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Barrett Ruth 2024-11-29 21:53:04 -06:00
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34
posts/algorithms/extrema-circular-buffer.html
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@ -51,23 +51,19 @@
<p>Design a data structure supporting the following operations:</p>
<ul>
<li>
<span class="inline-code"
><code>build(size_t capacity)</code></span
>
<span><code>build(size_t capacity)</code></span>
: initialize the data structure with capacity/window size
<span class="inline-code"><code>capacity</code></span>
<span><code>capacity</code></span>
</li>
<ul>
<li>
The data structure must always hold \(\leq\)
<span class="inline-code"><code>capacity</code></span>
<span><code>capacity</code></span>
prices.
</li>
</ul>
<li>
<span class="inline-code"
><code>void push_back(double value)</code></span
>
<span><code>void push_back(double value)</code></span>
</li>
<ul>
<li>
@ -76,15 +72,15 @@
</li>
</ul>
<li>
<span class="inline-code"><code>void pop_front()</code></span>
<span><code>void pop_front()</code></span>
: remove the price from the front of the window
</li>
<li>
<span class="inline-code"><code>size_t size()</code></span>
<span><code>size_t size()</code></span>
: return the number of prices in the data structure
</li>
<li>
<span class="inline-code"><code>double get()</code></span>
<span><code>double get()</code></span>
: return the extrema (min or max)
</li>
</ul>
@ -104,9 +100,7 @@
<a
target="blank"
href="https://en.cppreference.com/w/cpp/container/deque"
><span class="inline-code"
><code>std::deque&lt;double&gt;</code></span
></a
><span><code>std::deque&lt;double&gt;</code></span></a
>.
</p>
<p>
@ -115,13 +109,13 @@
operations. The minimum/maximum element must be found via a linear
scan in \(O(n)\) time, certainly far from optimal.
</p>
<div class="code" data-file="naive.cpp"</div>
<div class="code" data-file="naive.cpp"></div>
</div>
<h3>optimizing the approach</h3>
<div class="problem-content">
<p>
Rather than bear the brunt of the work finding extrema in calls to
<span class="inline-code"><code>get()</code></span
<span><code>get()</code></span
>, we can distribute it across the data structure as it is built.
</p>
<p>
@ -214,13 +208,9 @@
</li>
<li>
The class could leverage templates to take in a comparator
<span class="inline-code"
><code>std::less&lt;double&gt;</code></span
>
<span><code>std::less&lt;double&gt;</code></span>
) to easily specify a minimum/maximum
<span class="inline-code"
><code>ExtremaCircularBuffer</code></span
>
<span><code>ExtremaCircularBuffer</code></span>
as well as a value type to support all operations.
</li>
<li>