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A hash table works as follows. We allocate a table of m slots. All the items...

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Advance Math

A hash table works as follows. We allocate a table of m slots.All the items we intend to store in the table belong to a large setU of items. We adopt a function f: U ->{0,1...m-1) which maps anitem to a slot.

Suppose we seek to store n items from U in a table of mslots.

(a) Suppose f maps every item in U with equal probability to oneof the m slots. What is the probability, given two distinct itemsi1,i2∈ U, that f(i1),f(i2)?

(b) Prove that if |U| > nm, then no matter what f is, thereexist n items in U all of which are mapped by f to the sameslot.

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