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/*
* Copyright (C) 2003-2015 Paolo Boldi and Sebastiano Vigna
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package PACKAGE;
#if #keyclass(Object)
import java.util.Comparator;
#endif
import it.unimi.dsi.fastutil.ints.IntArrays;
/** A class providing static methods and objects that do useful things with semi-indirect heaps.
*
* A semi-indirect heap is based on a reference array. Elements of
* a semi-indirect heap are integers that index the reference array (note that
* in an indirect heap you can also map elements of the reference
* array to heap positions).
*/
public class SEMI_INDIRECT_HEAPS {
private SEMI_INDIRECT_HEAPS() {}
/** Moves the given element down into the semi-indirect heap until it reaches the lowest possible position.
*
* @param refArray the reference array.
* @param heap the semi-indirect heap (starting at 0).
* @param size the number of elements in the heap.
* @param i the index in the heap of the element to be moved down.
* @param c a type-specific comparator, or null for the natural order.
* @return the new position in the heap of the element of heap index i.
*/
SUPPRESS_WARNINGS_KEY_UNCHECKED
public static KEY_GENERIC int downHeap( final KEY_GENERIC_TYPE[] refArray, final int[] heap, final int size, int i, final KEY_COMPARATOR KEY_GENERIC c ) {
assert i < size;
final int e = heap[ i ];
final KEY_GENERIC_TYPE E = refArray[ e ];
int child;
if ( c == null )
while ( ( child = ( i << 1 ) + 1 ) < size ) {
int t = heap[ child ];
final int right = child + 1;
if ( right < size && KEY_LESS( refArray[ heap[ right ] ], refArray[ t ] ) ) t = heap[ child = right ];
if ( KEY_LESSEQ( E, refArray[ t ] ) ) break;
heap[ i ] = t;
i = child;
}
else
while ( ( child = ( i << 1 ) + 1 ) < size ) {
int t = heap[ child ];
final int right = child + 1;
if ( right < size && c.compare( refArray[ heap[ right ] ], refArray[ t ] ) < 0 ) t = heap[ child = right ];
if ( c.compare( E, refArray[ t ] ) <= 0 ) break;
heap[ i ] = t;
i = child;
}
heap[ i ] = e;
return i;
}
/** Moves the given element up in the semi-indirect heap until it reaches the highest possible position.
*
* @param refArray the reference array.
* @param heap the semi-indirect heap (starting at 0).
* @param size the number of elements in the heap.
* @param i the index in the heap of the element to be moved up.
* @param c a type-specific comparator, or null for the natural order.
* @return the new position in the heap of the element of heap index i.
*/
SUPPRESS_WARNINGS_KEY_UNCHECKED
public static KEY_GENERIC int upHeap( final KEY_GENERIC_TYPE[] refArray, final int[] heap, final int size, int i, final KEY_COMPARATOR KEY_GENERIC c ) {
assert i < size;
final int e = heap[ i ];
final KEY_GENERIC_TYPE E = refArray[ e ];
if ( c == null )
while ( i != 0 ) {
final int parent = ( i - 1 ) >>> 1;
final int t = heap[ parent ];
if ( KEY_LESSEQ( refArray[ t ], E ) ) break;
heap[ i ] = t;
i = parent;
}
else
while ( i != 0 ) {
final int parent = ( i - 1 ) >>> 1;
final int t = heap[ parent ];
if ( c.compare( refArray[ t ], E ) <= 0 ) break;
heap[ i ] = t;
i = parent;
}
heap[ i ] = e;
return i;
}
/** Creates a semi-indirect heap in the given array.
*
* @param refArray the reference array.
* @param offset the first element of the reference array to be put in the heap.
* @param length the number of elements to be put in the heap.
* @param heap the array where the heap is to be created.
* @param c a type-specific comparator, or null for the natural order.
*/
public static KEY_GENERIC void makeHeap( final KEY_GENERIC_TYPE[] refArray, final int offset, final int length, final int[] heap, final KEY_COMPARATOR KEY_GENERIC c ) {
ARRAYS.ensureOffsetLength( refArray, offset, length );
if ( heap.length < length ) throw new IllegalArgumentException( "The heap length (" + heap.length + ") is smaller than the number of elements (" + length + ")" );
int i = length;
while( i-- != 0 ) heap[ i ] = offset + i;
i = length >>> 1;
while( i-- != 0 ) downHeap( refArray, heap, length, i, c );
}
/** Creates a semi-indirect heap, allocating its heap array.
*
* @param refArray the reference array.
* @param offset the first element of the reference array to be put in the heap.
* @param length the number of elements to be put in the heap.
* @param c a type-specific comparator, or null for the natural order.
* @return the heap array.
*/
public static KEY_GENERIC int[] makeHeap( final KEY_GENERIC_TYPE[] refArray, final int offset, final int length, final KEY_COMPARATOR KEY_GENERIC c ) {
final int[] heap = length <= 0 ? IntArrays.EMPTY_ARRAY : new int[ length ];
makeHeap( refArray, offset, length, heap, c );
return heap;
}
/** Creates a semi-indirect heap from a given index array.
*
* @param refArray the reference array.
* @param heap an array containing indices into refArray.
* @param size the number of elements in the heap.
* @param c a type-specific comparator, or null for the natural order.
*/
public static KEY_GENERIC void makeHeap( final KEY_GENERIC_TYPE[] refArray, final int[] heap, final int size, final KEY_COMPARATOR KEY_GENERIC c ) {
int i = size >>> 1;
while( i-- != 0 ) downHeap( refArray, heap, size, i, c );
}
/** Retrieves the front of a heap in a given array.
*
*
The front of a semi-indirect heap is the set of indices whose associated elements in the reference array
* are equal to the element associated to the first index.
*
*
In several circumstances you need to know the front, and scanning linearly the entire heap is not
* the best strategy. This method simulates (using a partial linear scan) a breadth-first visit that
* terminates when all visited nodes are larger than the element associated
* to the top index, which implies that no elements of the front can be found later.
* In most cases this trick yields a significant improvement.
*
* @param refArray the reference array.
* @param heap an array containing indices into refArray.
* @param size the number of elements in the heap.
* @param a an array large enough to hold the front (e.g., at least long as refArray).
* @return the number of elements actually written (starting from the first position of a).
*/
SUPPRESS_WARNINGS_KEY_UNCHECKED
public static KEY_GENERIC int front( final KEY_GENERIC_TYPE[] refArray, final int[] heap, final int size, final int[] a ) {
final KEY_GENERIC_TYPE top = refArray[ heap[ 0 ] ];
int j = 0, // The current position in a
l = 0, // The first position to visit in the next level (inclusive)
r = 1, // The last position to visit in the next level (exclusive)
f = 0; // The first position (in the heap array) of the next level
for( int i = 0; i < r; i++ ) {
if ( i == f ) { // New level
if ( l >= r ) break; // If we are crossing the two bounds, we're over
f = (f << 1) + 1; // Update the first position of the next level...
i = l; // ...and jump directly to position l
l = -1; // Invalidate l
}
if ( KEY_CMP_EQ( top, refArray[ heap[ i ] ] ) ) {
a[ j++ ] = heap[ i ];
if ( l == -1 ) l = i * 2 + 1; // If this is the first time in this level, set l
r = Math.min( size, i * 2 + 3 ); // Update r, but do not go beyond size
}
}
return j;
}
/** Retrieves the front of a heap in a given array using a given comparator.
*
*
The front of a semi-indirect heap is the set of indices whose associated elements in the reference array
* are equal to the element associated to the first index.
*
*
In several circumstances you need to know the front, and scanning linearly the entire heap is not
* the best strategy. This method simulates (using a partial linear scan) a breadth-first visit that
* terminates when all visited nodes are larger than the element associated
* to the top index, which implies that no elements of the front can be found later.
* In most cases this trick yields a significant improvement.
*
* @param refArray the reference array.
* @param heap an array containing indices into refArray.
* @param size the number of elements in the heap.
* @param a an array large enough to hold the front (e.g., at least long as refArray).
* @param c a type-specific comparator.
* @return the number of elements actually written (starting from the first position of a).
*/
public static KEY_GENERIC int front( final KEY_GENERIC_TYPE[] refArray, final int[] heap, final int size, final int[] a, final KEY_COMPARATOR KEY_GENERIC c ) {
final KEY_GENERIC_TYPE top = refArray[ heap[ 0 ] ];
int j = 0, // The current position in a
l = 0, // The first position to visit in the next level (inclusive)
r = 1, // The last position to visit in the next level (exclusive)
f = 0; // The first position (in the heap array) of the next level
for( int i = 0; i < r; i++ ) {
if ( i == f ) { // New level
if ( l >= r ) break; // If we are crossing the two bounds, we're over
f = (f << 1) + 1; // Update the first position of the next level...
i = l; // ...and jump directly to position l
l = -1; // Invalidate l
}
if ( c.compare( top, refArray[ heap[ i ] ] ) == 0 ) {
a[ j++ ] = heap[ i ];
if ( l == -1 ) l = i * 2 + 1; // If this is the first time in this level, set l
r = Math.min( size, i * 2 + 3 ); // Update r, but do not go beyond size
}
}
return j;
}
}