Wednesday, 16 January 2008

gnome sort

Gnome sort is a compact O(n²) algorithm to re-arrange a sequence of elements into order. In his article on Gnome sort, Dick Grune describes the algorithm as follows:
Gnome Sort is based on the technique used by the standard Dutch Garden Gnome (Du.: tuinkabouter). Here is how a garden gnome sorts a line of flower pots. Basically, he looks at the flower pot next to him and the previous one; if they are in the right order he steps one pot forward, otherwise he swaps them and steps one pot backwards. Boundary conditions: if there is no previous pot, he steps forwards; if there is no pot next to him, he is done.
The Gnome sort article on Wikipedia describes a slightly modified algorithm.

Implementation in Redcode:
          org    inner

temp equ (outer-1)

outer mov }p, temp
p mov FIRST+LENGTH-1, {p
nop >y, }p
mov temp, }p
sne y, #LENGTH
nop <y, {p
inner slt *p, {p
y djn inner, #LENGTH-1
jmn outer, y

The redcode implementation is just 9 lines long, and requires 4.5n²-3.5n cycles to sort the sequence in the worse case.

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