Consider a hash table with `n` slots and ahash function that distributes keysuniformly across the slots. Suppose `m`keys are inserted into the hash table,where `m` is much larger than `n`. What isthe expected number of collisions?Assume that each key is equally likely tobe hashed to any of the `n` slots, and thateach key is independent of all other keys.Express your answer in terms of `n` and`m`.

The expected number of collisions in a hash table can be determined using the formula E(C) = m -…

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hash table with 9+90!! distrib

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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Concept explainers

Hash Table

A hash table also called a hash map, is a data structure that maps key-value pairs. The hash table can be used in complex systems to provide fast access and compact storage. A hash table is a structure that stores data in an abstract data type kind of associative array. It keeps data in an array format, with a distinct index value for every data value. If the index of the required data is known, then the data can be accessed very easily.

Question

Consider a hash table with `n` slots and a
hash function that distributes keys
uniformly across the slots. Suppose `m`
keys are inserted into the hash table,
where `m` is much larger than `n`. What is
the expected number of collisions?
Assume that each key is equally likely to
be hashed to any of the `n` slots, and that
each key is independent of all other keys.
Express your answer in terms of `n` and
`m`.

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