Searching And Storing Similar Lists

Cover Searching And Storing Similar Lists
Searching And Storing Similar Lists
Richard Cole
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This space sav- ing is repeated recursively, separately for the left and right subtrees.
1i two identical left (right) subtrees are separated by a distinct subtree then we will keep two copies of the identical subtrees. This does not affect the current solution, but is important for the improved solution below.
Suppose we store u left subtrees and v right subtrees for the k trees associated with the k lists. An alternative view is that the u left subtrees represent u lists of length [nH^-l (the
... left sublists), with the sum of the differences between the lists being u-l = r, and the v right subtrees represent v lists of length n- {nH^ (the right sublists), with the sum of the differences between adjacent lists being v - 1 = j . We note r+s-^h.
We can still perform a binary search on any of the lists in time O(logn). The storage S(h, n) is given by: For A^l, S(h, n) ^ 0(h) + S{r, na) + S{s, nri) and 5(0, /i) = 0{n).
The solution is S{h, n) = 0{n + h\ogn).
3. A Second Solution The next attempt at a solution gives up the nice recursive structure we had above.


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