Testing of sequences by simulation

Let $\xi$ be a random integer vector, having uniform distribution $$\mathbf{P}\{\xi =(i_1,i_2,\mathrm{.}\mathrm{.}\mathrm{.},i_n)=1\mathrm{/}{n}^n\}\text{for}1\le i_1,i_2,\mathrm{.}\mathrm{.}\mathrm{.},i_n\le n\mathrm{.}$$ A realization $(i_1,i_2,\mathrm{.}\mathrm{.}\mathrm{.},i_n)$ of $\xi$ is called $\mathit{\text{good}}$, if its elements are different. We present algorithms $\text{textsc}Linear$, $\text{textsc}Backward$, $\text{textsc}Forward$, $\text{textsc}Tree$, $\text{textsc}Garbage$, $\text{textsc}Bucket$ which decide whether a given realization is good. We analyse the number of comparisons and running time of these algorithms using simulation gathering data on all possible inputs for small values of $n$ and generating random inputs for large values of $n$.