CS 411 Fall 2025  >  Outline for August 27, 2025

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CS 411 Fall 2025
Outline
for August 27, 2025

Outline

Framework for Analysis of Algorithms [L 2.1]

• Efficiency & Complexity
  • An efficient algorithm uses relatively little of some limited resource.
  • Complexity: measure of resources used.
  • Time. So time efficiency or time complexity.
  • Space. So space efficiency or space complexity. Memory used in addition to that for input & output.
• Measuring input size
  • Almost all algorithms run longer on larger inputs.
  • Size: number of items in input list?
  • Size: number of bits in input?
    • Representing positive integer \(k\) in binary requires \(1 + \lfloor \log_2 k\rfloor\) bits.
  • For an \(n \times n\) matrix, size could be \(n\) or \(n^2\).
  • This needs to be decided.
• Measuring time
  • Basic operation(s).
  • It matters what we count!
• Order of growth
  • Idea: look at fastest growing term, ignore coefficients.
• Worst, best, average case
  • Worst case (we mean this unless we say otherwise).
  • Best case. Little used.
  • Average case: usually something like average over all possible inputs of a given size.
  • Example of Sequential Search.
  • Amortized efficiency: average over large number of consecutive executions of algorithm.