CS 411 Fall 2025  >  Outline for October 17, 2025

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CS 411 Fall 2025
Outline
for October 17, 2025

Outline

Space-Time Trade-Offs [L Ch 7 intro]

• Idea: Allow an algorithm to use extra space, in order to save time.
  • Very common strategy.
• Examples you might have seen:
  • Merge Sort on an array: use a buffer.
  • Caching: disk blocks in memory, memory contents on processor.
  • Save result of a computation to avoid recomputing.
• We will look at:
  • Input enhancement
    • Preprocess input, store info about it to allow for faster code.
  • Prestructuring
    • Store input in form that requires more space, but allows for faster access.
  • Dynamic programming
    • Method for speeding up some recursive (or conceptually recursive) algorithms.
    • Save results of previous computations so that they do not need to be done again.
    • Often applied to optimization problems.
    • The text devotes a separate chapter to dynamic programming [L Ch 8].

Sorting by Counting [L 7.1]

• Can sort list by determining, for each item, how many items come before it.
• Naive implementation: \(\Theta(n^2)\) comparisons.
• If values in list can index an array, then can greatly improve performance by storing array of counts.
  • \(n\) is number of items to sort, basic ops are array look-ups & integer operations.
  • For an array whose values are integers in the range \([1,k]\), algorithm uses \(\Theta(k+n)\) ops.
  • For fixed set of integer values, only \(\Theta(n)\) ops!
  • This improvement is not a comparison sort.