Adapted Needleman-Wunsch algorithm for general array alignment implemented in Haxe (3).

NeedlemanWunsch.hx

/**
	Adapted Needleman-Wunsch algorithm for general array alignment
	If NeedlemanWunsch is used as entry point the unit tests are executed

	Copyright (c) 2013, Jonas Malaco Filho
	All rights reserved.

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	modification, are permitted provided that the following conditions are met:
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	This is a BSD 2-clause license. Information available at:
	http://opensource.org/licenses/BSD-2-Clause.
**/

class NeedlemanWunsch<T> {
	
	public var alignedA( default, null ): Array<Null<T>>;
	public var alignedB( default, null ): Array<Null<T>>;
	public var distance( default, null ): Float;
	public var length( default, null ): Int;

	/**
		Global alignment of two arrays, using a modified version of the quadratic running time
		Needleman-Wunsch algorithm with gap penalties
		Params:
			dist( a, b ) should give the (edit) distance between a and b
			skip( a, b, c ) should give (an estimate of) the penalty incured when skipping b
				a (nullable) is the previous element
				c (nullable) is the next element
		Return:
			A Alignment<T> object, with both a and b aligned arrays and the (edit) distance computed
	**/
	public static function globalAlignment<T>( a: Array<T>, b: Array<T>, dist: T -> T -> Float,
	                            ?skip: Null<T> -> T -> Null<T> -> Float): NeedlemanWunsch<T> {
		// array lengths
		var n = a.length;
		var m = b.length;

		// F (?) matrix initialization, size( F ) = n+1, m+1
		// *** the corresponding a and b elements for Fij are a[i - 1] and b[i - 1] ***
		var F = buildMatrix( n + 1, m + 1, function ( i, j ) return Math.POSITIVE_INFINITY );
		
		// pre-computed distance matrix, size( D ) = n+1, m+1
		var D = buildMatrix( n + 1, m + 1, function ( i, j ) return i*j != 0 ? dist( a[i - 1], b[j - 1] ) : Math.NaN );

		// default gap penalty function is cte 1. (as in Levenshtein distance)
		if ( skip == null )
			skip = function ( a, b, c ) return 1.;

		// basis
		F[0][0] = 0.;
		for ( i in 1...n+1 )
			F[i][0] = F[i - 1][0] + skip( ( i > 1 ? a[i - 2] : null ), a[i - 1], ( i < n ? a[i] : null ) );
		for ( j in 1...m+1 )
			F[0][j] = F[0][j - 1] + skip( ( j > 1 ? b[j - 2] : null ), b[j - 1], ( j < m ? b[j] : null ) );

		// recursion
		// for i,j <=> a[i - 1],b[j - 1] there are 3 possible outcomes:
		//     move down and left, a[i - 1] aligns with b[j - 1], AKA "match"
		//     move down, a[i - 1] aligns with a gap in b, AKA "skipA" (one element of a is discarted), AKA "delete"
		//     move left, b[j - 1] aligns with a gap in a, AKA "skipB" (one element of b is discarted), AKA "insert"
		for ( i in 1...n+1 )
			for ( j in 1...m+1 ) {
					var match = F[i - 1][j - 1] + D[i][j];
					var skipA = F[i - 1][j] + skip( ( i > 1 ? a[i - 2] : null ), a[i - 1], ( i < n ? a[i] : null ) );
					var skipB = F[i][j - 1] + skip( ( j > 1 ? b[j - 2] : null ), b[j - 1], ( j < m ? b[j] : null ) );
					F[i][j] = Math.min( match, Math.min( skipA, skipB ) );
				}

		// trace( F.join( '\n' ) );

		if ( !Math.isFinite( F[n][m] ) )
			throw 'Supplied distance or skip penalty functions resulted in infeasible alignment';

		// alignment
		var aligA = new List();
		var aligB = new List();
		var i = n;
		var j = m;
		while ( i > 0 && j > 0 ) {
			if ( Math.isFinite( F[i - 1][j - 1] ) && F[i][j] == F[i - 1][j - 1] + D[i][j] ) {
				// results from match
				aligA.push( a[--i] );
				aligB.push( b[--j] );
			}
			else if ( Math.isFinite( F[i - 1][j] )
			  && F[i][j] == F[i - 1][j] + skip( ( i > 1 ? a[i - 2] : null ), a[i - 1], ( i < n ? a[i] : null ) ) ) {
				// results from skipA
				aligA.push( a[--i] );
				aligB.push( null );
			}
			else if ( Math.isFinite( F[i][j - 1] )
			  && F[i][j] == F[i][j - 1] + skip( ( j > 1 ? b[j - 2] : null ), b[j - 1], ( j < m ? b[j] : null ) ) ) {
				// results from skipB
				aligA.push( null );
				aligB.push( b[--j] );
			}
			else
				throw 'Internal error in alignment reconstruction; F=\n' + F.join( '\n' );
		}
		while ( i > 0 || j > 0 ) {
			aligA.push( i > 0 ? a[--i] : null );
			aligB.push( j > 0 ? b[--j] : null );
		}

		return new NeedlemanWunsch( Lambda.array( aligA ), Lambda.array( aligB ), F[n][m] );
	}

	static function buildMatrix<A>( n: Int, m: Int, init: Int -> Int -> A ) {
		var M = [];
		for ( i in 0...n ) {
			var _i = n - 1 - i;
			M[_i] = [];
			for ( j in 0...m ) {
				var _j = m - 1 - j;
				M[_i][_j] = init( _i, _j );
			}
		}
		return M;
	}
	
	function new( a: Array<Null<T>>, b: Array<Null<T>>, dist: Float ) {
		if ( a.length != b.length )
			throw 'a.length != b.length'; 
		alignedA = a;
		alignedB = b;
		length = alignedA.length;
		distance = dist;
	}

	// Testing entry point
	static function main() {
		var runner = new haxe.unit.TestRunner();
		runner.add( new NeedlemanWunschTest() );
		runner.run();
	}

}

class NeedlemanWunschTest extends haxe.unit.TestCase {

	// Tests

	// Test alignment using Levenshtein distance penalties
	function testLevenshteinDistance() {
		var dist = function ( a, b ) return a==b ? 0 : 1;
		var skip = function ( a, b, c ) return 1;

		assertEquals( '3|kitten_|sitting', stAl( 'kitten', 'sitting', dist, skip ) );
		assertEquals( '6|industry|interest', stAl( 'industry', 'interest', dist, skip ) );
		assertEquals( '3|horse|ror__', stAl( 'horse', 'ror', dist, skip ) );

		assertEquals( '1|start|_tart', stAl( 'start', 'tart', dist, skip ) );
		assertEquals( '1|finish|finis_', stAl( 'finish', 'finis', dist, skip ) );
		assertEquals( '1|skipped|ski_ped', stAl( 'skipped', 'skiped', dist, skip ) );
	}

	// Test different skip functions, specially one that does not allow
	// gaps in the beginning or end
	function testSkipFunction() {
		var dist = function ( a, b ) return a==b ? 0 : 1;
		var skip = function ( a, b, c ) {
			if ( a == null )
				return Math.POSITIVE_INFINITY;
			else if ( c == null )
				return Math.POSITIVE_INFINITY;
			else if ( b == a || b == c )
				return 0.;
			else
				return 1.;
		};

		assertEquals( '2|start|t_art', stAl( 'start', 'tart', dist, skip ) );
		assertEquals( '2|finish|fini_s', stAl( 'finish', 'finis', dist, skip ) );
		assertEquals( '0|skipped|ski_ped', stAl( 'skipped', 'skiped', dist, skip ) );

		// expect exception if b is only one char long and a has more than one char
		assertRaises( null, stAl( 'ar', 'b', dist, skip ) );
		assertEquals( '1|a|b', stAl( 'a', 'b', dist, skip ) );
	}

	// Helpers

	// Assert exception
	macro static function assertRaises( expected: haxe.macro.Expr, test: haxe.macro.Expr ) {
		return macro {
			var _exp: Null<Dynamic> = $expected;
			var err = _exp != null? 'Expected exception ' + _exp: 'Expected exception';
			var done = false;
			try {
				$test;
				done = true;
			}
			catch ( e: Dynamic ) {
				if ( _exp != null && Std.string( e ) != Std.string( _exp ) )
					throw err;
			}
			if ( done )
				throw err;
		};
	}

	// Global alignment of strings
	static function stAl( a: String, b: String, dist: Int -> Int -> Float, skip: Int -> Int -> Int -> Float ): String {
		var _a = stAr( a );
		var _b = stAr( b );
		var nwa = NeedlemanWunsch.globalAlignment( _a, _b, dist, skip );
		return stRes( nwa );
	}

	// String to Array<Int>
	static function stAr( s: String ): Array<Int> {
		var bytes = haxe.io.Bytes.ofString( s );
		var a = [];
		for ( i in 0...bytes.length ) {
			a.push( bytes.get( i ) );
		}
		return a;
	}

	// Array<Int> to String
	static function arSt( a: Array<Int>, ?nullValue = '_' ): String {
		var bytes = haxe.io.Bytes.alloc( a.length );
		var nl = nullValue.charCodeAt( 0 );
		for ( i in 0...a.length )
			bytes.set( i, a[i] == null ? nl : a[i] );
		return bytes.toString();
	}

	// Alignment results printer
	static function stRes( x: NeedlemanWunsch<Int>, ?sep='|', ?nl='_'  ): String {
		return '${x.distance}$sep${arSt( x.alignedA, nl )}$sep${arSt( x.alignedB, nl )}';
	}

}