Topics and Basic Concepts

Topics

Fundamental data structures

• Array, list, stack, queue, heap, tree, and graph
• Graph traversal algorithms: DFS and BFS

Algorithm analysis

• Asymptotic notations and analysis
• Time and space complexities

Fundamental algorithms:

• Sorting
• Shortest path
• Minimum spanning tree
• Topological sort
• Dynamic programming

Stack and Queue

• Stack
• Queue

Tree and Graph

• Tree
• Graph

Algorithm Analysis

Suppose that we have two algorithms. As a computer scientist, how can you tell which is better?

• Insertion sort vs merge sort
• Merge sort vs quicksort

(Asymptotic) Algorithm analysis to evaluate solutions

• Time/space complexities
• Weak ordering

Shortest Path

• A path between two nodes in a graph such that the sum of weights of its constituent edges is minimized.

Minimum Spanning Tree

Topological Sort and Critical Path

Dynamic Programming

Interval scheduling

• A largest set of non-overlapping intervals

Edit distance

Matrix chain multiplication

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