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/*
 * (C) Copyright 2014-2016, by Dimitrios Michail
 *
 * JHeaps Library
 * 
 * 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 org.jheaps.monotone;

import java.io.Serializable;
import java.lang.reflect.Array;
import java.math.BigInteger;

/**
 * An addressable radix heap for double keys. The heap stores double keys sorted
 * according to the {@linkplain Comparable natural ordering} of its keys. A
 * radix heap is a monotone heap, especially designed for algorithms (such as
 * Dijkstra) which scan elements in order of nondecreasing keys.
 *
 * 

* Note that this implementation uses the fact that the IEEE floating-point * standard has the property that for any valid floating-point numbers a and b, * {@literal a<=b} if and only if {@literal bits(a)<= bits(b)}, where * {@literal bits(x)} denotes the re-interpretation of x as an unsigned integer * (long in our case). * *

* The implementation use arrays in order to store the elements. Operations * {@code insert} and {@code findMin} are worst-case constant time. The cost of * operation {@code deleteMin} is amortized O(logC) assuming the radix-heap * contains keys in the range {@literal [0, C]} or equivalently * {@literal [a,a+C]}. Note, however, that C here depends on the distance of the * minimum and maximum value when they are translated into unsigned longs. * *

* Note that this implementation is not synchronized. If * multiple threads access a heap concurrently, and at least one of the threads * modifies the heap structurally, it must be synchronized externally. * (A structural modification is any operation that adds or deletes one or more * elements or changing the key of some element.) This is typically accomplished * by synchronizing on some object that naturally encapsulates the heap. * * @author Dimitrios Michail * * @param * the type of values maintained by this heap * * @see Serializable */ public class DoubleRadixAddressableHeap extends AbstractRadixAddressableHeap { private final static long serialVersionUID = 1; /** * Constructs a new heap which can store values between a minimum and a * maximum key value (inclusive). * * It is important to use the smallest key range as the heap uses O(logC) * where C=maxKey-minKey+1 buckets to store elements. Moreover, the * operation {@code deleteMin} requires amortized O(logC) time. * * @param minKey * the non-negative minimum key that this heap supports * (inclusive) * @param maxKey * the maximum key that this heap supports (inclusive) * @throws IllegalArgumentException * if the minimum key is negative * @throws IllegalArgumentException * if the maximum key is less than the minimum key */ @SuppressWarnings("unchecked") public DoubleRadixAddressableHeap(double minKey, double maxKey) { super(); if (!Double.isFinite(minKey) || minKey < 0.0) { throw new IllegalArgumentException("Minimum key must be finite and non-negative"); } this.minKey = minKey; this.lastDeletedKey = minKey; if (!Double.isFinite(maxKey) || maxKey < minKey) { throw new IllegalArgumentException("Maximum key must be finite and not less than the minimum"); } this.maxKey = maxKey; // compute number of buckets BigInteger minKeyAsBigInt = UnsignedUtils.unsignedLongToBigInt(Double.doubleToLongBits(minKey)); BigInteger maxKeyAsBigInt = UnsignedUtils.unsignedLongToBigInt(Double.doubleToLongBits(maxKey)); BigInteger diff = maxKeyAsBigInt.subtract(minKeyAsBigInt); int numBuckets = 2 + 1 + diff.bitLength(); // construct representation this.buckets = (Node[]) Array.newInstance(Node.class, numBuckets); this.size = 0; this.currentMin = null; } /** * {@inheritDoc} */ @Override protected int compare(Double o1, Double o2) { /* * Convert to IEEE and compare as unsigned */ long x = Double.doubleToLongBits(o1) ^ Long.MIN_VALUE; long y = Double.doubleToLongBits(o2) ^ Long.MIN_VALUE; // assert if (o1.doubleValue() < o2.doubleValue()) { assert x < y; } else if (o1.doubleValue() == o2.doubleValue()) { assert x == y; } else { assert x > y; } return (x < y) ? -1 : ((x == y) ? 0 : 1); } /** * {@inheritDoc} */ @Override protected int msd(Double a, Double b) { /* * For this to work, arithmetic must be unsigned */ long ux = Double.doubleToLongBits(a); long uy = Double.doubleToLongBits(b); if (ux == uy) { return -1; } double d = UnsignedUtils.unsignedLongToDouble(ux ^ uy); return Math.getExponent(d); } }





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