Chapter 4: Orders of Growth and Tree Recursion

• Questions To Ask About Computational Processes (Again)
• Algorithms
• Example: Sorting
• Selection Sort
• Merge Sort
• An Experiment in Sorting Efficiency
• Chart Comparing Times
• Drawbacks of Timing Physical Processes
• Analyzing Selection Sort
• Θ (Big Theta) Terminology
• Computing Time Spent on Selection Sort
• Analyzing Merge Sort 1
• Analyzing Merge Sort 2
• Analyzing Merge Sort 3
• Analyzing Merge Sort 4
• Comparing n, nlogn, and n²
• Recursion in Merge Sort
• Linear vs Tree Recursion
• Divide and Conquer
• Digital Signatures
• Digital Signature System Components
• Digital Signature System Component Diagram
• Digest Functions
• Simplified Digital Signature System Component Diagram
• Signing Functions
• Verification Functions
• Signing and Verifying Using Modular Arithmetic
• Modular Arithmetic (Remainder Arithmetic)
• Some Properties of Modular Arithmetic
• Making the Signing and Verification Functions Inverses
• Determining the Signing Exponent and Modulus
• The Verification Function
• Creating the Signature
• Solving the Huge Number Problem
• First Attempt: mod-expt
• Testing mod-expt
• Using Tree Recursion
• Second Attempt: mod-expt
• Tree of Multiplications
• Exercise 4.2a(1), p. 92
• Third Attempt: mod-expt
• A Dramatic Improvement
• From Tree to Single Branch
• Logarithmic Recursion
• Logarithmic Iteration
• Converting Linear to Logarithmic Iteration
• Space and Time Comparisons
• Fractal Curves
• Sierpinski's Gasket
• Self-Similarity in Sierpinski's Gasket
• Curve Levels
• Sierpinski's Gasket Levels 0, 1, 2
• Basis Similarity
• Drawing Lines in DrRacket
• C-curve Level 0
• C-curve Level 1
• Subdividing a Curve
• C-curve Level 2
• C-curve Level 3
• C-curve Levels 6 and 10
• Defining c-curve