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/*
* Copyright (C) 2003-2022 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 KEY_CLASS_Object
import java.util.Comparator;
#endif
#if ! KEY_CLASS_Integer
import it.unimi.dsi.fastutil.ints.IntArrays;
#endif
/** 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 final 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 {@code null} for the natural order.
* @return the new position in the heap of the element of heap index {@code 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 {@code null} for the natural order.
* @return the new position in the heap of the element of heap index {@code 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 {@code 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 {@code 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 {@code refArray}.
* @param size the number of elements in the heap.
* @param c a type-specific comparator, or {@code 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 {@code 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 {@code refArray}).
* @return the number of elements actually written (starting from the first position of {@code 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 {@code 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 {@code refArray}).
* @param c a type-specific comparator.
* @return the number of elements actually written (starting from the first position of {@code 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;
}
}