README.md in union_find-0.0.1 vs README.md in union_find-0.0.2

@@ -10,14 +10,12 @@
 * Pixels in a digital photo
 * Metallic sites in a composite system
 
 Click [here](https://www.cs.princeton.edu/~rs/AlgsDS07/01UnionFind.pdf) for more information.
 
-The running time of this algorithm is linear.
+This a Ruby implementation of a modified version of [Robert Sedgewick](http://www.cs.princeton.edu/~rs/)'s and [Kevin Wayne](http://www.cs.princeton.edu/~wayne/contact/)'s [weighted quick-union algorithm with path compression](http://algs4.cs.princeton.edu/15uf/UF.java.html). Credit goes to these two authors of the book [Algorithms](http://www.amazon.com/gp/product/032157351X/ref=as_li_qf_sp_asin_il_tl?ie=UTF8&tag=algs4-20&linkCode=as2&camp=1789&creative=9325&creativeASIN=032157351X) and to the many computer scientists that have contributed to this algorithm in the past decades.
 
-This a Ruby implementation of [Robert Sedgewick](http://www.cs.princeton.edu/~rs/)'s and [Kevin Wayne](http://www.cs.princeton.edu/~wayne/contact/)'s [weighted quick-union algorithm with path compression](http://algs4.cs.princeton.edu/15uf/UF.java.html). Credit goes to these two authors of the book [Algorithms](http://www.amazon.com/gp/product/032157351X/ref=as_li_qf_sp_asin_il_tl?ie=UTF8&tag=algs4-20&linkCode=as2&camp=1789&creative=9325&creativeASIN=032157351X) and to the many computer scientists that have contributed to this algorithm in the past decades.
-
 ## Installation
 
 Add this line to your application's Gemfile:
 
     gem 'union_find'
@@ -30,19 +28,36 @@
 
     $ gem install union_find
 
 ## Usage
 
-Create a new instance of `UnionFind` and pass in an array of items:
+Create a new instance of `UnionFind` and pass in a `Set` of items:
 
 ```ruby
-union_find = UnionFind::UnionFind.new(['Grandfather', 'Father', 'Daughter', 'Single Person'])
+require 'set'
+people = Set.new ['Grandfather', 'Father', 'Daughter', 'Single Person']
+union_find = UnionFind::UnionFind.new(people)
 ```
 
+A `Set` is used instead of an `Array` because `Sets` filter out duplicate entries without having to call an expensive `#uniq!` method. If your data comes in form of an `Array`, you can convert it to a `Set` like so:
+
+```ruby
+require 'set'
+array = ['Grandfather', 'Father', 'Daughter', 'Single Person']
+set = array.to_set
+```
+
+Add more items on the fly:
+
+```ruby
+union_find.add('Grandmother')
+```
+
 Connect items (in any order):
 
 ```ruby
+union_find.union('Grandfather', 'Grandmother')
 union_find.union('Grandfather', 'Father')
 union_find.union('Father', 'Daughter')
 ```
 
 Check whether two items are connected (in any order):
@@ -54,15 +69,23 @@
 => true
 union_find.connected?('Grandfather', 'Single Person')
 => false
 ```
 
-Check how many isolated items there are. In this example, there are 2, namely the family the family tree (Grandfather - Father - Daugther) and the Single Person:
+Check how many isolated items there are. In this example, there are 2, namely the family (Grandfather - Grandmother - Father - Daugther) and the Single Person:
 
 ```ruby
 union_find.count_isolated_components
 => 2
 ```
+
+## Performance
+
+Initializing a data structure takes constant time: θ(1).
+
+Afterwards, the `union()` and `connected?()` operations take logarithmic time in the worst case: O(log n).
+
+The `count_isolated_components()` operation takes constant time: θ(1).
 
 ## Contributing
 
 1. Fork it ( https://github.com/[my-github-username]/union_find/fork )
 2. Create your feature branch (`git checkout -b my-new-feature`)