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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 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.

$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 more 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” 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).

$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

$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'),
// );