vikashkodati / Algorithm-Design-Manual

Data structures, algorithms, and practice problems from Steven S. Skiena's "The Algorithm Design Manual" (Second Edition).

Implementations of data structures and algorithms inspired by Steven S. Skiena's The Algorithm Design Manual, The Second Edition.

Algorithms currently implemented:

Graphs

• A generic network flow algorithm for calculating the maximum flow possible in a network.
• A bipartite matching algorithm which uses a network flow algorithm to find the largest possible matching in a graph.
• Breadth-First Search
• Dijkstra's Algorithm for finding the shortest path.
• Floyd's Algorithm for finding all shortest path pairs in a graph.
• hamiltonian_cycle: Determine whether a graph G = (V, E) contains a hamiltonian cycle.
• Kruskal's Algorithm for finding the minimum-spanning-tree.
• Prim's Algorithm for finding the minimum-spanning tree.

Backtracking

• Backtracking for subsets and permutations.

Dynamic Programming

• A brute-force recursive partition-optimization routine.
• Matrix-based edit distance.
• Matrix-based integer partition.

Reductions

• is_satisfiable: Whether a given set of clauses C over a set of variables V can be satisfied via some truth assignment of each variable v_i.
• set_cover: Whether a set cover for a set X can be constructed from k subsets chosen from a family of subsets F.
• Translations into 3SAT for any satisfiability instance.
• vertex_cover_to_set: Solve a vertex cover instance by converting it to a satisfiability instance.
• vertex_cover_to_set_cover: Prove that set cover is NP-complete with a reduction from vertex cover.