# Hash table

In computinga hash table hash map is a data structure that implements an associative array abstract data typea structure that can map keys to values. A hash table uses a hash function to compute an indexalso called a hash codeinto an array of buckets or slotsfrom which the desired value can be found. During lookup, the key is hashed and the resulting hash indicates where the corresponding value is stored.

Ideally, the hash function will assign each key to a unique bucket, but most hash table designs employ an imperfect hash function, which might cause hash collisions where the hash function generates the same index for more than one key. Such collisions are typically accommodated in some way. In a well-dimensioned hash table, the average cost number of instructions for each lookup is independent of the number of elements stored in the table.

Many hash table designs also allow arbitrary insertions and deletions of key-value pairs, at amortized [2] constant average cost per operation. In many situations, hash tables turn out to be on average more efficient than search trees or any other table lookup structure. For this reason, they are widely used in many kinds of computer softwareparticularly for associative arraysdatabase indexingcachesand sets.

Given a key, the algorithm computes an index that suggests where the entry can be found:. In the case that the array size is a power of twothe remainder operation is reduced to maskingwhich improves speed, but can increase problems with a poor hash function.

A basic requirement is that the function should provide a uniform distribution of hash values. A non-uniform distribution increases the number of collisions and the cost of resolving them.

Uniformity is sometimes difficult to ensure by design, but may be evaluated empirically using statistical tests, e. The distribution needs to be uniform only for table sizes that occur in the application.

In particular, if one uses dynamic resizing with exact doubling and halving of the table size, then the hash function needs to be uniform only when the size is a power of two.

## Hash Table in Data Structure: Python Example

Here the index can be computed as some range of bits of the hash function. On the other hand, some hashing algorithms prefer to have the size be a prime number. For open addressing schemes, the hash function should also avoid clusteringthe mapping of two or more keys to consecutive slots. Such clustering may cause the lookup cost to skyrocket, even if the load factor is low and collisions are infrequent. The popular multiplicative hash [3] is claimed to have particularly poor clustering behavior.

Cryptographic hash functions are believed to provide good hash functions for any table size, either by modulo reduction or by bit masking [ citation needed ]. They may also be appropriate if there is a risk of malicious users trying to sabotage a network service by submitting requests designed to generate a large number of collisions in the server's hash tables. However, the risk of sabotage can also be avoided by cheaper methods such as applying a secret salt to the data, or using a universal hash function.

A drawback of cryptographic hashing functions is that they are often slower to compute, which means that in cases where the uniformity for any size is not necessary, a non-cryptographic hashing function might be preferable. If all keys are known ahead of time, a perfect hash function can be used to create a perfect hash table that has no collisions. If minimal perfect hashing is used, every location in the hash table can be used as well.

Perfect hashing allows for constant time lookups in all cases. This is in contrast to most chaining and open addressing methods, where the time for lookup is low on average, but may be very large, O nfor instance when all the keys hash to a few values.

As the load factor grows larger, the hash table becomes slower, and it may even fail to work depending on the method used.A hash is a value that has a fixed length, and it is generated using a mathematical formula.

Hash values are used in data compression, cryptology, etc. In data indexing, hash values are used because they have fixed length size regardless of the values that were used to generate them.

It makes hash values to occupy minimal space compared to other values of varying lengths. A hash function employs a mathematical algorithm to convert the key into a hash.

A collision occurs when a hash function produces the same hash value for more than one key.

In this Algorithm tutorial, you will learn: What is Hashing? What is a Hash Table?

Understanding and implementing a Hash Table (in C)

Each value is assigned a unique key that is generated using a hash function. The name of the key is used to access its associated value. This makes searching for values in a hash table very fast, irrespective of the number of items in the hash table.

Hash functions For example, if we want to store employee records, and each employee is uniquely identified using an employee number. We can use the employee number as the key and assign the employee data as the value. This approach introduces a storage space problem.

A hash function solves the above problem by getting the employee number and using it to generate a hash integer value, fixed digits, and optimizing storage space. The purpose of a hash function is to create a key that will be used to reference the value that we want to store. The function accepts the value to be saved then uses an algorithm to calculate the value of the key.

The parameter k is the value that we want to calculate the key for. We use the modulus operator to calculate the key. Example Let's assume that we have a list with a fixed size of 3 and the following values [1,2,3] We can use the above formula to calculate the positions that each value should occupy. The following image shows the available indexes in our hash table.

Qualities of a good hash function A good hash function should have the following qualities. The formula for generating the hash should use the data's value to be stored in the algorithm. The hash function should generate unique hash values even for input data that has the same amount. The function should minimize the number of collisions. Collisions occur when the same value is generated for more than one value. The values must be distributed consistently across the whole possible hashes.

Collision A collision occurs when the algorithm generates the same hash for more than one value. Let's look at an example.A hash table organizes data so you can quickly look up values for a given key. Java has two hash table classes: HashTable and HashMap. In general, you should use a HashMap. While both classes use keys to look up values, there are some important differences, including:. Arrays are pretty similar to hash maps already. Arrays let you quickly look up the value for a given "key".

Think of a hash map as a "hack" on top of an array to let us use flexible keys instead of being stuck with sequential integer "indices.

All we need is a function to convert a key into an array index an integer.

That function is called a hashing function. To look up the value for a given key, we just run the key through our hashing function to get the index to go to in our underlying array to grab the value. How does that hashing method work?

There are a few different approaches, and they can get pretty complicated. But here's a simple proof of concept:. The result is But what if we only have 30 slots in our array?

Modding our sum by 30 ensures we get a whole number that's less than 30 and at least 0 :.

The hashing method s used in modern systems get pretty complicated—the one we used here is a simplified example. What if two keys hash to the same index in our array? In our example above, look at "lies" and "foes":.

This is called a hash collision. There are a few different strategies for dealing with them.

## Hash Table

Here's a common one: instead of storing the actual values in our array, let's have each array slot hold a pointer to a linked list holding the values for all the keys that hash to that index:. Notice that we included the keys as well as the values in each linked list node. Otherwise we wouldn't know which key was for which value! There are other ways to deal with hash collisions. This is just one of them.

If all our keys caused hash collisions, we'd be at risk of having to walk through all of our values for a single lookup in the example above, we'd have one big linked list.

### Hash tables explained [step-by-step example]

This is unlikely, but it could happen. That's the worst case. Suppose we keep adding more items to our hash map. As the number of keys and values in our hash map exceeds the number of indices in the underlying array, hash collisions become inevitable.

To mitigate this, we could expand our underlying array whenever things start to get crowded. That requires allocating a larger array and rehashing all of our existing keys to figure out their new position— time.

Sets often come up when we're tracking groups of items—nodes we've visited in a graph, characters we've seen in a string, or colors used by neighboring nodes.

Usually, we're interested in whether something is in a set or not.In computing, a hash table hash map is a data structure used to implement an associative array, a structure that can map keys to values. A hash table uses a hash function to compute an index into an array of buckets or slots, from which the desired value can be found.

Hash collisions are practically unavoidable when hashing a random subset of a large set of possible keys. Therefore, almost all hash table implementations have some collision resolution strategy to handle such events. Some common strategies are described below. All these methods require that the keys or pointers to them be stored in the table, together with the associated values.

Separate chaining Open addressing Robin Hood hashing. Separate chaining In the method known as separate chaining, each bucket is independent, and has some sort of list of entries with the same index.

### Data Structure and Algorithms - Hash Table

The time for hash table operations is the time to find the bucket which is constant plus the time for the list operation.

In a good hash table, each bucket has zero or one entries, and sometimes two or three, but rarely more than that. Therefore, structures that are efficient in time and space for these cases are preferred. Structures that are efficient for a fairly large number of entries per bucket are not needed or desirable. If these cases happen often, the hashing is not working well, and this needs to be fixed. In another strategy, called open addressing, all entry records are stored in the bucket array itself.

When a new entry has to be inserted, the buckets are examined, starting with the hashed-to slot and proceeding in some probe sequence, until an unoccupied slot is found. When searching for an entry, the buckets are scanned in the same sequence, until either the target record is found, or an unused array slot is found, which indicates that there is no such key in the table.

This method is also called closed hashing; it should not be confused with "open hashing" or "closed addressing" that usually mean separate chaining. One interesting variation on double-hashing collision resolution is Robin Hood hashing. The net effect of this is that it reduces worst case search times in the table. This is similar to ordered hash tables[17] except that the criterion for bumping a key does not depend on a direct relationship between the keys.

Since both the worst case and the variation in the number of probes is reduced dramatically, an interesting variation is to probe the table starting at the expected successful probe value and then expand from that position in both directions. Hash tables are the fastest data storage structure. This makes them a necessity for situations in which a computer program, rather than a human, is interacting with the data.

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Hash tables are typically used in spelling checkers and as symbol tables in computer language compilers, where a program must check thousands of words or symbols in a fraction of a second. Associative arrays Hash tables are commonly used to implement many types of in-memory tables.

They are used to implement associative arrays arrays whose indices are arbitrary strings or other complicated objectsespecially in interpreted programming languages like Perl, Ruby, Python, and PHP. Database indexing Hash tables may also be used as disk-based data structures and database indices such as in dbm although B-trees are more popular in these applications.

In multi-node database systems, hash tables are commonly used to distribute rows amongst nodes, reducing network traffic for hash joins.Hash tables are used to implement map and set data structures in most common programming languages.

Hash tables offer a combination of efficient lookupinsert and delete operations. Neither arrays nor linked lists can achieve this :. The most common hash table implementation uses chaining with linked lists to resolve collisions.

This combines the best properties of arrays and linked lists. To distribute the data evenly, we use several short lists. All records with keys that end with belong to one list, those with keys that end with belong to another one, and so on. There is a total of such lists. This structure can be represented as an array of lists:. Since the keys are random, there will be roughly the same number of records in each list.

Using the same technique, deletion can also be implemented in constant average time. The number of records in each list must remain small, and the records must be evenly distributed over the lists. To achieve this we just need to change the hash functionthe function which selects the list where a key belongs. In general, a hash function is a function from E to We want this function to be uniform: it should map the expected inputs as evenly as possible over its output range.

The efficiency of a hash table depends on the fact that the table size is proportional to the number of records. If the table size is increased by a constant factor for each resizing, i. For more on the performance of this strategy, see Amortized time complexity. Share this page :. This hash table consists of an array with entries, each of which refers to a linked lists of key-value pairs.Hash Table is a data structure which stores data in an associative manner.

In a hash table, data is stored in an array format, where each data value has its own unique index value. Access of data becomes very fast if we know the index of the desired data. Thus, it becomes a data structure in which insertion and search operations are very fast irrespective of the size of the data. Hash Table uses an array as a storage medium and uses hash technique to generate an index where an element is to be inserted or is to be located from.

Hashing is a technique to convert a range of key values into a range of indexes of an array. We're going to use modulo operator to get a range of key values.

Consider an example of hash table of size 20, and the following items are to be stored.

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Item are in the key,value format. As we can see, it may happen that the hashing technique is used to create an already used index of the array. In such a case, we can search the next empty location in the array by looking into the next cell until we find an empty cell. This technique is called linear probing. Define a data item having some data and key, based on which the search is to be conducted in a hash table.

Whenever an element is to be searched, compute the hash code of the key passed and locate the element using that hash code as index in the array. Use linear probing to get the element ahead if the element is not found at the computed hash code. Whenever an element is to be inserted, compute the hash code of the key passed and locate the index using that hash code as an index in the array.

Use linear probing for empty location, if an element is found at the computed hash code. Whenever an element is to be deleted, compute the hash code of the key passed and locate the index using that hash code as an index in the array. Use linear probing to get the element ahead if an element is not found at the computed hash code.

When found, store a dummy item there to keep the performance of the hash table intact. To know about hash implementation in C programming language, please click here. Previous Page. Next Page. Previous Page Print Page.Media and digital devices are an integral part of our world today. The benefits of these devices, if used moderately and appropriately, can be great. But, research has shown that face-to-face time with family, friends, and teachers plays a pivotal and even more important role in promoting children's learning and healthy development.

Keep the face-to-face up front, and don't let it get lost behind a stream of media and tech. Editor's Note: The tips above were written from two AAP policies, "Media Use in School-Aged Children and Adolescents" and "Media and Young Minds," and the technical report entitled "Children and Adolescents and Digital Media," which were published in the November 2016 edition of Pediatrics. They were also drawn from the proceedings of the AAP Sponsored Growing Up Digital: Media Research Symposium, a gathering of media experts, researchers and pediatricians held in 2015 to address new developments in research and media and their impact on children.

Tips AAP to Help Families Manage the Ever Changing Digital Landscape:Make your own family media use plan. Additional Information from HealthyChildren. There may be variations in treatment that your pediatrician may recommend based on individual facts and circumstances.

When reviewing business headlines and news stories it can be difficult to decide which topic is mentioned more often -- data analytics or social media. This can be even more frustrating if you, as an entrepreneur, are trying to decide where to focus your limited time, money, and energy to help give your business an edge. Making adoption of social media strategies even more difficult is the fact that this field changes so rapidly. Many of the negative reactions to social media are usually based on an understanding of social media that is limited to snarky Tweets, sharing funny cat videos, and using different filters on Snapchat.

This understanding, however, provides only an incomplete view of what social media can do for you and your business.

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As I am sure you have seen, however, there are many different types of social media you could use for your business. It is also important to recognize that while most social media tools are free to use, there are certain products and services that provide a base level of services for free, but charge for more sophisticated services.

Fortunately there are some common sense, and budget friendly, things you can do to increase the impact of your social media bucks. For example, if you own a bakery, work in retail, or own a floral business on the side, Pinterest might be the best way to showcase your business. Focusing on showcasing your business in the best possible light always makes sense, and is no different for social media utilization.

Both platforms, especially Facebook, have incredibly large platforms that can boost the reach of your business without costing you an arm and a leg. After you have selected your social media platform of choice, it is important to put together a plan (even a simple plan) on how often you will update, post, or otherwise engage on social media.

Chambers of commerce, small business development centers, and other local resources are just a few of the groups that you should be sure to engage with, and they are always happy to hear from interested parties.

Especially for social media, where content is posted and shared on a minute-by-minute basis, it is even easier to adapt your approach to your customers and professional associations. Social media is a potentially great tool, should be used to help build and expand your business, and can be implemented without breaking the bank. That said, it is impossible to overlook the benefits of building a social media strategy, engaging with customers, and expanding the reach of your business in an increasingly digital environment.

Approaching social media from a business perspective, setting up a plan, and selecting the right strategy for your business can set your business up for an effective social media campaign. Sean serves on the Board of Governors at Fairleigh Dickinson University, and is an incoming member of the 2017 class of the AICPA Leadership Academy.

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A member of the AICPA Commission on Financial Literacy, NJCPA Content Advisory Board, and NJCPA Emerging Leaders Council, Sean has published dozens of articles on technology, finance, and personal finance issues.