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<a class="category-link" href="/categories/coding/">Coding</a> >
<a
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>Data Structures and Algorithms (DSA)</a
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<h1>Learning Algorithms from Scratch / Algorithms for Dummies</h1>
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<p>
When you are programming you face challenges all the way.
Getting the problems solved is just the tip of the iceberg,
getting it done efficiently is the rest.
</p>
<a id="more"></a>
<hr />
**Update**
<p>
Graphs are gone in this post. I re-made this post and added more
information and images. Checkout it out clicking here:
<a
href="/blog/2018/04/04/how-you-can-change-the-world-learning-data-structures-algorithms-free-online-course-tutorial/"
>Data Structures and Algorithms (DSA) for Beginners</a
>
</p>
<hr />
<p class="p1"><b>Why should you care for efficiency?</b></p>
<p class="p1">
Solutions to the same problem might take years with certain
algorithm, and just minutes using efficient algorithms. For
instance, if you have applications that are used for thousands
of people over internet, every fraction of second counts.
Therefore, efficient algorithms is a must.
</p>
<p class="p1"><b>How I do my algorithms more efficient?</b></p>
<p class="p1">
To improve something you first need to know the actual state. In
this case you need to measure the actual effectiveness of your
algorithm in other to improve it. It's very common to use
running time analysis to measure the speed of algorithms
independently from the hardware used (old pc, supercomputer it
doesn't matter).
</p>
<p class="p1"><b>Run-time analysis</b></p>
<p class="p1">
A common way to analyze the algorithms is using the big-O
notation. The good thing about this notation is that is
independent from the computer used to run the algorithm. You
know that if you use a very slow computer (e.g. pentium I) v.s.
a supercomputer use in NASA, the latter will run the program
much faster. Big-O notation abstract the hardware and just focus
in the algorithm per se. The only variable in the big-O notation
gives the relative time needed to process an algorithm in
function of the input n. Let's clarify this with an example.
</p>
<p class="p1">
<strong>Ex.1</strong> - You want to sort an array A of n
integers.
</p>
<p class="p1">
Depending in the algorithm used to do that you may have:
</p>
<ul>
<li class="p1">
<b>selection</b> sort has a running time of O(n^2);
</li>
<li class="p1"><b>merge sort</b> --> O(n log n)</li>
</ul>
<p class="p1">
Right now, it doesn't matter if are not familiar with these
algorithms (we will cover this the next lessons), the point here
is that we have n integer and big-O notations give us a
mathematical expression that is in function of the input n. If
you <a
target="_blank"
rel="noopener"
href="http://fooplot.com/index.php?&type0=0&type1=0&type2=0&type3=0&type4=0&y0=x%5E2&y1=x*log%28x%29&y2=&y3=&y4=&r0=&r1=&r2=&r3=&r4=&px0=&px1=&px2=&px3=&px4=&py0=&py1=&py2=&py3=&py4=&smin0=0&smin1=0&smin2=0&smin3=0&smin4=0&smax0=2pi&smax1=2pi&smax2=2pi&smax3=2pi&smax4=2pi&thetamin0=0&thetamin1=0&thetamin2=0&thetamin3=0&thetamin4=0&thetamax0=2pi&thetamax1=2pi&thetamax2=2pi&thetamax3=2pi&thetamax4=2pi&ipw=0&ixmin=-5&ixmax=5&iymin=-3&iymax=3&igx=1&igy=1&igl=1&igs=0&iax=1&ila=1&xmin=-5&xmax=5&ymin=-3&ymax=3"
><span class="s1">plot in a graph n^2 and n log n</span></a
>. You'll see that n^2 grows much faster than n log(n). That
means that the algorithm n^2 will take longer than n*log(n) to
process as the size of the array n increases.
</p>
<p class="p1"><b>Common order of Growth</b></p>
<p class="p1">
To give you an idea of the common order of growth of runtime
expressions. Take a look at the following graph and table. The
slower the function growth the better is the algorithm. In order
from better performance to worst is:
</p>
<p class="p1">
1 -- log n -- n -- n log n -- n^2 -- n^3 -- 2^n -- n! ...
</p>
<p class="p2">
<!-- <img alt="" src="http://adrianmejiarosario.com/sites/default/files/Screen%20Shot%202011-12-22%20at%203.22.12%20PM.png" /> -->
</p>
<p class="p2">
<!-- <img alt="" src="http://adrianmejiarosario.com/sites/default/files/Screen%20Shot%202011-12-22%20at%203.23.45%20PM.png" /> -->
</p>
<p class="p1"><b>Approximate growth rate from code.</b></p>
<p class="p1">
There are a whole theory and math behind the Big-O notation and
other notations related. At this time, just take a look of the
typical code and its growth order.
</p>
<p class="p1">
<!-- <img alt="" src="http://adrianmejiarosario.com/sites/default/files/Screen%20Shot%202011-12-22%20at%204.51.48%20PM.png" /> -->
</p>
<p><strong>Cases (the good, the bad, and the ugly)</strong></p>
<p>
Remember that n is the number of elements in the input. All this
runtime growth rate are in function of the input elements. There
is another important thing to consider about the input elements:
the order! The order of the input elements matters, and
that's why algorithms are analyzed in 3 different cases:
</p>
<ol>
<li>
Worst-case performance: the input is distributed as worst as
it could be for an algorithm.
</li>
<li>
Average-case scenario: approximation of the most common
arrange of inputs.
</li>
<li>
Best-case scenario: most favorable distribution of the inputs.
</li>
<li>
One more: Space. this is how much space the algorithm cosume
to execute.
</li>
</ol>
<p class="p2">
If you want more depth in these topic read here:
</p>
<ul>
<li class="p2">
<span>Analysis (</span
><a
target="_blank"
rel="noopener"
href="http://gcu.googlecode.com/files/02Analysis.pdf"
>pdf</a
><span>) (</span
><a
target="_blank"
rel="noopener"
href="http://gcu.googlecode.com/files/02Analysis.key.zip"
>keynote</a
><span>)</span>
</li>
<li class="p2">
<span>Algorithm @ </span>ocw.mit.edu: lectures
<a
target="_blank"
rel="noopener"
href="http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-046j-introduction-to-algorithms-sma-5503-fall-2005/video-lectures/lecture-1-administrivia-introduction-analysis-of-algorithms-insertion-sort-mergesort"
>1 </a
>and
<a
target="_blank"
rel="noopener"
href="http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-046j-introduction-to-algorithms-sma-5503-fall-2005/video-lectures/lecture-2-asymptotic-notation-recurrences-substitution-master-method"
>2</a
>
</li>
<li class="p2">http://algs4.cs.princeton.edu/home/</li>
</ul>
<p class="p2"> </p>
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