475 lines
14 KiB
Java
475 lines
14 KiB
Java
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package com.jwetherell.algorithms.data_structures;
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import java.util.ArrayList;
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import java.util.Collection;
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import java.util.Collections;
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import java.util.Comparator;
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import java.util.HashSet;
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import java.util.List;
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import java.util.Set;
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/**
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* An interval tree is an ordered tree data structure to hold intervals.
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* Specifically, it allows one to efficiently find all intervals that overlap
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* with any given interval or point.
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*
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* http://en.wikipedia.org/wiki/Interval_tree
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*
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* @author Justin Wetherell <phishman3579@gmail.com>
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*/
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public class IntervalTree<O extends Object> {
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private Interval<O> root = null;
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private static final Comparator<IntervalData<?>> START_COMPARATOR = new Comparator<IntervalData<?>>() {
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/**
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* {@inheritDoc}
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*/
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@Override
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public int compare(IntervalData<?> arg0, IntervalData<?> arg1) {
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// Compare start first
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if (arg0.start < arg1.start)
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return -1;
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if (arg1.start < arg0.start)
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return 1;
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return 0;
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}
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};
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private static final Comparator<IntervalData<?>> END_COMPARATOR = new Comparator<IntervalData<?>>() {
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/**
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* {@inheritDoc}
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*/
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@Override
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public int compare(IntervalData<?> arg0, IntervalData<?> arg1) {
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// Compare end first
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if (arg0.end > arg1.end)
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return -1;
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if (arg1.end > arg0.end)
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return 1;
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return 0;
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}
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};
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/**
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* Create interval tree from list of IntervalData objects;
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*
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* @param intervals
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* is a list of IntervalData objects
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*/
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public IntervalTree(List<IntervalData<O>> intervals) {
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if (intervals.size() <= 0)
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return;
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root = createFromList(intervals);
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}
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protected static final <O extends Object> Interval<O> createFromList(List<IntervalData<O>> intervals) {
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Interval<O> newInterval = new Interval<O>();
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if (intervals.size()==1) {
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IntervalData<O> middle = intervals.get(0);
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newInterval.center = ((middle.start + middle.end) / 2);
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newInterval.add(middle);
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return newInterval;
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}
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int half = intervals.size() / 2;
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IntervalData<O> middle = intervals.get(half);
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newInterval.center = ((middle.start + middle.end) / 2);
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List<IntervalData<O>> leftIntervals = new ArrayList<IntervalData<O>>();
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List<IntervalData<O>> rightIntervals = new ArrayList<IntervalData<O>>();
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for (IntervalData<O> interval : intervals) {
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if (interval.end < newInterval.center) {
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leftIntervals.add(interval);
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} else if (interval.start > newInterval.center) {
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rightIntervals.add(interval);
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} else {
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newInterval.add(interval);
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}
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}
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if (leftIntervals.size() > 0)
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newInterval.left = createFromList(leftIntervals);
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if (rightIntervals.size() > 0)
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newInterval.right = createFromList(rightIntervals);
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return newInterval;
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}
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/**
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* Stabbing query
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*
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* @param index
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* to query for.
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* @return data at index.
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*/
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public IntervalData<O> query(long index) {
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return root.query(index);
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}
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/**
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* Range query
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*
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* @param start
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* of range to query for.
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* @param end
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* of range to query for.
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* @return data for range.
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*/
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public IntervalData<O> query(long start, long end) {
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return root.query(start, end);
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}
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/**
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* {@inheritDoc}
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*/
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@Override
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public String toString() {
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StringBuilder builder = new StringBuilder();
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builder.append(IntervalTreePrinter.getString(this));
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return builder.toString();
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}
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protected static class IntervalTreePrinter {
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public static <O extends Object> String getString(IntervalTree<O> tree) {
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if (tree.root == null)
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return "Tree has no nodes.";
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return getString(tree.root, "", true);
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}
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private static <O extends Object> String getString(Interval<O> interval, String prefix, boolean isTail) {
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StringBuilder builder = new StringBuilder();
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builder.append(prefix + (isTail ? "└── " : "├── ") + interval.toString() + "\n");
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List<Interval<O>> children = new ArrayList<Interval<O>>();
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if (interval.left != null)
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children.add(interval.left);
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if (interval.right != null)
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children.add(interval.right);
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if (children.size() > 0) {
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for (int i = 0; i < children.size() - 1; i++)
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builder.append(getString(children.get(i), prefix + (isTail ? " " : "│ "), false));
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if (children.size() > 0)
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builder.append(getString(children.get(children.size() - 1), prefix + (isTail ? " " : "│ "), true));
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}
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return builder.toString();
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}
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}
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public static final class Interval<O> {
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private long center = Long.MIN_VALUE;
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private Interval<O> left = null;
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private Interval<O> right = null;
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private List<IntervalData<O>> overlap = new ArrayList<IntervalData<O>>();
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private void add(IntervalData<O> data) {
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overlap.add(data);
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}
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/**
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* Stabbing query
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*
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* @param index
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* to query for.
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* @return data at index.
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*/
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public IntervalData<O> query(long index) {
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IntervalData<O> results = null;
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if (index < center) {
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// overlap is sorted by start point
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Collections.sort(overlap,START_COMPARATOR);
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for (IntervalData<O> data : overlap) {
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if (data.start > index)
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break;
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IntervalData<O> temp = data.query(index);
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if (results == null && temp != null)
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results = temp;
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else if (results != null && temp != null)
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results.combined(temp);
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}
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} else if (index >= center) {
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// overlap is reverse sorted by end point
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Collections.sort(overlap,END_COMPARATOR);
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for (IntervalData<O> data : overlap) {
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if (data.end < index)
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break;
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IntervalData<O> temp = data.query(index);
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if (results == null && temp != null)
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results = temp;
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else if (results != null && temp != null)
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results.combined(temp);
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}
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}
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if (index < center) {
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if (left != null) {
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IntervalData<O> temp = left.query(index);
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if (results == null && temp != null)
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results = temp;
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else if (results != null && temp != null)
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results.combined(temp);
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}
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} else if (index >= center) {
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if (right != null) {
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IntervalData<O> temp = right.query(index);
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if (results == null && temp != null)
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results = temp;
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else if (results != null && temp != null)
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results.combined(temp);
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}
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}
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return results;
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}
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/**
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* Range query
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*
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* @param start
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* of range to query for.
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* @param end
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* of range to query for.
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* @return data for range.
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*/
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public IntervalData<O> query(long start, long end) {
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IntervalData<O> results = null;
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for (IntervalData<O> data : overlap) {
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if (data.start > end)
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break;
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IntervalData<O> temp = data.query(start, end);
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if (results == null && temp != null)
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results = temp;
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else if (results != null && temp != null)
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results.combined(temp);
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}
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if (left != null && start < center) {
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IntervalData<O> temp = left.query(start, end);
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if (temp != null && results == null)
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results = temp;
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else if (results != null && temp != null)
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results.combined(temp);
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}
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if (right != null && end >= center) {
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IntervalData<O> temp = right.query(start, end);
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if (temp != null && results == null)
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results = temp;
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else if (results != null && temp != null)
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results.combined(temp);
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}
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return results;
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}
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/**
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* {@inheritDoc}
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*/
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@Override
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public String toString() {
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StringBuilder builder = new StringBuilder();
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builder.append("Center=").append(center);
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builder.append(" Set=").append(overlap);
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return builder.toString();
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}
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}
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/**
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* Data structure representing an interval.
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*/
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public static class IntervalData<O> implements Comparable<IntervalData<O>> {
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private long start = Long.MIN_VALUE;
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private long end = Long.MAX_VALUE;
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private Set<O> set = new HashSet<O>();
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/**
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* Interval data using O as it's unique identifier
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*
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* @param object
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* Object which defines the interval data
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*/
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public IntervalData(long index, O object) {
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this.start = index;
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this.end = index;
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this.set.add(object);
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}
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/**
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* Interval data using O as it's unique identifier
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*
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* @param object
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* Object which defines the interval data
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*/
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public IntervalData(long start, long end, O object) {
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this.start = start;
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this.end = end;
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this.set.add(object);
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}
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/**
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* Interval data list which should all be unique
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*
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* @param list
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* of interval data objects
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*/
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public IntervalData(long start, long end, Set<O> set) {
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this.start = start;
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this.end = end;
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this.set = set;
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}
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/**
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* Get the start of this interval
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*
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* @return Start of interval
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*/
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public long getStart() {
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return start;
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}
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/**
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* Get the end of this interval
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*
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* @return End of interval
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*/
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public long getEnd() {
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return end;
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}
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/**
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* Get the data set in this interval
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*
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* @return Unmodifiable collection of data objects
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*/
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public Collection<O> getData() {
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return Collections.unmodifiableCollection(this.set);
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}
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/**
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* Clear the indices.
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*/
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public void clear() {
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this.start = Long.MIN_VALUE;
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this.end = Long.MAX_VALUE;
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this.set.clear();
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}
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/**
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* Combined this IntervalData with data.
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*
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* @param data
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* to combined with.
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* @return Data which represents the combination.
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*/
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public IntervalData<O> combined(IntervalData<O> data) {
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if (data.start < this.start)
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this.start = data.start;
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if (data.end > this.end)
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this.end = data.end;
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this.set.addAll(data.set);
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return this;
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}
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/**
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* Deep copy of data.
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*
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* @return deep copy.
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*/
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public IntervalData<O> copy() {
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Set<O> copy = new HashSet<O>();
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copy.addAll(set);
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return new IntervalData<O>(start, end, copy);
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}
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/**
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* Query inside this data object.
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*
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* @param start
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* of range to query for.
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* @param end
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* of range to query for.
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* @return Data queried for or NULL if it doesn't match the query.
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*/
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public IntervalData<O> query(long index) {
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if (index < this.start || index > this.end)
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return null;
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return copy();
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}
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/**
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* Query inside this data object.
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*
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* @param startOfQuery
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* of range to query for.
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* @param endOfQuery
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|
|
* of range to query for.
|
||
|
|
* @return Data queried for or NULL if it doesn't match the query.
|
||
|
|
*/
|
||
|
|
public IntervalData<O> query(long startOfQuery, long endOfQuery) {
|
||
|
|
if (endOfQuery < this.start || startOfQuery > this.end)
|
||
|
|
return null;
|
||
|
|
|
||
|
|
return copy();
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* {@inheritDoc}
|
||
|
|
*/
|
||
|
|
@Override
|
||
|
|
public int hashCode() {
|
||
|
|
return 31 * ((int)(this.start + this.end)) + this.set.size();
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* {@inheritDoc}
|
||
|
|
*/
|
||
|
|
@SuppressWarnings("unchecked")
|
||
|
|
@Override
|
||
|
|
public boolean equals(Object obj) {
|
||
|
|
if (!(obj instanceof IntervalData))
|
||
|
|
return false;
|
||
|
|
|
||
|
|
IntervalData<O> data = (IntervalData<O>) obj;
|
||
|
|
if (this.start == data.start && this.end == data.end) {
|
||
|
|
if (this.set.size() != data.set.size())
|
||
|
|
return false;
|
||
|
|
for (O o : set) {
|
||
|
|
if (!data.set.contains(o))
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* {@inheritDoc}
|
||
|
|
*/
|
||
|
|
@Override
|
||
|
|
public int compareTo(IntervalData<O> d) {
|
||
|
|
if (this.end < d.end)
|
||
|
|
return -1;
|
||
|
|
if (d.end < this.end)
|
||
|
|
return 1;
|
||
|
|
return 0;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* {@inheritDoc}
|
||
|
|
*/
|
||
|
|
@Override
|
||
|
|
public String toString() {
|
||
|
|
StringBuilder builder = new StringBuilder();
|
||
|
|
builder.append(start).append("->").append(end);
|
||
|
|
builder.append(" set=").append(set);
|
||
|
|
return builder.toString();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|