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Unformatted text preview: x into S only if it is not already there. Delete ( S, x ): delete the key x from S (if it is there). FindSmallest ( S, k ): Fnd the kth smallest key in S . All these operations should take O (log n ) time in the worst case, where n is the number of elements in S . 4. Let H be a universal family of hash functions mapping [ n ] = { , 1 , . . . , n1 } to [ m ] = { , 1 , . . . , m1 } . ind the most general relation of m and n that guarantees the existence of a hash function in H that causes no collision when hashing [ n ] into [ m ]. (Hint: Consider that the probability of a random hash function from H causing some collision is strictly less than 1.) 1...
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 Spring '10
 Ray

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