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Design and Analysis of Algorithms 2015 Design and Analysis of Algorithms 2015 DESIGN AND ANALYSIS OF ALGORITHMS UNIT-I ________________________________________________________________________________ INTRODUCTION: Algorithm,pseudocode for expressing algorithms,performance analysis- Time complexity and space complexity, asymptotic noatation- O notation Omega notation and Theta notation and little on notation,probabilistic analysis,amortized complexity. DIVIDE AND CONQUER: General Method, applications-Binary search,merge sort, quick sort, strassen’s matrix multiplication. ___________________________________________________________________________________- P.Harikrishna Assistant Professor CSE Dept MRCET Page 1 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 2 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 3 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 4 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 5 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 6 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 7 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 8 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 9 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 10 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 11 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 12 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 13 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 14 Design and Analysis of Algorithms 2015 Divide and conquer P.Harikrishna Assistant Professor CSE Dept MRCET Page 15 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 16 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 17 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 18 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 19 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 20 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 21 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 22 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 23 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 24 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 25 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 26 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 27 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 28 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 29 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 30 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 31 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 32 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 33 Design and Analysis of Algorithms 2015 Worst case Strassen matrix multiplication P.Harikrishna Assistant Professor CSE Dept MRCET Page 34 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 35 Design and Analysis of Algorithms 2015 P.Harikrishna Assistant Professor CSE Dept MRCET Page 36 Design and2015 analysis of algorithms 2015 UNIT-2 Efficient non recursive tree traversal algorithms Non recursive Inorder traversal algorithm P .HARIKRISHNA Assistant professor CSE Dept MRCET Page 1 Design and2015 analysis of algorithms 2015 Non recursive preorder traversal algorithm Non recursive postorder traversal algorithm P .HARIKRISHNA Assistant professor CSE Dept MRCET Page 2 Design and2015 analysis of algorithms 2015 P .HARIKRISHNA Assistant professor CSE Dept MRCET Page 3 Design and2015 analysis of algorithms 2015 P .HARIKRISHNA Assistant professor CSE Dept MRCET Page 4 Design and2015 analysis of algorithms 2015 P .HARIKRISHNA Assistant professor CSE Dept MRCET Page 5 Design and2015 analysis of algorithms 2015 P .HARIKRISHNA Assistant professor CSE Dept MRCET Page 6 Design and2015 analysis of algorithms 2015 P .HARIKRISHNA Assistant professor CSE Dept MRCET Page 7 Design and2015 analysis of algorithms 2015 Graph Traversals P .HARIKRISHNA Assistant professor CSE Dept MRCET Page 8 Design and2015 analysis of algorithms 2015 P .HARIKRISHNA Assistant professor CSE Dept MRCET Page 9 Design and2015 analysis of algorithms 2015 P .HARIKRISHNA Assistant professor CSE Dept MRCET Page 10 Design and2015 analysis of algorithms 2015 P .HARIKRISHNA Assistant professor CSE Dept MRCET Page 11 Design and2015 analysis of algorithms 2015 P .HARIKRISHNA Assistant professor CSE Dept MRCET Page 12 Design and2015 analysis of algorithms 2015 P .HARIKRISHNA Assistant professor CSE Dept MRCET Page 13 Design and2015 analysis of algorithms 2015 P .HARIKRISHNA Assistant professor CSE Dept MRCET Page 14 Design and2015 analysis of algorithms 2015 Prims algorithm 1. Start with a tree which contains only one node. 2. Identify a node (outside the tree) which is closest to the tree and add the minimum weight edge from that node to some node in the tree and incorporate the additional node as a part of the tree. 3. If there are less then n – 1 edges in the tree, go to 2 T = a spanning tree containing a single node s; E = set of edges adjacent to s; while T does not contain all the nodes { remove an edge (v, w) of lowest cost from E if w is already in T then discard edge (v, w) else { add edge (v, w) and node w to T add to E the edges adjacent to w } } P .HARIKRISHNA Assistant professor CSE Dept MRCET Page 15 Design and2015 analysis of algorithms 2015 Time complexity is O(n2) time. P .HARIKRISHNA Assistant professor CSE Dept MRCET Page 16 Design and2015 analysis of algorithms 2015 P .HARIKRISHNA Assistant professor CSE Dept MRCET Page 17 Design and2015 analysis of algorithms 2015 P .HARIKRISHNA Assistant professor CSE Dept MRCET Page 18 Design and2015 analysis of algorithms 2015 return max; P .HARIKRISHNA Assistant professor CSE Dept MRCET Page 19 Design and2015 analysis of algorithms 2015 P .HARIKRISHNA Assistant professor CSE Dept MRCET Page 20 Design and2015 analysis of algorithms 2015 P .HARIKRISHNA Assistant professor CSE Dept MRCET Page 21 Design and2015 analysis of algorithms 2015 P .HARIKRISHNA Assistant professor CSE Dept MRCET Page 22 Design and2015 analysis of algorithms 2015 P .HARIKRISHNA Assistant professor CSE Dept MRCET Page 23 Design and2015 analysis of algorithms 2015 P .HARIKRISHNA Assistant professor CSE Dept MRCET Page 24 Design and2015 analysis of algorithms 2015 P .HARIKRISHNA Assistant professor CSE Dept MRCET Page 25 Design and analysis of algorithms UNIT-3 UNIT-3 NOTES Greedy method P.Harikrishna Assistant Professor CSE Department MRCET Page 1 Design and analysis of algorithms UNIT-3 P.Harikrishna Assistant Professor CSE Department MRCET Page 2 Design and analysis of algorithms UNIT-3 P.Harikrishna Assistant Professor CSE Department MRCET Page 3 Design and analysis of algorithms UNIT-3 Time complexity is P.Harikrishna Assistant Professor CSE Department MRCET Page 4 Design and analysis of algorithms UNIT-3 P.Harikrishna Assistant Professor CSE Department MRCET Page 5 Design and analysis of algorithms UNIT-3 P.Harikrishna Assistant Professor CSE Department MRCET Page 6 Design and analysis of algorithms UNIT-3 P.Harikrishna Assistant Professor CSE Department MRCET Page 7 Design and analysis of algorithms UNIT-3 Algorithm: Time complexity is O(n). P.Harikrishna Assistant Professor CSE Department MRCET Page 8 Design and analysis of algorithms UNIT-3 Minimum weight is 7 P.Harikrishna Assistant Professor CSE Department MRCET Page 9 Design and analysis of algorithms UNIT-3 Prims algorithm Time complexity= n=number of nodes P.Harikrishna Assistant Professor CSE Department MRCET Page 10 Design and analysis of algorithms UNIT-3 P.Harikrishna Assistant Professor CSE Department MRCET Page 11 Design and analysis of algorithms UNIT-3 P.Harikrishna Assistant Professor CSE Department MRCET Page 12 Design and analysis of algorithms UNIT-3 Cost=14 P.Harikrishna Assistant Professor CSE Department MRCET Page 13 Design and analysis of algorithms UNIT-3 Cost=17 P.Harikrishna Assistant Professor CSE Department MRCET Page 14 Design and analysis of algorithms UNIT-3 Kruskal algorithm P.Harikrishna Assistant Professor CSE Department MRCET Page 15 Design and analysis of algorithms UNIT-3 Time complexity=O(E log V) E is total number of edges. V=total number of vertices. n=number of nodes P.Harikrishna Assistant Professor CSE Department MRCET Page 16 Design and analysis of algorithms UNIT-3 P.Harikrishna Assistant Professor CSE Department MRCET Page 17 Design and analysis of algorithms UNIT-3 P.Harikrishna Assistant Professor CSE Department
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