## CERTIFICATE IN DESIGN AND ANALYSIS OF ALGORITHMS

Duration: 3 MONTHS

## Course Syllabus

• INTRODUCTION
• Notion of an Algorithm , Fundamentals of Algorithmic Problem Solving , Important Problem Types ,Fundamentals of the Analysis of Algorithm Efficiency , Analysis Framework , Asymptotic Notations and its properties , Mathematical analysis for Recursive and Non,recursive algorithms.
• BRUTE FORCE AND DIVIDE AND CONQUER
• Brute Force , Closest,Pair and Convex,Hull Problems,Exhaustive Search , Traveling Salesman Problem , Knapsack Problem , Assignment problem. Divide and conquer methodology , Merge sort ,Quick sort , Binary search , Multiplication of Large Integers , Strassen’s Matrix Multiplication Closest, Pairand Convex,Hull Problems.
• DYNAMIC PROGRAMMING AND GREEDY TECHNIQUE
• Computing a Binomial Coefficient , Warshall’s and Floyd’ algorithm , Optimal Binary Search Trees ,Knapsack Problem and Memory functions. Greedy Technique, Prim’s algorithm, Kruskal's Algorithm ,Dijkstra's Algorithm,Huffman Trees.
• ITERATIVE IMPROVEMENT
• The Simplex Method,The Maximum,Flow Problem , Maximum Matching in Bipartite Graphs, The Stable marriage Problem.
• COPING WITH THE LIMITATIONS OF ALGORITHM POWER
• Limitations of Algorithm Power,Lower,Bound Arguments,Decision Trees,P, NP and NP,Complete Problems,,Coping with the Limitations , Backtracking , n-Queens problem , Hamiltonian CircuitProblem , Subset Sum Problem,Branch and Bound , Assignment problem , Knapsack Problem ,Traveling Salesman Problem, Approximation Algorithms for NP , Hard Problems , Traveling Salesman problem , Knapsack problem.

## Eligibility

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