@ -22,14 +22,32 @@
this . MaxVectorsCount = maxVectorsCount ;
this . Dictionary = ImmutableArray . Create ( FilterVectors ( dictionary , target ) . ToArray ( ) ) ;
var normsIndex = new int [ GetVectorNorm ( target , target ) + 1 ] ;
var wordOffset = 0 ;
for ( var norm = normsIndex . Length - 1 ; norm > = 0 ; norm - - )
{
while ( wordOffset < this . Dictionary . Length & & this . Dictionary [ wordOffset ] . Norm > norm )
{
wordOffset + + ;
}
normsIndex [ norm ] = wordOffset ;
}
this . NormsIndex = ImmutableArray . Create ( normsIndex ) ;
}
private Vector < byte > Target { get ; }
private int MaxVectorsCount { get ; }
// Ordered by norm, descending
private ImmutableArray < VectorInfo > Dictionary { get ; }
// Contains index of first vector in Dictionary with norm less than or equal to key
private ImmutableArray < int > NormsIndex { get ; }
// Produces all sets of vectors with the target sum
#if SINGLE_THREADED
public IEnumerable < int [ ] > GenerateSequences ( )
@ -37,7 +55,7 @@
public ParallelQuery < int [ ] > GenerateSequences ( )
# endif
{
return GenerateUnorderedSequences ( this . Target , GetVectorNorm ( this . Target , this . Target ) , this . MaxVectorsCount , this . Dictionary , 0 )
return GenerateUnorderedSequences ( this . Target , GetVectorNorm ( this . Target , this . Target ) , this . MaxVectorsCount , this . Dictionary , 0 , this . NormsIndex )
#if !SINGLE_THREADED
. AsParallel ( )
# endif
@ -74,7 +92,7 @@
// In every sequence, next vector always goes after the previous one from dictionary.
// E.g. if dictionary is [x, y, z], then only [x, y] sequence could be generated, and [y, x] will never be generated.
// That way, the complexity of search goes down by a factor of MaxVectorsCount! (as if [x, y] does not add up to a required target, there is no point in checking [y, x])
private static IEnumerable < ImmutableStack < int > > GenerateUnorderedSequences ( Vector < byte > remainder , int remainderNorm , int allowedRemainingWords , ImmutableArray < VectorInfo > dictionary , int currentDictionaryPosition )
private static IEnumerable < ImmutableStack < int > > GenerateUnorderedSequences ( Vector < byte > remainder , int remainderNorm , int allowedRemainingWords , ImmutableArray < VectorInfo > dictionary , int currentDictionaryPosition , ImmutableArray < int > normsIndex )
{
if ( allowedRemainingWords > 1 )
{
@ -84,7 +102,7 @@
// we need the largest remaining word to have a norm of at least 3
var requiredRemainderPerWord = ( remainderNorm + allowedRemainingWords - 1 ) / allowedRemainingWords ;
for ( var i = FindFirstWithNormLessOrEqual ( remainderNorm , dictionary , currentDictionaryPosition ) ; i < dictionary . Length ; i + + )
for ( var i = Math . Max ( normsIndex [ remainderNorm ] , currentDictionaryPosition ) ; i < dictionary . Length ; i + + )
{
var currentVectorInfo = dictionary [ i ] ;
if ( currentVectorInfo . Vector = = remainder )
@ -99,7 +117,7 @@
{
var newRemainder = remainder - currentVectorInfo . Vector ;
var newRemainderNorm = remainderNorm - currentVectorInfo . Norm ;
foreach ( var result in GenerateUnorderedSequences ( newRemainder , newRemainderNorm , newAllowedRemainingWords , dictionary , i ) )
foreach ( var result in GenerateUnorderedSequences ( newRemainder , newRemainderNorm , newAllowedRemainingWords , dictionary , i , normsIndex ) )
{
yield return result . Push ( currentVectorInfo . Index ) ;
}
@ -108,7 +126,7 @@
}
else
{
for ( var i = FindFirstWithNormLessOrEqual ( remainderNorm , dictionary , currentDictionaryPosition ) ; i < dictionary . Length ; i + + )
for ( var i = Math . Max ( normsIndex [ remainderNorm ] , currentDictionaryPosition ) ; i < dictionary . Length ; i + + )
{
var currentVectorInfo = dictionary [ i ] ;
if ( currentVectorInfo . Vector = = remainder )
@ -123,41 +141,6 @@
}
}
// BCL BinarySearch would find any vector with required norm, not the first one; or would find nothing if there is no such vector
private static int FindFirstWithNormLessOrEqual ( int expectedNorm , ImmutableArray < VectorInfo > dictionary , int offset )
{
var start = offset ;
var end = dictionary . Length - 1 ;
if ( dictionary [ start ] . Norm < = expectedNorm )
{
return start ;
}
if ( dictionary [ end ] . Norm > expectedNorm )
{
return dictionary . Length ;
}
// Norm for start is always greater than expected norm, or start is the required position; norm for end is always less than or equal to expected norm
// The loop always ends, because the difference always decreases; if start + 1 = end, then middle will be equal to start, and either end := middle = start or start := middle + 1 = end.
while ( start < end )
{
var middle = ( start + end ) / 2 ;
var newNorm = dictionary [ middle ] . Norm ;
if ( dictionary [ middle ] . Norm < = expectedNorm )
{
end = middle ;
}
else
{
start = middle + 1 ;
}
}
return start ;
}
private struct VectorInfo
{
public VectorInfo ( Vector < byte > vector , int norm , int index )
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