Small edits to doubly linked list notes.

Author: aubertc

source/lectures/data/DLList.md

@@ -5,16 +5,22 @@ tags:
 
 # Doubly Linked List
 
-Here is *yet* another implementation of the list abstract data type, using *doubly linked list*.
+## Motivation
 
-```{download="./code/projects/DLList_ICollection.zip"}
-!include code/projects/DLList_ICollection/DLList_ICollection/DLList.cs
-```
+We can implement the list abstract datatype using *doubly linked lists*.
 
 The main differences with *singly* linked list are as follows:
 
 - Instead of keeping only track of the first element (`first`), we keep track of both the first (`head`) and last (`tail`) elements.
 - Each `Cell` contains a pointer to the "next" element (as before), but also to the "previous" element.
 - Adding (or removing) to the right is now done in constant time, instead of linear time.
-- Traversing the list in opposite order (from end to beginning, or right to left) is now straightforward (cf. the `ToString` method above).
+- Traversing the list in opposite order (from end to beginning, or right to left) is now straightforward (cf. the `ToString` method).
 - The rest of the edits are about bookkeeping the `Previous` and `Next` attributes of the `Cell`, as well as updating the `tail` attribute. This makes removing and adding "in the middle of the list" a bit tricky.
+
+## Implementation
+
+Our implementation of doubly linked list realizes the ICollection interface:
+
+```{download="./code/projects/DLList_ICollection.zip"}
+!include code/projects/DLList_ICollection/DLList_ICollection/DLList.cs
+```