If we start from an empty max binomial heap, and insert integers 1, 2, . . , n into the heap in a random ordering, what is the probability that integer n forms a singleton binomial tree by itself in the final heap? what is the probability that n is the root of the largest binomial tree in the final heap?

Why should characters such as / \ " ' * ; - ? [ ] ( ) ~ ! $ { } < > # @ & | space, tab, and newline be avoided in file names?

1. before plugging in a new device to a computer you should unplug all other devices turn off the computer turn on the computer 2. many of the maintenance tools for a computer can be found in the control panel under administrative tools display personalization

Suppose there is a relation r(a, b, c) with a b+-tree index with search keys (a, b).1. what is the worst-case cost of finding records satisfying 10 < a < 50 using this index, in terms of the number of records n1, retrieved and the height h of the tree? 2. what is the worst-case cost of finding records satisfying 10 < a < 50 and 5 < b < 10 using this index, in terms of the number of records n2 that satisfy this selection, as well as n1 and h defined above? 3. under what conditions on n1 and n2, would the index be an efficient way of finding records satisfying the condition from part (2)?