Review for Midterm Exam

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Review for Midterm Exam

• Andreas Klappenecker

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Topics Covered

• Finding Primes in the Digits of Euler's Number
• Asymptotic Notations Big Oh, Big Omega, Big
  Theta
• Time complexity of Insertion Sort
• Lower bounds for sorting
• Divide-and-Conquer Algorithms
• Mergesort
• Strassen's method for Matrix Multiplication
• Greedy Algorithms, Huffman codes
• Greedy Algorithms for Matroids
• Matroid Embeddings
• Dynamic Programming, Matrix Chain Multiplication
• Dynamic Programming, Longest Common Subsequence
• Amortized Analysis
• Disjoint Sets

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Asymptotic Notations

• O(g) fN-gtR there exists an integer n0
  and a real constant C such that f(n) lt
  Cg(n)
• for all ngt n0
• ?(g) fN-gtR there exists an integer n0
  and a real constant c such that f(n) gt
  cg(n)
• for all ngt n0

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Asymptotic Notation

• ½(n2n6) O(n2)
• 6n2 O(n2)
• 10765432n22n7 ?(n2)
• ½(n2n6) ?(n2)
• ?(g) ?(g) ? O(g)
• ½(n2n6) ?(n2)

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Sorting

• Insertion Sort
• Best case running time linear
• Worst case running time quadratic
• Merge Sort O(n log n)
• Any comparison based sorting ?(n log n)

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Divide-and-Conquer

• Mergesort
• Quicksort
• Strassens matrix multiplication algorithm
• Recurrence relations
• Master theorem (no need to memorize)

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Greedy Algorithms

• Coin change
• Huffman codes
• Matroids
• Kruskals algorithm
• Matroid embeddings
• Prims algorithm

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Dynamic Programming

• Matrix chain multiplication
• Longest common subsequences
• Variations Edit distance

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Amortized Analysis

• Aggregate Analysis
• Accounting Method
• Stacks
• Counter
• Disjoint Sets

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Exam

• Some short questions
• Some workout problems
• Lectures
• Slides
• Textbook
• Quizzes
• Homework