequences/LongestPalin­dromicSub­se­quence.java)
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## Sorts
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* [American Flag Sort](src/com/jwetherell/algorithms/Sorts/AmericanFlagSort.java)
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* [Bubble Sort](src/com/jwetherell/algorithms/Sorts/BubbleSort.java)
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* [Counting Sort (Integers only)](src/com/jwetherell/algorithms/Sorts/CountingSort.java)
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* [Heap Sort](src/com/jwetherell/algorithms/Sorts/HeapSort.java)
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* [Insertion Sort](src/com/jwetherell/algorithms/Sorts/InsertionSort.java)
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* [Merge Sort](src/com/jwetherell/algorithms/Sorts/AMergeSort.java)
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* [Quick Sort](src/com/jwetherell/algorithms/Sorts/QuickSort.java)
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* [Radix Sort (Integers only)](src/com/jwetherell/algorithms/Sorts/RadixSort.java)
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* [Shell's Sort](src/com/jwetherell/algorithms/Sorts/ShellSort.java)
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## String Functions
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### [String Functions](src/com/jwetherell/algorithms/strings/StringFunctions.java)
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* Reverse characters in a string
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+ using additional storage (a String or StringBuilder)
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+ using in-place swaps
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+ using in-place symetric element compares
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* Subsets of characters in a String
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* Edit (Levenshtein) Distance of two Strings
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* KMP (Knuth–Morris–Pratt) Algorithm - Length of maximal prefix-suffix for each prefix
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* String rotations
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=======
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* [KMP (Knuth–Morris–Pratt) Algorithm - Length of maximal prefix-suffix for each prefix](src/com/jwetherell/algorithms/strings/KnuthMorrisPratt.java)
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* [String rotations](src/com/jwetherell/algorithms/strings/Rotation.java)
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+ Findin lexicographically minimal string rotation
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+ Findin lexicographically maximal string rotation
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‎src/com/jwetherell/algorithms/graph/DepthFirstTraversal.java

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import java.util.Stack;
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//implemented Depth First Travesal in given "Directed graph" (Adjacany matrix)
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class DepthFirstTraversal {
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public static int[] arr;
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public static int k = 0;
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public static void depthFirstTraversal(int[][] a, int[] visited,int source){
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for (int i = 0; i < visited.length; i++) {
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visited[i] = -1;
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}
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Stack<Integer>stack = new Stack();
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int element = source;
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int i = source;
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int n = visited.length - 1;
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arr[k] = element;
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k++;
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visited[source] = 1;
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stack.push(source);
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while (!stack.isEmpty()) {
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element = stack.peek();
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i = element;
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while (i <= n) {
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if (a[element][i] == 1 && visited[i] == -1) {
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stack.push(i);
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visited[i] = 1;
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element = i;
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i = 1;
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arr[k] = element;
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k++;
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continue;
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}
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i++;
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}
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stack.pop();
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}
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}
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}
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