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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.
Updated on: 13-Jul-2020
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