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    <p>Ok, so the graph displays a measurement of the cost of inserting <code>n</code> elements into your tree, where the x axis is how many elements we've inserted, and the y axis is the total time.</p> <p>Let's call the function that totals the time it takes to insert n elements into the tree <code>f(n)</code>.</p> <p>Then we can get a rough idea of what <code>f</code> might look like:</p> <pre><code>f(1) &lt; k*log(1) for some constant k. f(2) &lt; k*log(1) + k*log(2) for some constant k ... f(n) &lt; k * [log(1) + log(2) + ... + log(n)] for some constant k. </code></pre> <p>Due to how logs work, we can collapse <code>log(1) + ... + log(n)</code>:</p> <pre><code>f(n) &lt; k * [log(1*2*3*...*n)] for some constant k f(n) &lt; k * log(n!) for some constant k </code></pre> <p>We can take a look at Wikipedia to see a <a href="http://en.wikipedia.org/wiki/Factorial#Rate_of_growth_and_approximations_for_large_n" rel="nofollow">graph</a> of what <code>log(n!)</code> looks like. Take a look at the graph in the article. Should look pretty familiar to you. :)</p> <p>That is, I think you've done this by accident:</p> <pre><code>for n in (5000, 50000, 500000): startTime = ... ## .. make a fresh tree ## insert n elements into the tree stopTime = ... ## record the tuple (n, stopTime - startTime) for plotting </code></pre> <p>and plotted total time to construct the tree of size n, rather than the individual cost of inserting one element into a tree of size n:</p> <pre><code>for n in range(50000): startTime = ... ## insert an element into the tree stopTime = ... ## record the tuple (n, stopTime - startTime) for plotting </code></pre> <hr> <p>Chris Taylor notes in the comments that if you plot <code>f(n)/n</code>, you'll see a log graph. That's because a fairly tight approximation to <code>log(n!)</code> is <code>n*log(n)</code> (see the Wikipedia page). So we can go back to our bound:</p> <pre><code>f(n) &lt; k * log(n!) for some constant k </code></pre> <p>and get:</p> <pre><code>f(n) &lt; k * n * log(n) for some constant k </code></pre> <p>And now it's should be easier to see that if you divide <code>f(n)</code> by <code>n</code>, your graph will be bounded above by the shape of a logarithm.</p>
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    1. POStrange results when plotting (Cormen) Red-black tree insert
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    1. POStrange results when plotting (Cormen) Red-black tree insert
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    1. COExactly the answer I was about to post! Zack, if you plot `f(n)/n` then you will see your log graph appear plain as day.
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    2. COSpot on. Now it looks much better http://i.imgur.com/3GIiK.png :)
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