Lecture 3: Big Oh and Growth Rates

Background Material

• Lecture 2
• Geometric and Arithmetic Series
• logarithm, exponential, polynomials
• limits, derivative and L'Hopital's Rule

Reading

• Chapter 3 (all sections) of the text.

Topics

• Finish materials from Lecture 2
• Computing Time
  • Analyzing the running time of a program
  • Big-Oh, little-oh, and Big-Theta and approximate running time
  • Properties of Big-Oh, little-oh, and Big-Theta
  • Sums and loops
    • computing powers
    • gcd
    • insertion sort
  • Recurrence relations and recursion
    • computing powers
    • gcd
    • insertion sort
• Divide and Conquer
  • Divide and conquer recurrence
  • Merge Sort
  • Karatsuba's algorithm for integer product

Lecture Notes

• lec3.ppt

Programs

• sort.cpp - insertion sort and merge sort
• power.cpp - 4 functions (recursive and iterative) to compute powers
• gcd.cpp - Euclidean algorithm
• minmax.cpp - recursive function to simultaneously compute the minimum and maximum elements of a vector.

Resources

• None posted

Assignments

• Assignment 3 - due by the beginning of class on Tue. Oct. 19.