Lecture 2: Divide and Conquer

Background Material

• Recursive Programs
• Iterative constructs (for, while)
  
• Geometric and Arithmetic Series
  
• logarithm
  

Reading

• Chapter 2 (sec. 2.2, 2.5, 2.8, 2.9) of the text.
• Chapter 3 (sec. 3.1-3.4,3.10,3.11) of the text. This material will be covered in greater detail next lecture.
  

Topics

• Reasoning about programs (correctness)
• Proving properties of iterative programs (loop invariants)
  • computing powers
  • gcd
  • insertion sort
• Proving properties of recursive programs
  • computing powers
  • gcd
  • insertion sort
• Reasoning about programs (cost)
• Analyzing the running time of a program
• Big-Oh and approximate running time
• 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

• lec2.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 2 - due at the beginning of next class.