Rearranging a Bitonic Sequence
Let s = <a0, a1, … , an-1>
- an/2 is the beginning of the decreasing seq.
Let s1= <min{a0, an/2}, min{a1, an/2 +1}…min{an/2-1,an-1}>
Let s2=<max{a0, an/2}, max{a1,an/2+1}… max{an/2-1,an-1} >
In sequence s1 there is an element bi = min{ai, an/2+i}
- all elements before bi are from increasing
- all elements after bi are from decreasing
Sequence s2 has a similar point
Sequences s1 and s2 are bitonic