It’s not very often that someone invents a new sort, but I have certainly never seen that one before:
#!/bin/bash
function f() {
sleep "$1"
echo "$1"
}
while [ -n "$1" ]
do
f "$1" &
shift
done
wait
The idea is simple: you take the first element of the array, say n, you fork a new process which sleeps n seconds then displays that number. Repeat for the next element.
Calculation of the average complexity of this algorithm left as an exercise to the reader.
Related: Quantum bogosort.
For some reason, I feel like taking a nap.