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Recall that a skiplist stores elements in a sequence of smaller and smaller lists Lo, ..., Lh. The list L, is obtained from Lp-1 by tossing a fair coin for each element in Lp-1 and including the element in L, if that coin comes up heads. In this way, tossing a coin and counting how many times it comes up heads before the first tail is equal to the height of an element x. Suppose instead of a fair coin (a coin in which heads and tails are equally likely at 1/2-1/2), we instead have a biased coin that comes up heads 1/3 of the time and tails 2/3 of the time. With this new coin, which of the following is expected? ) The expected height of an element x would increase. The expected height of an element x would decrease. The expected length of the search path to x would increase. The expected length of the search path to x would decrease. ) both a. and d. ) both b. and c. ) None of the above.

Recall that a skiplist stores elements in a sequence of smaller and smaller lists Lo, ..., Lh. The list L, is obtained from Lp-1 by tossing a fair coin for each element in Lp-1 and including the element in L, if that coin comes up heads. In this way, tossing a coin and counting how many times it comes up heads before the first tail is equal to the height of an element x. Suppose instead of a fair coin (a coin in which heads and tails are equally likely at 1/2-1/2), we instead have a biased coin that comes up heads 1/3 of the time and tails 2/3 of the time. With this new coin, which of the following is expected? ) The expected height of an element x would increase. The expected height of an element x would decrease. The expected length of the search path to x would increase. The expected length of the search path to x would decrease. ) both a. and d. ) both b. and c. ) None of the above.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Recall that a skiplist stores elements in a sequence of smaller and smaller lists Lo, ..., Lh. The list L, is obtained from Lp-1 by tossing a fair coin for each element in Lr-1 and including the element in L, if that coin comes up heads. In this way, tossing a coin and counting how many times it comes up heads before the first tail is equal to the height of an element x. Suppose instead of a fair coin (a coin in which heads and tails are equally likely at 1/2-1/2), we instead have a biased coin that comes up heads 1/3 of the time and tails 2/3 of the time. With this new coin, which of the following is expected? The expected height of an element x would increase. ) The expected height of an element x would decrease. The expected length of the search path to x would increase. ) The expected length of the search path to x would decrease. both a. and d. both b. and c. None of the above.
Transcribed Image Text:Recall that a skiplist stores elements in a sequence of smaller and smaller lists Lo, ..., Lh. The list L, is obtained from Lp-1 by tossing a fair coin for each element in Lr-1 and including the element in L, if that coin comes up heads. In this way, tossing a coin and counting how many times it comes up heads before the first tail is equal to the height of an element x. Suppose instead of a fair coin (a coin in which heads and tails are equally likely at 1/2-1/2), we instead have a biased coin that comes up heads 1/3 of the time and tails 2/3 of the time. With this new coin, which of the following is expected? The expected height of an element x would increase. ) The expected height of an element x would decrease. The expected length of the search path to x would increase. ) The expected length of the search path to x would decrease. both a. and d. both b. and c. None of the above.
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