From b05e956b5a6617807043e429e6bd891b5dbede09 Mon Sep 17 00:00:00 2001
From: Avi Parshan <avipars@users.noreply.github.com>
Date: Sun, 17 Mar 2024 19:23:03 +0200
Subject: [PATCH] dsa2

---
 _data/navigation.yml   |  3 +++
 data_struct2/README.md | 60 ++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 63 insertions(+)
 create mode 100644 data_struct2/README.md

diff --git a/_data/navigation.yml b/_data/navigation.yml
index 505482c..d3970d5 100644
--- a/_data/navigation.yml
+++ b/_data/navigation.yml
@@ -16,6 +16,9 @@
 - name: Data Structures
   link: /data_struct/
   
+- name: Data Structures2
+  link: /data_struct2/
+  
 - name: Digital Systems
   link: /DigitalSystems/
 
diff --git a/data_struct2/README.md b/data_struct2/README.md
new file mode 100644
index 0000000..9ecb5ec
--- /dev/null
+++ b/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)
\ No newline at end of file