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Copy file name to clipboardExpand all lines: book/chapters/algorithms-analysis.adoc
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@@ -47,7 +47,7 @@ TIP: Algorithms are instructions on how to perform a task.
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Not all algorithms are created equal. There are "good" and "bad" algorithms. The good ones are fast; the bad ones are slow. Slow algorithms cost more money to run. Inefficient algorithms could make some calculations impossible in our lifespan!
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To give you a clearer picture of how different algorithms perform as the input size grows, take a look at the following problems and how their relative execution time changes as the input size increases.
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(((Tables, Algorithms input size vs Time)))
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.Relationship between algorithm input size and time taken to complete
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TIP: Asymptotic analysis describes the behavior of functions as their inputs approach to infinity.
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In the previous example, we analyzed `getMin` with an array of size 3; what happen size is 10 or 10k or a million?
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.Operations performed by an algorithm with a time complexity of `3n + 3`
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Again, time complexity is not a direct measure of how long a program takes to execute but rather how many operations it performs in given the input size. Nevertheless, there’s a relationship between time complexity and clock time as we can see in the following table.
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.How long an algorithm takes to run based on their time complexity and input size
Copy file name to clipboardExpand all lines: book/chapters/big-o-examples.adoc
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== Summary
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We went through 8 of the most common time complexities and provided examples for each of them. Hopefully, this will give you a toolbox to analyze algorithms.
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// tag::table[]
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.Most common algorithmic running times and their examples
Hash Map it’s very optimal for searching values by key in constant time *O(1)*. However, searching by value is not any better than an array since we have to visit every value *O(n)*.
Copy file name to clipboardExpand all lines: book/chapters/queue.adoc
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== Queue Complexity
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As an experiment, we can see in the following table that if we had implemented the Queue using an array, its enqueue time would be _O(n)_ instead of _O(1)_. Check it out:
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