Static Finger Theorem in Data Structure

STATIC FINGER THEOREM − Let f is treated as a specific element called the finger.

Then the below expression is a bound on the cost of splaying a sequence

O(m + n log(n) + Σ Sum log (|f - i[j]| + 1))j

NOTE − |f-i| is denoted as the distance in the symmetric ordering of the items between the finger and item i.

Where m is denoted as number of update or access operations on a tree having at most n nodes.

Observe that, at least in amortized sense, the time taken for first m operations on a tree that never exceeds more than n nodes is the similar as the time taken for balanced binary search trees like AVL trees, 2-3 trees, etc.