9 Questions
What is a characteristic of an undirected graph?
Edges do not have direction
What algorithm is used to find the shortest path in weighted graphs with negative weight edges?
Bellman-Ford algorithm
What is the main difference between DFS and BFS algorithms?
DFS traverses as far as possible along each branch, BFS traverses level by level
What is the main goal of a Minimum Spanning Tree algorithm?
To find the minimum spanning tree in a weighted graph
What is the main characteristic of a greedy algorithm?
Make optimal choice at each step
What is the main goal of a Dynamic Programming algorithm?
To break down problem into smaller sub-problems and solve each sub-problem recursively
What is the main characteristic of a Divide and Conquer algorithm?
Break down problem into smaller sub-problems
What is the main goal of a Backtracking algorithm?
To try different solutions until a valid solution is found
What is the main characteristic of a Dynamic Search algorithm?
Use heuristics to guide search towards optimal solution
Study Notes
Graph Algorithms
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Types of Graphs
- Undirected graphs: edges do not have direction
- Directed graphs (digraphs): edges have direction
- Weighted graphs: edges have weights or labels
-
Graph Traversal Algorithms
- Breadth-First Search (BFS): traverses graph level by level
- Depth-First Search (DFS): traverses graph by exploring as far as possible along each branch
-
Shortest Path Algorithms
- Dijkstra's algorithm: finds shortest path in weighted graphs
- Bellman-Ford algorithm: finds shortest path in weighted graphs with negative weight edges
-
Minimum Spanning Tree Algorithms
- Kruskal's algorithm: finds minimum spanning tree in weighted graphs
- Prim's algorithm: finds minimum spanning tree in weighted graphs
Algorithm Design Techniques
-
Divide and Conquer
- Break down problem into smaller sub-problems
- Solve each sub-problem recursively
- Combine solutions to solve original problem
-
Dynamic Programming
- Break down problem into smaller sub-problems
- Solve each sub-problem and store solution
- Combine solutions to solve original problem
-
Greedy Algorithms
- Make optimal choice at each step
- Hope that local optimum leads to global optimum
-
Backtracking
- Try different solutions until a valid solution is found
- Use recursion to explore different possibilities
-
Dynamic Search
- Use heuristics to guide search towards optimal solution
- Use iterative improvement to refine solution
Test your understanding of graph algorithms and design techniques, including graph traversal, shortest path, and minimum spanning tree algorithms, as well as divide and conquer, dynamic programming, greedy algorithms, and backtracking.
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