deletions | additions       diff --git a/c) Imposing a restriction.tex b/c) Imposing a restriction.tex  index 3be8046..f085a1c 100644  --- a/c) Imposing a restriction.tex  +++ b/c) Imposing a restriction.tex 
...
\section{c) Imposing a restriction}  One possible restriction would be to limit the amount possible to invest in each company to a constant amount $c$, so that the choice of how much to invest in a specific company instead becomes a choice of whether to invest money in the company or not. This makes the problem equivalent to the 0/1 knapsack. In this case, the algorithm becomes:  \begin{verbatim}  function maxReturn(i, x) begin  initialise mem[0..i, 0..x] to -1  return mr(i, x)  end  function mr(i, x) begin  if mem[i, x] != -1 then  if i = 0 then  let mem[i, x] = 0  end  let mem[i, x] = max(mr(i - 1, x), g(i, c) + mr(i - 1, x - c))  end  return mem[i, x]  end  \end{verbatim}  \begin{algorithm}[H]  \caption{Computes the maximum return of investing $x$ dollars in $i$ companies Input: $i$ is the set of companies or the index of the last element, $x$ is the amount of dollars available for investment. Uses dynamic programming.  \label{alg:max-return-dp}}  \begin{algorithmic}[1]  \Function{maxReturn}{$i, x$}  \Let{$mem$}{$matrix[i, x]$ with each element to $-1$}  \Return{$\Call{mr}{i, x}$}  \EndFunction  \Statex  \Function{mr}{$i, x$}  \If{$mem[i,x] \neq -1$}  \If{$i = 0$}  \Let{$mem[i,x]$}{$0$}  \EndIf  \Let{$mem[i,x]$}{$max[mr(i - 1, x), g(i, c) + mr(i - 1, x - c)]$}  \EndIf  \Return{$mem[i,x]$}  \EndFunction  \end{algorithmic}  \end{algorithm}