The Contraction Method on C([0,1]) and Donsker's ... - Eurandom
The Contraction Method on C([0,1]) and Donsker's ... - Eurandom
The Contraction Method on C([0,1]) and Donsker's ... - Eurandom
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Quickselect / Find<br />
Task: Given a list of n different elements S , FIND the element of<br />
rank k .<br />
Algorithm:<br />
◮ Choose <strong>on</strong>e element x at r<strong>and</strong>om (pivot),<br />
◮ Comparing all other elements with x gives sublists S≤, S>,<br />
◮ If In = |S≤| ≥ k, search recursively in S≤ for the element of<br />
rank k, otherwise search recursively inS> for element of rank<br />
k − In.<br />
Henning Sulzbach J. W. Goethe-Universität Frankfurt a. M. <str<strong>on</strong>g>The</str<strong>on</strong>g> <str<strong>on</strong>g>C<strong>on</strong>tracti<strong>on</strong></str<strong>on</strong>g> <str<strong>on</strong>g>Method</str<strong>on</strong>g> <strong>on</strong> C([0, 1]) <strong>and</strong> D<strong>on</strong>sker’s <str<strong>on</strong>g>The</str<strong>on</strong>g>orem