(classic problem)

**Definition:**
Find the k^{th} smallest element of a set. Two approaches are a modified *distribution sort* or *select and partition*.

**Also known as** selection problem, find k^{th} least element, k^{th} smallest element.

**See also**
*Select*, *MODIFIND*, *Find*, *reservoir sampling*.

*Note:
The select-and-partition approximately divides in half the number of elements that must be considered at each step. The modified distribution sort divides by m the number of elements at each step. The latter is faster, but the former is more generally applicable.*

Author: PEB

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Entry modified 14 January 2009.

HTML page formatted Fri Feb 23 10:06:08 2018.

Cite this as:

Paul E. Black, "select k^{th} element", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 14 January 2009. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/selectkth.html