MathDB

Given are the real line and the two unique marked points

0

and

1

. We can perform as many times as we want the following operation: we take two already marked points

a

and

b

and mark the reflection of

a

over

b

. Let

f(n)

be the minimum number of operations needed to mark on the real line the number

n

(which is the number at a distance

\left| n\right|

from

0

and it is on the right of

0

n>0

and on the left of

0

n<0

). For example,

f(0)=f(1)=0

and

f(-1)=f(2)=1

. Find

f(n)

Problem Statement