Update README.md

Author: dan-on

README.md

@@ -1,46 +1,123 @@
 # PHP Interval tree
-Implementation of interval binary search tree.
 
-## Installing
+## Overview
+
+Package **dan-on/php-interval-tree** is an implementation of self balancing binary search tree data structure called Red-Black Tree.
+
+Based on interval tree described in "Introduction to Algorithms 3rd Edition", published by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein.
+
+## Complexity
+
+| Operation | Best, Average, Worst   |
+|-----------|------------------------|
+| Insertion | O(log(n))              |
+| Search    | O(log(n))              |
+| Remove    | O(log(n))              |
+| Space     | O(n)                   |
+
+## Installing via Composer
+
 ```
 composer require dan-on/php-interval-tree
 ```
 
 ## Usage
 
+### Intervals
+
+There are numeric and DateTimeInterface-based interval types included.
+
+#### Numeric interval
+
 ```php
-<?php
-require_once 'vendor/autoload.php';
+use Danon\IntervalTree\Interval\NumericInterval;
+
+// Instantiate numeric interval from array
+$numericInterval = NumericInterval::fromArray([1, 100]);
 
+// Instantiate numeric interval with constructor
+$numericInterval = new NumericInterval(1, 100);
+```
+
+#### DateTime interval
+```php
+use Danon\IntervalTree\Interval\DateTimeInterval;
+
+// Instantiate DateTime interval from array
+$dateTimeInterval = DateTimeInterval::fromArray([
+    new DateTimeImmutable('2021-01-01 00:00:00'),
+    new DateTimeImmutable('2021-01-02 00:00:00'),
+]);
+
+// Instantiate DateTime interval with constructor
+$dateTimeInterval = new DateTimeInterval(
+    new DateTimeImmutable('2021-01-01 00:00:00'), 
+    new DateTimeImmutable('2021-01-02 00:00:00')
+);
+```
+
+### Interval Tree
+
+#### insert(IntervalInterface $interval, mixed $value): void
+Insert new pair (interval + value) into interval tree
+```php
 use Danon\IntervalTree\IntervalTree;
 
 $tree = new IntervalTree();
-$intervals = [[6, 8], [1, 4], [2, 3], [5, 12], [1, 1], [3, 5], [5, 7]];
-        
-// Insert interval as a key and interval index as a value 
-for ($i=0; $i < count($intervals); $i++) {
-    $tree->insert($intervals[$i], $i);
-}
+$tree->insert(new NumericInterval(1, 10), 'val1');
+$tree->insert(new NumericInterval(2, 5), 'val2');
+$tree->insert(new NumericInterval(11, 12), 'val3');
+```
 
-// Iterate nodes which keys intersect with given interval
-$nodesInRange = $tree->iterateIntersections([2, 3]);
-$intersectedIntervalIndexes = [];
-foreach ($nodesInRange as $node) {
-    $intersectedIntervalIndexes[] = $node->getValue();
+#### findIntersections(IntervalInterface $interval): Iterator\<Pair>
+Find pairs which intervals intersect with given interval
+```php
+$intersections = $tree->findIntersections(new NumericInterval(3, 5));
+foreach($intersections as $pair) {
+    $pair->getInterval()->getLow(); // 1, 2
+    $pair->getInterval()->getHigh(); // 10, 5
+    $pair->getValue(); // 'val1', 'val2'
 }
-// Expected array: [1, 2, 5]
+```
+
+#### hasIntersection(IntervalInterface $interval): bool
+Returns true if interval has at least one intersection in tree
+```php
+$tree->hasIntersection(new NumericInterval(3, 5)); // true
+```
 
-// Check that interval has at least one intersection
-$tree->hasIntersection([2, 3]);
-// Expected value: true
+#### countIntersections(IntervalInterface $interval): int
+Count intervals that has intersections
+```php
+$tree->countIntersections(new NumericInterval(3, 5)); // 2
+```
 
-// Count intervals that has intersections
-$tree->countIntersections([2, 3]);
-// Expected value: 3
+#### remove(IntervalInterface $interval, $value): bool
+Remove node from tree by interval and value
+```php
+$tree->remove(new NumericInterval(11, 12), 'val3'); // true
+```
+
+#### exist(IntervalInterface $interval, $value): bool
+Returns true if interval and value exist in the tree
+```php
+$tree->exists(new NumericInterval(11, 12), 'val3'); // true
+```
+
+#### isEmpty(): bool
+Returns true if tree is empty
+```php
+$tree->isEmpty(); // false
+```
+
+#### getSize(): int
+Returns number of items stored in the interval tree
+```php
+$tree->getSize(); // 3
 ```
 
 ## Tests
 
 ```
-./vendor/bin/phpunit tests
+./vendor/bin/phpunit
 ```