title: Intro to Algorithms (chapter 1-1)
body: <p>Just reading this book for fun, this isn't homework.</p>
  
  <p>However I am already confused on the first main assignment:</p>
  
  <p><em>1-1 Comparison of running times</em></p>
  
  <p><em>For each function f(n) and time t in the following table, determine the largest size n of a problem that can be solved in time t, assuming that the algorithm to solve the problem takes f(n) microseconds.</em></p>
  
  <p>What does this even mean? </p>
  
  <p>The next table shows a bunch of times along one axis (1 second, 1 minute, one hour, etc), and the other axis shows different f(n) such as lg n, sqrt(n), n, etc.</p>
  
  <p>I am not sure how to fill in the matrix because I can't understand the question. So if f(n) = lg n, it's asking the largest n that can be solved in, for example, 1 second, but the problem takes f(n) = lg n microseconds to solve? What does that last part even mean? I don't even know how to set up the equations / ratios to solve this problem because I literally can't even put together the meaning of the question.</p>
  
  <p>My hangup is over the sentence "assuming that the algorithm to solve the problem takes f(n) microseconds" because I don't know what this refers to. The time for <em>what</em> algorithm to solve <em>what</em> problem takes f(n) microseconds? So if I call f(100) it'll take lg 100 microseconds? So I need to find some n where f(n) = lg n microseconds = 1 second?</p>
  
  <p>Does this mean lg n microseconds = 1 second when lg n microseconds = 10^6 microseconds, so n = 2^(10^6)?</p>