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POFaster algorithm for counting active calls
 

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    <p>We are implementing a density report for a call center. The result must be displayed as table with a row per day showing the maximum number of <strong>simultaneously</strong> active calls during that day. </p> <p>We are building the lib behind the UI. The contract specifies we receive the number of calls for that day and two arrays of integers, one with the start time and one with the end time of each call, so, for example:</p> <p>For a given day just two calls are received: One goes from time 20 to 30 and the other one from 10 to 20. The maximum number simultaneously calls is 1. </p> <p>On the other hand, for another day, also two calls are received, one from 10 to 45 and the other from 15 to 40 then the maximum number of simultaneously calls is 2. </p> <p>The contract for the web service is this</p> <pre><code>public static int GetMaxDensity(int N, int[] X, int[] Y) </code></pre> <p>And the data looks like this (suppose 3 calls where received that day). First one from 10 to 25, second one from 12 to 30 and third one from 20 to 23.</p> <pre><code>N = 3, X = {10, 12, 20} Y = {25, 30, 23} </code></pre> <p>And the return must be: 3.</p> <p>I've implemented this solution:</p> <pre><code>public static int GetMaxDensity(int N, int[] X, int[] Y) { int result = 0; for (int i = 0; i &lt; N; i++) { int count = 0, t = X[i]; for (int j = 0; j &lt; N; j++) { if (X[j] &lt;= t &amp;&amp; t &lt; Y[j]) count++; } result = Math.max(count, result); } return result; } </code></pre> <p>And it works great when the number of calls is up to 1000 (weekends) but within work days the number is pretty big and the calculation takes so long (>5 minutes). I now the reason could be my solution is using two nested cycles but I don't have pretty much experience with complex algorithms so my question is:</p> <p>Given that I just need the maximum number of simultaneously calls (not the times nor the callers), which could be a faster way to perform this calculation if there is one.</p>
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    1. COif one call is from 10 to 40 and second call is from 20 to 45, what should be the density ? I think 2, is it ?
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    2. CO@mprabhat Yes. Cause from 20 to 40 two calls were active.
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    3. COI just copied your code and ran five tests of two 50,000 arrays. Each of the arrays are randomly generated values where x is less than 100, and y is less than the corresponding x+ 100. they came back in 24, 12, 12, 24, 18 seconds. This was on my laptop. Did you perhaps clean up the code so you could post it here? If so, maybe the loops aren't the problem. What has your profiler revealed?
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