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Graph Theory
2-SAT
Problemset
Discussion
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Graph Fundamentals
0/41
Depth First Search (DFS)
0/41
Breadth First Search (BFS)
0/40
Flood Fill & Grid Graphs
0/32
Bipartite Graphs
0/48
Tree Fundamentals
0/44
Tree Diameter & Center
0/45
Subtree DP
0/44
Floyd-Warshall Algorithm
0/41
Dijkstra's Algorithm
0/40
Bellman-Ford Algorithm
0/48
Mixed Practice - Shortest Paths
0/36
Disjoint Set Union (DSU)
0/49
Minimum Spanning Trees
0/48
Topological Sort
0/41
DP on DAGs
0/50
Mixed Practice: Graph Traversals
0/35
Strongly Connected Components
0/45
2-SAT
0/51
1
Intro
2
What is SAT
3
The 2-SAT Restriction
4
Variables and Negations
5
Implication Graphs
6
Converting OR to Implication
7
Why This Works
8
Example Conversion
9
Quiz: Implication Graph Construction
10
The SCC Connection
11
Why Same SCC Fails
12
Finding an Assignment
13
Why Topological Order Works
14
Algorithm Summary
15
Complexity Analysis
16
Quiz: Satisfiability Check
17
Problem - Giant Pizza
18
Modeling as 2-SAT
19
Building the Implication Graph
20
Checking Satisfiability
21
Constructing the Assignment
22
Giant Pizza - Implementation
23
Edge Case - All Positive
24
Edge Case - Contradiction
25
Lessons from Giant Pizza
26
Quiz: Assignment Construction
27
Constraint Pattern - At Most One
28
Constraint Pattern - Exactly One
29
Constraint Pattern - If-Then
30
Multiple Clauses on Same Variables
31
Quiz: Clause Conversion
32
Problem - Course Scheduling
33
Modeling Scheduling
34
Scheduling Solution
35
Lessons from Scheduling
36
When to Use 2-SAT
37
Extensions Beyond 2-SAT
38
Common Mistakes
39
Debugging 2-SAT Solutions
40
Quiz: Debugging 2-SAT
41
Vocabulary - Clause
42
Vocabulary - Literal
43
Vocabulary - Satisfiable
44
Vocabulary - Implication
45
Practice Problem 1
46
Practice Problem 2
47
Practice Problem 3
48
Visualization Tip
49
Connection to Other Topics
50
Quiz: Recognizing 2-SAT
51
Section Recap
Mixed Practice: Connectivity & MST
0/35
Rerooting Technique
0/39
Euler Tour Technique
0/51
Mixed Practice: Tree Fundamentals
0/29
Binary Lifting
0/50
Lowest Common Ancestor (LCA)
0/51
Games on Graphs
0/62
Heavy-Light Decomposition
0/49
Centroid Decomposition
0/55
Small-to-Large Merging
0/40
Functional Graphs
0/47
Mixed Practice: Advanced Tree Techniques
0/36
Bridges and Articulation Points
0/58
Network Flow
0/54
Maximum Bipartite Matching
0/50
Minimum Cut
0/47
Euler Paths and Circuits
0/37
Mixed Practice: Advanced Graphs
0/24
19.1
Intro
3 minutes
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Tasks
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