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• Select.java

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src.it.unimi.dsi.sux4j.bits.Select Maven / Gradle / Ivy

package it.unimi.dsi.sux4j.bits;

/*
 * Sux4J: Succinct data structures for Java
 *
 * Copyright (C) 2008-2017 Sebastiano Vigna
 *
 *  This library is free software; you can redistribute it and/or modify it
 *  under the terms of the GNU Lesser General Public License as published by the Free
 *  Software Foundation; either version 3 of the License, or (at your option)
 *  any later version.
 *
 *  This library is distributed in the hope that it will be useful, but
 *  WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
 *  or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public License
 *  for more details.
 *
 *  You should have received a copy of the GNU Lesser General Public License
 *  along with this program; if not, see .
 *
 */

import it.unimi.dsi.bits.BitVector;

import java.io.Serializable;

/** A data structure providing selection over a bit array.
 *
 * 
Selection is a basic building blocks for most succinct data structures. Usually,
 * instances of this class class provide quick (e.g., constant time) selection.
 *
 * 
There is some variance in the literature about the exact semantics of selection—in most
 * cases, it is a matter of off-by-ones. This interface specifies a zero-based selection.
 *
 * 
More precisely, select is applied to a bit vector in which bits positions are numbered
 * starting from zero. Then, select(r) is the position of the
 * leftmost bit set to one and preceded by r ones.
 *
 * 
A number of equations link {@link Rank#rank(long) rank()} and {@link #select(long) select()}:
 * 

 *  	
rank(0)=0;
 *  	
rank(length()) is the number of ones in the bit vector;
 *  	
if r < rank(length()), then rank(select(r))==r;
 *  	
if r ≥ rank(length()), then select(r)=-1;
 *  	
if p ≤ length(), then p≤select(rank(p)), and equality
 *  	holds iff there is a one at position p.
 *  
 */
public interface Select extends Serializable {

	/** Returns the position of the bit of given rank.
	 *  Equivalently, returns the greatest position that is preceded by the specified number of ones.
	 *
	 * @param rank a rank.
	 * @return the position of the bit of given rank; if no such position exists, −1 is returned.
	 */
	public long select(long rank);

	/** Returns the bit vector indexed by this structure.
	 *
	 * 
Note that you are not supposed to modify the returned vector.
	 *
	 * @return the bit vector indexed by this structure.
	 */
	public BitVector bitVector();

	/** Returns the overall number of bits allocated by this structure.
	 *
	 * @return the overall number of bits allocated by this structure (not including the bits
	 * of the {@linkplain #bitVector() indexed vector}).
	 */

	public long numBits();
}