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/*
* DSI utilities
*
* Copyright (C) 2003-2020 Paolo Boldi and 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 This class has no constructor: use the static factory methods
* {@link #valueOf(int, int)} and {@link #valueOf(int)}, instead.
*
*
Instances of this class are immutable, and moreover implement
* the {@link it.unimi.dsi.fastutil.ints.IntSortedSet} interface. The
* {@linkplain #equals(Object) equality method} allows to check equality with
* both sorted and non-sorted sets of integers.
*
*
To reduce garbage collection,
* intervals made of one non-negative small points are precomputed and returned upon request.
*/
public final class Interval extends AbstractIntSortedSet implements IntSortedSet, Serializable {
private static final long serialVersionUID = 1L;
/** One-point intervals between 0 (inclusive) and this number (exclusive) are generated
* from a pre-computed array of instances. */
private final static int MAX_SINGLE_POINT = 1024;
/** The precomputed array of one-point intervals. */
private final static Interval[] POINT_INTERVAL = new Interval[MAX_SINGLE_POINT];
static {
int i = MAX_SINGLE_POINT;
while(i-- != 0) POINT_INTERVAL[i] = new Interval(i, i);
}
/** The left extreme of the interval. */
public final int left;
/** The right extreme of the interval. */
public final int right;
/** Builds an interval with given extremes.
*
*
You cannot generate an empty interval with this constructor. Use {@link Intervals#EMPTY_INTERVAL} instead.
*
* @param left the left extreme.
* @param right the right extreme (which must be greater than
* or equal to the left extreme).
*/
protected Interval(final int left, final int right) {
this.left = left;
this.right = right;
}
/** Returns an interval with given extremes.
*
*
You cannot obtain an empty interval with this factory method. Use {@link Intervals#EMPTY_INTERVAL} instead.
*
* @param left the left extreme.
* @param right the right extreme (which must be greater than
* or equal to the left extreme).
* @return an interval with the given extremes.
*/
public static Interval valueOf(final int left, final int right) {
if (left > right) throw new IllegalArgumentException("The left extreme (" + left + ") is greater than the right extreme (" + right + ")");
if (left == right) return valueOf(left);
return new Interval(left, right);
}
/** Returns a one-point interval.
*
*
You cannot obtain an empty interval with this factory method. Use {@link Intervals#EMPTY_INTERVAL} instead.
*
* @param point a point.
* @return a one-point interval
*/
public static Interval valueOf(final int point) {
if (point >= 0 && point < MAX_SINGLE_POINT) return POINT_INTERVAL[point];
return new Interval(point, point);
}
/** Returns the interval length, that is, the number of integers
* contained in the interval.
*
* @return the interval length.
*/
public int length() {
return right - left + 1;
}
/** An alias for {@link #length()}.
* @return the interval length.
*/
@Override
public int size() {
return length();
}
/** Returns an iterator over the integers in this interval.
*
* @return an integer iterator over the elements in this interval.
*/
@Override
public IntBidirectionalIterator iterator() {
if (this == EMPTY_INTERVAL) return IntIterators.EMPTY_ITERATOR;
// Note that fromTo() does NOT include the last integer.
return IntIterators.fromTo(left, right + 1);
}
/** Returns an iterator over the integers in this interval larger than or equal to a given integer.
*
* @param from the starting integer.
* @return an integer iterator over the elements in this interval.
*/
@Override
public IntBidirectionalIterator iterator(final int from) {
if (this == EMPTY_INTERVAL) return IntIterators.EMPTY_ITERATOR;
// Note that fromTo() does NOT include the last integer.
final IntBidirectionalIterator i = IntIterators.fromTo(left, right + 1);
if (from >= left) i.skip(Math.min(length(), from + 1 - left));
return i;
}
/** Checks whether this interval contains the specified integer.
*
* @param x an integer.
* @return whether this interval contains x, that is,
* whether {@link #left} ≤ x ≤ {@link #right}.
*/
@Override
public boolean contains(final int x) {
return x >= left && x <= right;
}
/** Checks whether this interval contains the specified interval.
*
* @param interval an interval.
* @return whether this interval contains (as a set) interval.
*/
public boolean contains(final Interval interval) {
if (interval == EMPTY_INTERVAL) return true;
if (this == EMPTY_INTERVAL) return false;
return left <= interval.left && interval.right <= right;
}
/** Checks whether this interval would contain the specified integer if enlarged in both
* directions by the specified radius.
*
* @param x an integer.
* @param radius the radius.
* @return whether this interval enlarged by radius would contain x,
* e.g., whether {@link #left}−radius ≤ x ≤ {@link #right}+radius.
*/
public boolean contains(final int x, final int radius) {
if (this == EMPTY_INTERVAL) throw new IllegalArgumentException();
return x >= left - radius && x <= right + radius;
}
/** Checks whether this interval would contain the specified integer if enlarged in each
* direction with the respective radius.
* directions by the specified radius.
*
* @param x an integer.
* @param leftRadius the left radius.
* @param rightRadius the right radius.
* @return whether this interval enlarged to the left by leftRadius
* and to the right by rightRadius would contain x,
* e.g., whether {@link #left}−leftRadius ≤ x ≤ {@link #right}+rightRadius.
*/
public boolean contains(final int x, final int leftRadius, final int rightRadius) {
if (this == EMPTY_INTERVAL) throw new IllegalArgumentException();
return x >= left - leftRadius && x <= right + rightRadius;
}
/** Compares this interval to an integer.
*
* @param x an integer.
* @return a negative integer, zero, or a positive integer as x is positioned
* at the left, belongs, or is positioned to the right of this interval, e.g.,
* as x < {@link #left},
* {@link #left} ≤ x ≤ {@link #right} or
* {@link #right} < x.
*/
public int compareTo(final int x) {
if (this == EMPTY_INTERVAL) throw new IllegalArgumentException();
if (x < left) return -1;
if (x > right) return 1;
return 0;
}
/** Compares this interval to an integer with a specified radius.
*
* @param x an integer.
* @param radius the radius.
* @return a negative integer, zero, or a positive integer as x is positioned
* at the left, belongs, or is positioned to the right of this interval enlarged by radius, that is,
* as x < {@link #left}−radius,
* {@link #left}−radius ≤ x ≤ {@link #right}+radius or
* {@link #right}+radius < x.
*/
public int compareTo(final int x, final int radius) {
if (this == EMPTY_INTERVAL) throw new IllegalArgumentException();
if (x < left - radius) return -1;
if (x > right + radius) return 1;
return 0;
}
/** Compares this interval to an integer with specified left and right radii.
*
* @param x an integer.
* @param leftRadius the left radius.
* @param rightRadius the right radius.
* @return a negative integer, zero, or a positive integer as x is positioned
* at the left, belongs, or is positioned to the right of this interval enlarged by leftRadius
* on the left and rightRadius in the right, that is,
* as x < {@link #left}−leftRadius,
* {@link #left}−leftRadius ≤ x ≤ {@link #right}+rightRadius or
* {@link #right}+rightRadius < x.
*/
public int compareTo(final int x, final int leftRadius, final int rightRadius) {
if (this == EMPTY_INTERVAL) throw new IllegalArgumentException();
if (x < left - leftRadius) return -1;
if (x > right + rightRadius) return 1;
return 0;
}
@Override
public IntComparator comparator() {
return null;
}
@Override
public IntSortedSet headSet(final int to) {
if (this == EMPTY_INTERVAL) return this;
if (to > left) return to > right ? this : valueOf(left, to - 1);
else return EMPTY_INTERVAL;
}
@Override
public IntSortedSet tailSet(final int from) {
if (this == EMPTY_INTERVAL) return this;
if (from <= right) return from <= left ? this : valueOf(from, right);
else return EMPTY_INTERVAL;
}
@Override
public IntSortedSet subSet(final int from, final int to) {
if (this == EMPTY_INTERVAL) return this;
if (from > to) throw new IllegalArgumentException("Start element (" + from + ") is larger than end element (" + to + ")");
if (to <= left || from > right || from == to) return EMPTY_INTERVAL;
if (from <= left && to > right) return this;
return valueOf(Math.max(left, from), Math.min(right, to - 1));
}
@Override
public int firstInt() {
if (this == EMPTY_INTERVAL) throw new NoSuchElementException();
return left;
}
@Override
public int lastInt() {
if (this == EMPTY_INTERVAL) throw new NoSuchElementException();
return right;
}
@Override
public String toString() {
if (this == EMPTY_INTERVAL) return "\u2205";
if (left == right) return "[" + left + "]";
return "[" + left + ".." + right + "]"; // Hoare's notation.
}
@Override
public int hashCode() {
return left * 23 + right;
}
/** Checks whether this interval is equal to another set of integers.
*
* @param o an object.
* @return true if o is an ordered set of integer containing
* the same element of this interval in the same order, or if o
* is a set of integers containing the same elements of this interval.
*/
@Override
public boolean equals(final Object o) {
if (o instanceof Interval)
return ((Interval)o).left == left && ((Interval)o).right == right;
else if (o instanceof IntSortedSet) { // For sorted sets, we require the same order
final IntSortedSet s = (IntSortedSet) o;
if (s.size() != length()) return false;
int n = length();
final IntIterator i = iterator(), j = s.iterator();
while(n-- != 0) if (i.nextInt() != j.nextInt()) return false;
return true;
}
else if (o instanceof IntSet) { // For sets, we just require the same elements
final IntSet s = (IntSet) o;
if (s.size() != length()) return false;
int n = length();
final IntIterator i = iterator();
while(n-- != 0) if (! s.contains(i.nextInt())) return false;
return true;
}
else return false;
}
}