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# fisharebest/algorithm

General purpose algorithms in PHP

* Dijkstra
* Myers’ diff
* Connected/unconnected components of a graph

## Installation

Install using composer.

```
composer require fisharebest/algorithm
```


## Dijkstra

[Dijkstra's algorithm](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm) finds the
shortest path(s) between two nodes in a weighted, directed graph.

Graphs are specified as an array of edges, each with a cost.  The example below is
an undirected graph (i.e. if D→E is 9, then E→D is also 9.), because it is easy to
understand and easy to draw.  However, the algorithm works equally well for directed
graphs, where links can be one-way only or have different costs in each direction.
```
     D---9---E
    / \       \
  14   2       6
  /     \       \
 A---9---B--11--C
  \     /      /
   7  10      /
    \ /      /
     F-----15       G
```

Sample code for the above graph.

``` php
$graph = array(
  'A' => array('B' => 9, 'D' => 14, 'F' => 7),
  'B' => array('A' => 9, 'C' => 11, 'D' => 2, 'F' => 10),
  'C' => array('B' => 11, 'E' => 6, 'F' => 15),
  'D' => array('A' => 14, 'B' => 2, 'E' => 9),
  'E' => array('C' => 6, 'D' => 9),
  'F' => array('A' => 7, 'B' => 10, 'C' => 15),
  'G' => array(),
);

$algorithm = new \Fisharebest\Algorithm\Dijkstra($graph);

// There can be zero, one or more shortest (i.e. same total cost) paths.

// No shortest path.
$path = $algorithm->shortestPaths('A', 'G'); // array()

// Exactly one shortest path.
$path = $algorithm->shortestPaths('A', 'E'); // array(array('A', 'B', 'D', 'E'))

// Multiple solutions with the same shortest path.
$path = $algorithm->shortestPaths('E', 'F'); // array(array('E', 'D', 'B', 'F'), array('E', 'C', 'F'))

// To find next-shortest paths, exclude one or intermediate nodes from the shortest path.
$path = $algorithm->shortestPaths('A', 'E'); // array(array('A', 'B', 'D', 'E'))
$path = $algorithm->shortestPaths('A', 'E', array('B')); // array(array('A', 'B', 'D', 'E'))
$path = $algorithm->shortestPaths('A', 'E', array('D')); // array(array('A', 'B', 'C', 'E'))
$path = $algorithm->shortestPaths('A', 'E', array('B', 'D')); // array(array('A', 'F', 'C', 'E'))
```

## Myers’ diff

Find the difference between two sequences of tokens (characters, words, lines, etc.) using
“[An O(ND) Difference Algorithm and Its Variations](http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.4.6927)”
by Eugene W. Myers.

The output can be interpreted as either:

* A series of instructions to transform the first sequence into the second sequence.
* A list of matches (tokens that appear in both sequences) and mismatches (tokens that appear in
just one sequence).

``` php
$x = array('a', 'b', 'c', 'a', 'b', 'b', 'a');
$y = array('c', 'b', 'a', 'b', 'a', 'c');
$algorithm = new MyersDiff;
$diff = $algorithm->calculate($x, $y);
// array(
//  array('a', MyersDiff::DELETE),   i.e. 'a' occurs only in $x
//  array('b', MyersDiff::DELETE),   i.e. 'b' occurs only in $x
//  array('c', MyersDiff::KEEP),     i.e. 'c' occurs both $x and $y
//  array('b', MyersDiff::INSERT),   i.e. 'b' occurs only in $y
//  array('a', MyersDiff::KEEP),     i.e. 'a' occurs in both $x and $y
//  array('b', MyersDiff::KEEP),     i.e. 'b' occurs in both $x and $y
//  array('b', MyersDiff::DELETE),   i.e. 'b' occurs only in $x
//  array('a', MyersDiff::KEEP),     i.e. 'a' occurs in both $x and $y
//  array('c', MyersDiff::INSERT),   i.e. 'c' occurs only in $y
// );
```
## Connected components

A depth-first search of a graph to find isolated groups of nodes.

```
    D    E
   / \    \
  /   \    \
 A-----B   C
  \   /
   \ /
    F
```

Sample code for the above graph

```php
$graph = array(
	'A' => array('B' => 1, 'D' => 1, 'F' => 1),
	'B' => array('A' => 1, 'D' => 1, 'F' => 1),
	'C' => array('E' => 1),
	'D' => array('A' => 1, 'B' => 1),
	'E' => array('C' => 1),
	'F' => array('A' => 1, 'B' => 1),
);

$algorithm  = new \Fisharebest\Algorithm\ConnectedComponent($graph);
$components = $algorithm->findConnectedComponents());
// array(
//  1 => array('A', 'B', 'D', 'F'),
//  2 => array('C', 'E'),
// );
```
## Connected components

A depth-first search of a graph to find isolated groups of nodes.

```
    D    E
   / \    \
  /   \    \
 A-----B   C
  \   /
   \ /
    F
```

Sample code for the above graph

```php
$graph = array(
	'A' => array('B' => 1, 'D' => 1, 'F' => 1),
	'B' => array('A' => 1, 'D' => 1, 'F' => 1),
	'C' => array('E' => 1),
	'D' => array('A' => 1, 'B' => 1),
	'E' => array('C' => 1),
	'F' => array('A' => 1, 'B' => 1),
);

$algorithm  = new \Fisharebest\Algorithm\ConnectedComponent($graph);
$components = $algorithm->findConnectedComponents());
// array(
//  1 => array('A', 'B', 'D', 'F'),
//  2 => array('C', 'E'),
// );
```

