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Tik-61.183 Special course on information technology III \\
Randomized algorithms \\ Spring 2000 \\ Heikki Mannila

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\textbf{Exercises 3, due March 15, 2000}

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\item Complete last time's exercise 2.4: show that the given algorithm 
  does indeed select a permutation uniformly.
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    Set~$X\leftarrow(1,2,\dots,n)$.\\
    Repeat for~$i=1,2,\dots,n-1$:\\
    \>Select a number $r\in\{i,i+1,\dots,n\}$ at random.\\
    \>Exchange~$X[i]\leftrightarrow X[r]$.\\
    Output~$X$.\\
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