yinengy / Algorithm-Implementation

Personal implementation of algorithms in Algorithm Design and some other useful algorithms and data structures

Algorithms in Algorithm Design

Summary

Personal implementation of Algorithm Design (Jon Kleinberg and Éva Tardos, 1st Edition, ISBN: 9780321295354) in Java.

Introduction

• Gale-Shapley - for Stable Matching Problem. Section 1.1, 9/6/2018

Graphs

• Adjacency List - a way to represent graph, support the implement of BFS and DFS. 9/22/2018
• Breadth-First Search - BFS for graph traversal. Section 3.3, 9/22/2018
• Depth-First Search - DFS for graph traversal. Section 3.3, 9/22/2018
• Find Topological Ordering - show the topological ordering of a DAG. Section 3.6, 9/24/2018
• Bipartite Graph - generate, label, and test a bipartite graph. To help the implementation of the Bipartite Matching Problem. Section 3.4, 11/14/2018

Greedy Algorithm

• Interval Scheduling - interval scheduling problem. Section 4.1, 10/5/2018
• Interval Partitioning - interval partitioning problem (interval coloring problem). Section 4.1, 10/5/2018
• Minimizing Lateness - scheduling to minimize lateness. Section 4.2, 10/5/2018
• Dijkstra's Algorithm - single-pair shortest path problem. Section 4.4, 10/7/2018
• Prim's Algorithm - minimum spanning tree problem. Section 4.5, 10/8/2018
• Union-Find Data Structure - help to implement Kruskal's Algorithm. Section 4.6, 10/8/2018
• Kruskal's Algorithm - another algorithm to solve minimum spanning tree problem. Section 4.6, 10/8/2018

Dynamic Programming

• Weighted Interval Scheduling - a version of interval scheduling problem with weight. Section 6.1, 11/3/2018
• Segmented Least Squares - segmented least squares problem. Section 6.3, 11/3/2018
• Knapsack Problem - a pseudo-polynomial time algorithm for Knapsack Problem. Section 6.4, 11/4/2018
• Sequence Alignment Problem - an algorithm for Sequence Alignment Problem. Section 6.6, 11/4/2018
• Bellman-Ford Algorithm - an algorithm for shortest path problem (with negative edges). Section 6.8, 11/10/2018

Network Flow

• Ford-Fulkerson Algorithm - find max flow in graph. Section 7.1, 11/11/2018.
  Update: two versions with improved time complexity by shortest augmenting path or capacity scaling. Section 7.3, 11/14/2018.
• Bipartite Matching - use max flow to find matching in a bipartite graph. Section 7.5, 11/15/2018.

Others

personal implementation of some useful algorithms and data structure.

• Trie Data Structure - use trie to speedup looking up word and finding prefixes. C++, 3/22/2019