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13869539
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2012-12-13T22:21:47.540
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2012-12-14T11:44:38.573
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2012-12-14T11:44:38.573
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1146303
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1146303
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13866211
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2
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text
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A first idea to speed up the computation (works if <code>|e-b|</code> is not too large): <ul> <li>Question: how much can the Levestein distance change when we compare <code>s</code> with <code>n</code> and then with <code>n+1</code>? </li> <li>Answer: not too much! </li> </ul> Let's see the dynamic-programming tables for <code>s = 12007</code> and two consecutive <code>n</code> <pre><code>n = 12296 0 1 2 3 4 5 1 0 1 2 3 4 2 1 0 1 2 3 3 2 1 1 2 3 4 3 2 2 2 3 5 4 3 3 3 3 </code></pre> and <pre><code>n = 12297 0 1 2 3 4 5 1 0 1 2 3 4 2 1 0 1 2 3 3 2 1 1 2 3 4 3 2 2 2 3 5 4 3 3 3 2 </code></pre> As you can see, only the last column changes, since <code>n</code> and <code>n+1</code> have the same digits, except for the last one. If you have the dynamic-programming table for the edit-distance of <code>s = 12001</code> and <code>n = 12296</code>, you already have the table for <code>n = 12297</code>, you just need to update the last column! Obviously if <code>n = 12299</code> then <code>n+1 = 12300</code> and you need to update the last 3 columns of the previous table.. but this happens just once every 100 iteration. In general, you have to <ul> <li>update the last column on every iterations (so, length(s) cells)</li> <li>update the second-to-last too, once every 10 iterations</li> <li>update the third-to-last, too, once every 100 iterations</li> </ul> so let <code>L = length(s)</code> and <code>D = e-b</code>. First you compute the edit-distance between <code>s</code> and <code>b</code>. Then you can find the minimum Levenstein distance over <code>[b,e]</code> looping over every integer in the interval. There are <code>D</code> of them, so the execution time is about: <img src="https://i.stack.imgur.com/llvRH.gif" alt="enter image description here"> Now since <img src="https://i.stack.imgur.com/7VZu0.gif" alt="enter image description here"> we have an algorithm wich is <img src="https://i.stack.imgur.com/qSXb1.gif" alt="enter image description here">
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1. This table or related slice is empty.
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1. POLevenstein distance from particular group of numbers
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 PTQuestion
PostTypePostTypeId
1. PTAnswer
UserLastEditorUserId
1. USHaile
UserOwnerUserId
1. USHaile
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