Medians and Order Statistics

The selection problem (assume distinct elements)

Input:

Set A of n numbers and integer i such that 1 $\leq$ i $\leq$ n.

Output:

x $\in$ A such that x is larger than i-1 elements of A (x is the ith smallest element).

i=1:

minimum

i=n:

maximum

i = : median (actually and ).

Simple Solution:

Sort(A)
return(A[i]).
This is O(nlgn).