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PODistribute prizes for a tournament system
 

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    <p>I'm looking for a way to distribute a number across x units. I don't even know how to put this words so I'll give an example:</p> <p>There's a tournament in which the total prize is $1000. I want that the top 20 winners/entrants will win something out of it.<br>I need a mathematical algorithm/formula which will distibute it across those players, and which gives me the power to control certain other factors of the distribution.</p> <p>A factor for example is that I want the top #1 winner will get $300. The top #2 winner will get smaller percentage of it. The total distribution must give everyone something, until the top #20 winner (the last one) which will get at least X$.<br> X$ is another factor I want to control.</p> <p>Any idea? Does this problem has a name (and what's that name is)? Any code example?</p> <p><strong>Edit #1 - my first proposal</strong>:</p> <pre><code>#include &lt;conio.h&gt; #include &lt;vector&gt; #define TOTAL 100 #define WINNERS 15 #define FIRST_WINNER_PERCENTAGE 0.30 void distribute_1(::std::vector&lt;double&gt; * const prizes) { prizes-&gt;clear(); double total = TOTAL; double winning_percentage = FIRST_WINNER_PERCENTAGE; double slope = 0.5; int winners = WINNERS; double winning = 0; for(int i = 0; i &lt; winners; i++, total -= winning, winning_percentage /= 2) { winning = total * winning_percentage; prizes-&gt;push_back(winning); } } void distribute_2(::std::vector&lt;double&gt; * const prizes) { prizes-&gt;clear(); double total = TOTAL; double winning_percentage = FIRST_WINNER_PERCENTAGE; double slope = 0.5; int winners = WINNERS; double winning = 0; for(int i = 0; i &lt; winners; i++, total -= winning/*, winning_percentage /= 2*/) { winning = total * winning_percentage; prizes-&gt;push_back(winning); } } void distribute_3(::std::vector&lt;double&gt; * const prizes) { prizes-&gt;clear(); double total = TOTAL; double winning_percentage = FIRST_WINNER_PERCENTAGE; double slope = 0.0005; int winners = WINNERS; double winning = 0; for(int i = 0; i &lt; winners; i++, total -= winning, winning_percentage -= slope) { winning = total * winning_percentage; prizes-&gt;push_back(winning); } } void distribute_4(::std::vector&lt;double&gt; * const prizes) { prizes-&gt;clear(); double total = TOTAL; double winning_percentage = FIRST_WINNER_PERCENTAGE; double slope = 1 / WINNERS; int winners = WINNERS; double winning = 0; for(int i = 0; i &lt; winners; i++, total -= winning, winning_percentage -= slope) { winning = total * winning_percentage; prizes-&gt;push_back(winning); } } void main() { ::std::vector&lt;double&gt; prizes; distribute_1(&amp;prizes); distribute_2(&amp;prizes); distribute_3(&amp;prizes); distribute_4(&amp;prizes); double total_granted = 0; for(int i = 0; i &lt; WINNERS; i++) { total_granted += prizes[i]; printf("%lf\n", prizes[i]); } printf("-\n%lf\n", total_granted); _getch(); } </code></pre> <p>This is as far as I could reach. The issue with this one is for example, if that if you set 'WINNERS' to 5 for example, the algorithm doesn't reach the 'TOTAL' amount (100 in this example) or even closer (I get a total of 83).</p> <p><strong>Cristy's solution</strong>:</p> <pre><code>#include &lt;conio.h&gt; #include&lt;iostream&gt; //using arithmetic progression using namespace std; int i; float ratio; float first_prize; float s; int main() { float money=1000; const int total_prizes = 10; float last_prize = 99; float prizes[total_prizes+1]; /**/first_prize=2*money/total_prizes-last_prize; //last member of the progresion ratio=(first_prize-last_prize)/(total_prizes-1); prizes[total_prizes]=last_prize; for(i=total_prizes-1;i&gt;=1;i--){ prizes[i]=prizes[i+1]+ratio; money-=prizes[i]; } for(i=1;i&lt;=total_prizes;i++){ printf("%d) %.2f\n",i,prizes[i]); s+=prizes[i]; } printf("TOTAL SUM:%.2f\n",s); printf("Ratio: %.2f", ratio); _getch(); } </code></pre>
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    1. COWithout more constraints, it's not possible to define an algorithm! What sort of distribution do you want? Linear? Quadratic? Something else?
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    2. COThere are literally countless ways that you could do this, and it isn't really a programming related question at this stage.
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    3. COAlso, besides the two factors mentioned above I'd like to control another factor which I define as a "momentum": The stepping in which the prizes will reduce, from the #1 winner to the #20 (last).
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