\begin{algorithm} \caption{Randomize in Place - Modified for Proof} \begin{algorithmic} \INPUT An array $A$ of size $n$ \OUTPUT A uniform randomized permutation of $A$ \STATE swap $A[1]$ with $A[$ \CALL{Random}{$1, n$} $]$ \FOR{$i = 2$ \TO $n$} \STATE swap $A[i]$ with $A[$ \CALL{Random}{$i, n$} $]$ \ENDFOR \end{algorithmic} \end{algorithm}