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POOverloading operator[] for a template Polynom class
 

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    <p>I am writing a template <code>Polynom&lt;T&gt;</code> class where <code>T</code> is the numeric type of its coefficients.</p> <p>The coefficients of the polynom are stored in an <code>std::vector&lt;T&gt; coefficients</code>, where <code>coefficients[i]</code> corresponds to <code>x^i</code> in a real polynom. (so the powers of x are in increasing order). </p> <p>It is guaranteed that <code>coefficients</code> vector always contains at least one element. - for a zero polynom it is <code>T()</code>.</p> <p>I want to overload the <code>operator[]</code> to do the following:</p> <ol> <li>The index passed to the operator[] corresponds to the power of X whose coefficient we want to modify / read.</li> <li>If the user wants to just <strong>read</strong> the coefficient, it should throw for negative indices, return <code>coefficients.at(i)</code> for indices within the stored range - and <strong>reasonably</strong> return 0 for all other indices, not throw.</li> <li>If the user wants to <strong>modify</strong> the coefficient, it should throw for negative indices, but let user modify all other indices freely, even if the index specified is bigger than or equal to <code>coefficients.size()</code>. So we want to somehow resize the vector.</li> </ol> <p>The main problem I have collided with is as follows:</p> <p>1.</p> <p>How do I distinguish between the read case and the write case? One person left me without an explanation but said that writing two versions:</p> <pre><code>const T&amp; operator[] (int index) const; T&amp; operator[] (int index); </code></pre> <p>was insufficient. However, I thought that the compiler would prefer the const version in the read case, won't it? </p> <p>2.</p> <p>I want to make sure that no trailing zeros are ever stored in the <code>coefficients</code> vector. So I somehow have to know in advance, "before" I return a mutable <code>T&amp;</code> of my coefficient, what value user wants to assign. And I know that <code>operator[]</code> doesn't receive a second argument.</p> <p>Obviously, if this value is not zero (not T()), then I have to resize my vector and set the appropriate coefficient to the value passed.</p> <p>But I cannot do it in advance (before returning a <code>T&amp;</code> from <code>operator[]</code>), because if the value to be assigned is T(), then, provided I resize my coefficients vector in advance, it will eventually have lots of trailing "zeroes".</p> <p><em>Of course I can check for trailing zeroes in every other function of the class and remove them in that case. Seems a very weird decision to me, and I want every function to start working in assumption that there are no zeroes at the end of the vector if its size > 1.</em></p> <p>Could you please advise me as concrete solution as possible to this problem? I heard something about writing an inner class implicitly convertible to <code>T&amp;</code> with overloaded <code>operator=</code>, but I lack the details. </p> <p>Thank you very much in advance!</p>
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