Course Objectives: |
The objective of the course is to introduce the fundamental mathematical tools needed to analyze algorithms, basic algorithm design techniques, advanced data structures, and important algorithms from different problem domains. |
Course Content: |
Introduction, asymptotic notation, empirical analysis of algorithms, designing algorithms, amortized analysis, brute force algorithms, divide and conquer algorithms, transform and conquer algorithms, space and time trade-offs, dynamic programming, greedy algorithms, advanced data structures, B-trees, Insertion and Deletion from B-trees, graphs and graph algorithms, P, NP, and NP-complete problems. |
Week |
Subject |
Related Preparation |
1) |
Introduction, asymptotic notation. |
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2) |
Empirical analysis of algorithms, analysis of algorithms, amortized analysis |
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3) |
Recurrences, substitution method, recursion-tree method, master method. |
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4) |
Brute Force Algorithms |
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5) |
Divide and Conquer Algorithms |
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6) |
Merge sort, quicksort, randomized quicksort, binary search |
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7) |
Transform and Conquer Algorithms: Solving systems of linear equations with Gaussian ination elimination, Balanced Search Trees, Heaps and Heapsort, Horner's Rule and Binary Exponentiation
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8) |
Space and Time Trade-offs: Input Enhancement (Counting based sorting, string matching), Prestructuring (Hashing, Hash functions, open addressing).
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9) |
Midterm |
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10) |
Dynamic Programming: Coin-row problem, Knapsack problem, Longest common subsequence. |
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11) |
Dynamic Programming: Knapsack problem, Longest common subsequence. |
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12) |
Greedy Algorithms: Activity selection, Huffman codes, Prim’s algorithm, Kruskal’s Algorithm |
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13) |
Single-source shortest paths: The Bellman-Ford algorithm, Dijkstra's algorithm. |
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14) |
P, NP, and NP-complete problems |
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Course Notes / Textbooks: |
Anany Levitin, The Design and Analysis of Algorithms, Pearson International Third Edition.
Cormen, T. H., Leiserson, C. E., Rivest, R. L. and Stein, C., Introduction to Algorithms (3rd Edition), MIT Press, 2009.
Sanjoy Dasgupta , Christos Papadimitriou, Umesh Vazirani, Algorithms, McGraw-Hill Education.
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References: |
Yok - None |