ReviewProblems4 - Faculty of Computers and Information...

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Unformatted text preview: Faculty of Computers and Information Faculty of Computers and Information Faculty of Computers and Information Faculty of Computers and Information Review Problems 4 Department of Computer Science Data Structures 1. Prove that the number of elements in the left and right sub-trees produced by the binary search (studied in lectures) are given by L = „ n- 1 2 ” = l n 2 m- 1 (1) R = » n- 1 2 … = j n 2 k (2) 2. Give an example of a tree that is not complete, still, with leaves only at the last two levels. 3. Some authors, e.g., (Knuth, 1997, Sec. 2.3.4.5, Eq. (4)), derive the internal path length as: I n = ( n + 1) q- 2 q +1 + 2 , where (3) q = b lg ( n + 1) c (4) This is similar to what we have derived in lectures, except that we had q = b lg n c . (a) Show that b lg ( n + 1) c and b lg n c are not always equal to each other. When are they equal? (b) Show that although b lg ( n + 1) c 6 = b lg n c , both expressions for internal path are exactly the same....
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