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    <p>My short answer: in no way.</p> <p>Just because the problem definition is <strong>incorrect</strong>. As <a href="https://stackoverflow.com/users/497358/axn">Axn</a> brilliantly noticed:</p> <blockquote> <p>There is a little bit of contradiction going on in the requirement. It states that K &lt;= N. But as K approaches N, the frequency requirement will be contradicted by the Uniqueness requirement. Worst case, if K=N, all elements will be returned (i.e appear with same frequency), irrespective of their weight.</p> </blockquote> <p>Anyway, when K is pretty small relative to N, calculated frequencies will be pretty close to theoretical values.</p> <p>The task may be splitted on two subtasks:</p> <ol> <li>Generate random numbers with a given distribution (specified by weights)</li> <li>Generate unique random numbers</li> </ol> <h2>Generate random numbers with a given distribution</h2> <ol> <li>Calculate sum of weights (<code>sumOfWeights</code>)</li> <li>Generate random number from the range <code>[1; sumOfWeights]</code></li> <li>Find an array element where the sum of weights from the beginning of the array is greater than or equal to the generated random number</li> </ol> <p>Code</p> <pre><code>#include &lt;iostream&gt; #include &lt;cstdlib&gt; #include &lt;ctime&gt; // 0 - id, 1 - weight typedef unsigned Pair[2]; unsigned Random(Pair* i_set, unsigned* i_indexes, unsigned i_size) { unsigned sumOfWeights = 0; for (unsigned i = 0; i &lt; i_size; ++i) { const unsigned index = i_indexes[i]; sumOfWeights += i_set[index][2]; } const unsigned random = rand() % sumOfWeights + 1; sumOfWeights = 0; unsigned i = 0; for (; i &lt; i_size; ++i) { const unsigned index = i_indexes[i]; sumOfWeights += i_set[index][3]; if (sumOfWeights &gt;= random) { break; } } return i; } </code></pre> <h2>Generate unique random numbers</h2> <p>Well known Durstenfeld-Fisher-Yates algorithm may be used for generation unique random numbers. See <a href="https://stackoverflow.com/questions/196017/unique-random-numbers-in-o1">this great explanation</a>.</p> <p>It requires N bytes of space, so if N value is defined at compiled time, we are able to allocate necessary space at compile time.</p> <p>Now, we have to combine these two algorithms. We just need to use our own <code>Random()</code> function instead of standard <code>rand()</code> in unique numbers generation algorithm.</p> <p>Code</p> <pre><code>template&lt;unsigned N, unsigned K&gt; void Generate(Pair (&amp;i_set)[N], unsigned (&amp;o_res)[K]) { unsigned deck[N]; for (unsigned i = 0; i &lt; N; ++i) { deck[i] = i; } unsigned max = N - 1; for (unsigned i = 0; i &lt; K; ++i) { const unsigned index = Random(i_set, deck, max + 1); std::swap(deck[max], deck[index]); o_res[i] = i_set[deck[max]][0]; --max; } } </code></pre> <h2>Usage</h2> <pre><code>int main() { srand((unsigned)time(0)); const unsigned c_N = 5; // N const unsigned c_K = 2; // K Pair input[c_N] = {{0, 5}, {1, 3}, {2, 2}, {3, 5}, {4, 4}}; // input array unsigned result[c_K] = {}; const unsigned c_total = 1000000; // number of iterations unsigned counts[c_N] = {0}; // frequency counters for (unsigned i = 0; i &lt; c_total; ++i) { Generate&lt;c_N, c_K&gt;(input, result); for (unsigned j = 0; j &lt; c_K; ++j) { ++counts[result[j]]; } } unsigned sumOfWeights = 0; for (unsigned i = 0; i &lt; c_N; ++i) { sumOfWeights += input[i][1]; } for (unsigned i = 0; i &lt; c_N; ++i) { std::cout &lt;&lt; (double)counts[i]/c_K/c_total // empirical frequency &lt;&lt; " | " &lt;&lt; (double)input[i][1]/sumOfWeights // expected frequency &lt;&lt; std::endl; } return 0; } </code></pre> <h2>Output</h2> <pre><code>N = 5, K = 2 Frequencies Empiricical | Expected 0.253813 | 0.263158 0.16584 | 0.157895 0.113878 | 0.105263 0.253582 | 0.263158 0.212888 | 0.210526 </code></pre> <p>Corner case when weights are actually ignored</p> <pre><code>N = 5, K = 5 Frequencies Empiricical | Expected 0.2 | 0.263158 0.2 | 0.157895 0.2 | 0.105263 0.2 | 0.263158 0.2 | 0.210526 </code></pre>
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