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POHow does this C++ function use memoization?
 

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    <pre><code>#include &lt;vector&gt; std::vector&lt;long int&gt; as; long int a(size_t n){ if(n==1) return 1; if(n==2) return -2; if(as.size()&lt;n+1) as.resize(n+1); if(as[n]&lt;=0) { as[n]=-4*a(n-1)-4*a(n-2); } return mod(as[n], 65535); } </code></pre> <p>The above code sample using memoization to calculate a recursive formula based on some input <code>n</code>. I know that this uses memoization, because I have written a purely recursive function that uses the same formula, but this one much, much faster for much larger values of <code>n</code>. I've never used vectors before, but I've done some research and I understand the concept of them. I understand that memoization is supposed to store each calculated value, so that instead of performing the same calculations over again, it can simply retrieve ones that have already been calculated. </p> <p>My question is: how is this memoization, and how does it work? I can't seem to see in the code at which point it checks to see if a value for n already exists. Also, I don't understand the purpose of the <code>if(as[n]&lt;=0)</code>. This formula can yield positive and negative values, so I'm not sure what this check is looking for.</p> <hr> <p>Thank you, I think I'm close to understanding how this works, it's actually a bit more simple than I was thinking it was.</p> <p>I do not think the values in the sequence can ever be 0, so this should work for me, as I think n has to start at 1. </p> <p>However, if zero was a viable number in my sequence, what is another way I could solve it? For example, what if five could never appear? Would I just need to fill my vector with fives?</p> <p>Edit: Wow, I got a lot of other responses while checking code and typing this one. Thanks for the help everyone, I think I understand it now.</p>
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