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**Theory of algorithms**

Theory of algorithms refers to the branch of mathematics which focuses on the ideas and methods to be applied on non costructuve objects only if these are encoded as constructive objects by dealing with general properties of algorithms.The important part of theory of algorithm is general properties of encodings which is basically the theory of enumeration.It is of two types i.e descriptive (qualitative) and the metric (quantitative) theory.

Few Topics are:

- Running time, Insertion sort
- binary search, merge two sorted arrays
- Merge sort+
- Binary trees, heaps,Heapsort
- Priority queues, Quicksort
- Analysis of quicksort, Randomized Quicksort
- Radix sort, Bucket sort
- stack and queues
- Linked lists
- Pointers and objects, representing rooted trees
- Hash tables, hashing with chaining
- Hash functions
- Binary search trees
- Red-black trees
- Graph representations, BFS
- DFS
- Topological sort

**Sample Assignment**

**Theory of algorithms**

- Reductions,Greedy algorithms,Minimum spanning trees,Dynamic programming,Shortest paths algorithms,Bellman-Ford,Floyd-Warshall, Depth First Search (DFS)
- strongly connected components,topological sort,Maximum flow algorithms of Ford-Fulkerson Dinitz,Applications to matching and assignment problems
- Randomized algorithms,String matching,Introduction to complexity theory,complexity classes,Cook-Levin theorem,techniques for proving NP-completenes
- Induction,Recurrence relations,Big-Oh and little-Oh notation,Merge sort,Graph Algorithms,Depth-first search,strongly connected components
- Breadth-first search,Dijkstra's algorithm,Greedy Algorithms,Minimum spanning tree,Union find,Set cover,Huffman coding,Dynamic Programming
- Longest common subsequence,Traveling salesman,Divide and Conquer,Integer multiplication,Matrix multiplication,Hashing,Balls into bins problems
- Bloom filters,Document similarity,Linear Programming,Problem definitions and solution techniques,Reductions,Maximum matching, Randomized Algorithms
- Primality testing and factoring, RSA,Random walks and 2-SAT,NP-completeness review,Basic NP-complete problems,Novel approaches to NP-complete problems

**Theory of algorithms includes:**

- Approximation algorithms,Heuristic algorithms,Stable matching, implementation, running times,Graphs and basic graph algorithms,Greedy algorithms for optimization problems
- Divide-and-conquer,fast multiplication of integers,matrices and polynomials,Dynamic programming ,Max-flow/min-cut, polynomial time algorithms,introduction to NP
- Lower bounds and approximation algorithms,Local search and heuristic approaches,Randomized algorithms, median-finding and order statistics,Introduction and document distance
- More document distance, mergesort,Binary search trees,Airplane scheduling, binary search trees,Balanced binary search trees,Hashing: chaining, hash functions
- table doubling, Karp-Rabin,open addressing ,Sorting:heaps , lower bounds, linear-time sorting,stable sorting, radix sort ,Searching: graph search, representations, and applications
- breadth-first search and depth-first search , topological sort and NP-completeness ,Shortest paths,Shortest paths: intro ,Bellman-Ford ,Dijkstra, Dijkstra speedups
- Dynamic programming:memoization, Fibonacci, Crazy Eights, guessing, longest common subsequence, parent pointers ,text justification, parenthesization, knapsack
- pseudopolynomial time, Tetris training,piano fingering, structural DP (trees), vertex cover, dominating set, and beyond,Numerics,Beyond 6.006: follow-on classes, geometric folding algorithms