# Select

(algorithm)

**Definition:**
A four-part algorithm to select the k^{th} smallest element of an *array*. Part 1) Consider the array as groups of 5 elements; sort and find the *median* of each group. 2) Use Select *recursively* to find *x*, the median of the medians. 3) Next *partition* the array around *x*. 4) Let i be the number of elements in the low side of the partition. If k ≤ i, use Select recursively to find the k^{th} element of the low side. Otherwise Select the k-i^{th} element of the high side.

**See also**
*select and partition*, *select k*^{th} element, *Find*, *MODIFIND*, *tournament*, *reservoir sampling*.

*Note:
After [CLR90, p 190]. Sometimes called "quick select". *

*
** The number of comparisons to select the i*^{th} smallest of n numbers is n+min(i,n-i)+*o(n)* or *Θ*(n).

Author: PEB

## More information

**Robert W. Floyd** and **Ronald L. Rivest**, *Expected time bounds for selection*, CACM, 18(3):165-172, March 1975

**Robert W. Floyd and Ronald L. Rivest**, *Algorithm #489 SELECT*, CACM, 18(3):173, March 1975

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Entry modified 14 January 2009.

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Cite this as:

Paul E. Black, "Select", 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/select.html