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POHow can one analyze the greatest percentage gain (burst) of numbers in sequence in an array?
 

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  1. POHow can one analyze the greatest percentage gain (burst) of numbers in sequence in an array?
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    <p>There are algorithms for detecting the maximum subarray within an array (both contiguous and non-continguous). Most of them are based around having both negative and positive numbers, though. How is it done with positive numbers only?</p> <p>I have an array of values of a stock over a consequtive range of time (let's say, the array contains values for all consecutive months).</p> <p><code>[15.42, 16.42, 17.36, 16.22, 14.72, 13.95, 14.73, 13.76, 12.88, 13.51, 12.67, 11.11, 10.04, 10.38, 10.14, 7.72, 7.46, 9.41, 11.39, 9.7, 12.67, 18.42, 18.44, 18.03, 17.48, 19.6, 19.57, 18.48, 17.36, 18.03, 18.1, 19.07, 21.02, 20.77, 19.92, 18.71, 20.29, 22.36, 22.38, 22.39, 22.94, 23.5, 21.66, 22.06, 21.07, 19.86, 19.49, 18.79, 18.16, 17.24, 17.74, 18.41, 17.56, 17.24, 16.04, 16.05, 15.4, 15.77, 15.68, 16.29, 15.23, 14.51, 14.05, 13.28, 13.49, 13.12, 14.33, 13.67, 13.13, 12.45, 12.48, 11.58, 11.52, 11.2, 10.46, 12.24, 11.62, 11.43, 10.96, 10.63, 10.19, 10.03, 9.7, 9.64, 9.16, 8.96, 8.49, 8.16, 8.0, 7.86, 8.08, 8.02, 7.67, 8.07, 8.37, 8.35, 8.82, 8.58, 8.47, 8.42, 7.92, 7.77, 7.79, 7.6, 7.18, 7.44, 7.74, 7.47, 7.63, 7.21, 7.06, 6.9, 6.84, 6.96, 6.93, 6.49, 6.38, 6.69, 6.49, 6.76]</code></p> <p>I need an algorithm to determine for each element the single time period where it had the biggest percentage gain. This could be a time period of 1 month, some span of several months, or the entire array (e.g., 120 months), depending on the stock. I then want to output the burst, in terms of percentage gain, as well as the return (change in price over the original price; so the peak price vs the starting price in the period).</p> <p>I've combined the max subarray type algorithms, but realized that this problem is a bit different; the array has no negative numbers, so those algorithms just report the entire array as the period and the sum of all elements as the gain.</p> <p>The algorithms I mentioned are located <a href="https://stackoverflow.com/questions/3733251/find-the-subsequence-with-largest-sum-of-elements-in-an-array/3733481#3733481">here</a> and <a href="https://stackoverflow.com/questions/7086464/interview-question-maximum-single-sell-profit?lq=1">here</a>, with the latter being based on the <a href="http://en.wikipedia.org/wiki/Master_theorem" rel="nofollow noreferrer">Master Theorem</a>. Hope this helps.</p> <p>I'm coding in Ruby but pseudocode would be welcome, too.</p>
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