dsa2

_data/navigation.yml

@@ -16,6 +16,9 @@
 - name: Data Structures
   link: /data_struct/
 
+- name: Data Structures2
+  link: /data_struct2/
+
 - name: Digital Systems
   link: /DigitalSystems/
 

data_struct2/README.md

@@ -0,0 +1,60 @@
+---
+layout: page
+title: Advanced Data Structures and Algorithms (DSA2)
+description: Linked Lists, Trees, Queues, Heaps, Stacks, etc. 
+date: '2024-03-17 12:24:11 -0400'
+permalink: /data_struct2/
+image: /static/post-image/bigo.png
+categories: DSA
+tags:
+- DataStruct
+- Algos
+- DataStructures2
+---
+
+## Advanced Data Structures and Algorithms (DSA2)
+
+Adjacency representation (for graphs)
+
+| Representation | Find Edge | Insert Edge | Delete Edge | Memory         |
+|----------------|-----------|-------------|-------------|----------------|
+| List           | O(|V|)    | O(1)        | O(|V|)      | Θ(|V|+|E|)    |
+| Matrix         | O(1)      | O(1)        | O(1)        | Θ(|V|^2)      |
+
+### Vertex colors
+
+- **White:** unprocessed/undiscovered
+- **Grey:** processing/not finished
+- **Black:** done/finished
+
+### Edge types
+
+- **Tree Edge**
+  - Parent to a child
+  - Goes to undiscovered vertex
+  - V finishes before U
+
+- **Back Edge**
+  - To an ancestor
+    - Of a vertex (parent, grandparent, etc.)
+  - Adding a back edge to tree edge makes a cycle
+    - To discovered but unfinished vertex
+  - In DFS, every back edge completes a cycle
+    - Removing back edges from a graph removes all cycles
+  - Self-edge = back edge
+  - V finishes after U
+
+- **Forward Edge**
+  - To a non-child descendant
+    - To a finished vertex discovered after the current vertex
+    - Indirect descendant (not child)
+  - V finishes before U
+
+- **Cross Edge**
+  - Everything else
+    - To a vertex finished before the current vertex's discovery
+  - One branch to another tree, or one tree to another
+  - V finishes before U
+
+
+[YouTube Playlist](https://www.youtube.com/playlist?list=PL9DdgseuDZgI4iVxPbjXJy4bMG-8DILVq)