Package it.unimi.dsi.sux4j.bits

Interface Select

All Superinterfaces:

java.io.Serializable

All Known Implementing Classes:

HintedBsearchSelect, RankSelect, Select9, SimpleSelect, SparseSelect

public interface Select
extends 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 rank() and 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.

Method Summary

Modifier and Type	Method	Description
BitVector	bitVector()	Returns the bit vector indexed by this structure.
long	numBits()	Returns the overall number of bits allocated by this structure.
long	select(long rank)	Returns the position of the bit of given rank.

Method Detail

select

long select(long rank)

Returns the position of the bit of given rank. Equivalently, returns the greatest position that is preceded by the specified number of ones.

Parameters:

rank - a rank.

Returns:

the position of the bit of given rank; if no such position exists, −1 is returned.

bitVector

BitVector bitVector()

Returns the bit vector indexed by this structure.

Note that you are not supposed to modify the returned vector.

Returns:

the bit vector indexed by this structure.

numBits

long numBits()

Returns the overall number of bits allocated by this structure.

Returns:

the overall number of bits allocated by this structure (not including the bits of the indexed vector).