* Sux4J: Succinct data structures for Java
* Copyright (C) 2008-2013 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 <http://www.gnu.org/licenses/>.
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
A number of equations link
rank(length())is the number of ones in the bit vector;
r < rank(length()), then
r ≥ rank(length()), then
p ≤ length(), then
p≤select(rank(p)), and equality holds iff there is a one at position