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Why do we check up to the square root of a prime number to determine if it is prime?

... is not a prime, it can be factored into two factors a and b: n = a * b Now a and b can't be both greater than the square root of n, since then the product a * b would be greater than sqrt(n) * sqrt(n) = n. So in any factorization of n, at least one of the factors must be smaller than the square ...
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What's a good rate limiting algorithm?

... = 8.0; // unit: seconds allowance = rate; // unit: messages last_check = now(); // floating-point, e.g. usec accuracy. Unit: seconds when (message_received): current = now(); time_passed = current - last_check; last_check = current; allowance += time_passed * (rate / per); if (allowance...
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Format Instant to String

...tant a time-zone is required. Without a time-zone, the formatter does not know how to convert the instant to human date-time fields, and therefore throws an exception. The time-zone can be added directly to the formatter using withZone(). DateTimeFormatter formatter = DateTimeFormatter.ofLocal...
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Explain ExtJS 4 event handling

...k event handler. Let's retrieve Element: var el = Ext.get('test_node'); Now let's check docs for click event. It's handler may have three parameters: click( Ext.EventObject e, HTMLElement t, Object eOpts ) Knowing all this stuff we can assign handler: // event name event handler...
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What is memory fragmentation?

...--- | | ---------------------------------- Now, allocate some of it (5 allocations): ---------------------------------- |aaaabbccccccddeeee | ---------------------------------- Now, free the first four allocations but not the fifth: ---------------------...
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I lost my .keystore file?

... Now it is possible don't worry, here is the full and final steps to reset .JKS file. Step-1 Download the UPLOAD CERTIFICATE (file name - upload_cert.der) from your Google Play Store Console Step-2 Go to this LINK http...
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PHP calculate age

...:createFromFormat('d/m/Y', '12/02/1973', $tz) ->diff(new DateTime('now', $tz)) ->y; As of PHP 5.3.0 you can use the handy DateTime::createFromFormat to ensure that your date does not get mistaken for m/d/Y format and the DateInterval class (via DateTime::diff) to get the number of ...
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Memoization in Haskell?

...u can check the work so far by verifying that toList nats gives you [0..] Now, f_tree :: Tree Int f_tree = fmap (f fastest_f) nats fastest_f :: Int -> Int fastest_f = index f_tree works just like with list above, but instead of taking linear time to find each node, can chase it down in loga...
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How to round the minute of a datetime object

...ect to any time lapse in seconds dt : datetime.datetime object, default now. roundTo : Closest number of seconds to round to, default 1 minute. Author: Thierry Husson 2012 - Use it as you want but don't blame me. """ if dt == None : dt = datetime.datetime.now() seconds = (dt.replac...
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Ukkonen's suffix tree algorithm in plain English

...e an initial tree, which looks like this: And what it means is this: Now we progress to position 2 (right after b). Our goal at each step is to insert all suffixes up to the current position. We do this by expanding the existing a-edge to ab inserting one new edge for b In our representati...