CS51A - Spring 2019 - Class 36

Lecture notes

  • nim tournament

  • "For me, great algorithms are the poetry of computation. Just like verse, they can be terse, allusive, dense and even mysterious. But once unlocked, they cast a brilliant new light on some aspect of computing." -- Francis Sullivan

  • What is an algorithm?
       - way for solving a problem
       - method of steps to accomplish a task

  • Examples
       - sort a list of numbers
       - find a route from one place to another (cars, packet routing, phone routing, ...)
       - find the longest common substring between two strings
       - add two numbers
       - microchip wiring/design (VLSI)
       - solving sudoku
       - cryptography
       - compression (file, audio, video)
       - spell checking
       - pagerank
       - classify a web page
       - ...

  • Main parts to algorithm analysis
       - developing algorithms that work
       - making them faster
       - analyzing/understanding the efficiency/run-time

  • What questions might we want to ask/measure about an algorithm?
       - how long does it take to run? How efficient is it?
       - how much memory does it use?
       - does it finish?
       - is it right?
       - how hard is it to code?

  • asymptotic analysis
       - Key idea: how does the run-time grow as we increase the input size?
          - for example, if we double the input, what will happen to the run-time?
             - unchanged?
             - double?
             - triple?
             - quadruple?
       - Big-O notation: an upper bound on the run-time
          - describe how the run-time changes as the input time changes
          - this gives us groups of methods/functions that behave similarly
          - O(f(n)): as n increases, the run-time increases wrt f(n)
             - O(n) = linear
                - double the input size, double the run-time
             - O(n^2) = quadratic
                - double the input size, quadruple the run-time
             - ..
       - runtimes table


  • Revisit contains function on a list (i.e., "in")
       - What is the Big-O for contains?
          - O(n)
          - the runtime increases linearly with the size of the list
    •