Correctness and Analysis of Time Complexity of Dynamic Programming

Unit 1: Searching, Sorting, Selection

• Linear Search
• Binary Search
• Insertion Sort
• Selection Sort
• Bubble Sort
• Heapsort
• Linear Time Sorting
• Selection Problem
• running time analysis and correctness

Unit 2: Graphs

• Review of graph traversals
• Graph connectivity
• Testing bipartite-ness
• Directed Acyclic Graphs and Topological Ordering

Unit 3: Divide and Conquer

• Introduction to divide and conquer technique
• Merge Sort
• Quick Sort
• Maximum-subarray problem
• Strassen’s algorithm for matrix multiplication

Unit 4: Greedy Algorithms

• Introduction to the Greedy algorithm design approach
• application to minimum spanning trees
• Fractional knapsack problem
• Correctness and Analysis of time complexity of Greedy Algorithms

Unit 5: Dynamic Programming

• Introduction to the Dynamic Programming Approach
• Application to subset sum
• integer knapsack problem
• Correctness and analysis of time complexity of Dynamic Programming

Unit 6: Intractability

• Concept of polynomial time computation
• Polynomial time reductions
• Decision vs optimization problems
• Introduction to NP
• NP-hard and NP-Complete classes

Unit 7: Advanced Analysis Technique

• Amortized Analysis