# Linear probing rehashing

Open Addressing - when a data item cannot be placed at the index calculated by the hash function, another location in the aray is sought. In Linear Probing we search sequentially for vacant cells. As more items are inserted in the array clusters grow larger.

It is not a problem when the array is half full, and still not bad when it is two- thirds full. Beyond this, however, the performance degrades seriously as the clusters grow larger and larger. The performance is determined by the Load Factor.

The Load Factor is the ratio of the number of items in a table to the table's size. The problem with Quadratic Probing is that it gives rise to secondary clustering.

Double Hashing or rehashing: Hash the key a second time, using a different hash function, and use the result as the step size. For a given key the step size remains constant throughout a probe, but it is different for different keys. The secondary hash function must not be the same as the primary hash function and it must not output 0 zero. Double hashing requires that the size of the hash table is a prime number.

Using a prime number as the array size makes it impossible for any number to divide it evenly, so the probe sequence will eventually check every cell. Suppose the array size is 15 indices from 0 to 14 and that a particular key hashes to an initial index of 0 and a step size of 5. For example consider hashing the following sequence of numbers 15, 30, 45, 60, 75, 90, Then the probe sequence will be 0, 5, 10, 0, 5, 10, and so on, repeating endlessly.

If the array size was 13 and the numbers were [13, 26, 39, 42, 65, 78, 91] then the step size would be [2, 4, 1, 3, 5, 2, 4]. Supposing the step size was the same for a set of numbers then the sequence of steps would be [0, 5, 10, 2, 7, 12, 4, 9, 1, 6, 11, 3] and so on.

If there is even one empty cell, the probe will find it. In Separate Chaining a data item's key is hashed to the index in the usual way, and the item is inserted into the linked list at that index. Other items that hash to the same index are simply added to the linked list. In separate chaining it is normal to put N or more items into an N-cell array.

Finding the initial cell takes fast O 1 time, but searching through a list takes time proportional to the number of items on the list - O m. In separate chaining the load factor can rise above 1 without hurting performance very much. It is not important to make the table size a prime number. Buckets: Another approach similar to separate chaining is to use an array at each location in the hash table instead of a linked list. Such arrays are called buckets.Tag: chash.

In an attempt to learn hashing, I am trying to make a hash table where hashing is done by linear probing. Following is the code for the same. But the program stops in between when I execute it. The confusing part is that sometimes the resizing of table occurs for a number of steps, while the other times it does not. The resizing is done in the rehashing function. It is required for the the initial table size to be 31 and go up till When you rehashyou pass the old and new has arrays as pointer.

You also do some rather strage things at the end of your function:. Let's look at the end first. At ayou allocate space, initialise everything and then immediately overwrite a with the copy, effectively giving up the handle to the new memory. Also, why initialise at the end? Is that a leftover from copying and pasting? Skip the allocation and initialisation. Next, you assign the handle of copy to a. These arrays are now the same. When you free them at byou free both.

Because you have passed the hash arrays as pointers, the calling function cannot know about the change you make. In functions where you change the contents of arrays, it is enough to pass a pointer. But malloc changes the pointer itself, so at least copy should be a pointer to pointer. Better yet, you can just pass the original array:. Alternatively, you could return the new pointer.

You can do that safely withz malloc ed memory, but not with local arrays. So your function might look like:. There is no need for copy outside the rehash function, so you shouldn't pass it to insertfor example. Yes, ptr2 is unaffected by reallocit has no connection to realloc call whatsoever as per the current code.We strongly recommend to refer below post as a prerequisite of this. Open Addressing Like separate chaining, open addressing is a method for handling collisions.

In Open Addressing, all elements are stored in the hash table itself. So at any point, size of the table must be greater than or equal to the total number of keys Note that we can increase table size by copying old data if needed.

Delete k : Delete operation is interesting. If we simply delete a key, then search may fail. For example, typical gap between two probes is 1 as taken in below example also. Clustering: The main problem with linear probing is clustering, many consecutive elements form groups and it starts taking time to find a free slot or to search an element.

See this for step by step diagrams. Comparison of above three: Linear probing has the best cache performance but suffers from clustering. One more advantage of Linear probing is easy to compute. Double hashing has poor cache performance but no clustering. Double hashing requires more computation time as two hash functions need to be computed. Performance of Open Addressing: Like Chaining, the performance of hashing can be evaluated under the assumption that each key is equally likely to be hashed to any slot of the table simple uniform hashing.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. Writing code in comment? Please use ide. Insert k : Keep probing until an empty slot is found.

Once an empty slot is found, insert k. Load Comments.Prerequisites: Hashing Introduction and Collision handling by separate chaining. As the name suggests, rehashing means hashing again.

Basically, when the load factor increases to more than its pre-defined value default value of load factor is 0.

So to overcome this, the size of the array is increased doubled and all the values are hashed again and stored in the new double sized array to maintain a low load factor and low complexity. Rehashing is done because whenever key value pairs are inserted into the map, the load factor increases, which implies that the time complexity also increases as explained above. This might not give the required time complexity of O 1. Hence, rehash must be done, increasing the size of the bucketArray so as to reduce the load factor and the time complexity.

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Prerequisites: Hashing Introduction and Collision handling by separate chaining How hashing works: For insertion of a key K — value V pair into a hash map, 2 steps are required: K is converted into a small integer called its hash code using a hash function. Complexity and Load Factor For the first steptime taken depends on the K and the hash function.

But for very large values of n, the number of entries into the map, length of the keys is almost negligible in comparison to n so hash computation can be considered to take place in constant time, i. For the second steptraversal of the list of K-V pairs present at that index needs to be done. For this, the worst case may be that all the n entries are at the same index. So, time complexity would be O n. But, enough research has been done to make hash functions uniformly distribute the keys in the array so this almost never happens.

This Load Factor needs to be kept low, so that number of entries at one index is less and so is the complexity almost constant, i. Rehashing: As the name suggests, rehashing means hashing again. K key. V value. Check out this Author's contributed articles. Load Comments.To store data into the hash table, one must know that in order to do this, a certain value must be divided. For example if the data is consist of n integers and we have k number of cells.

Then the address wherein the data would be stored is the function:. The above algorithm will only work if the given data is in integer. How about strings or character datas?

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For strings of integers this is done by splitting the string into equal numbers of substring, where each substring can be represented as an integer. In this way, the n in the hash function can be found by adding the value of each substring.

While in the character scenario, this can be solved by assigning each letter to their corresponding place in the alphabet. For example, the letter A is 1 while Z is In this manner, all letters has their own number correspondence. In the string of character problem, this problem can be solved by just adding the corresponding number of each letter, thus gaining a single number to be hashed.

The main problem that would occur is the collision, this is a scenario wherein, there will be a limited number of memory, and two or more data can collide in a single address. This problem can be solved by a rehashing algorithm. The need to have a rehash function arises when a collision occurs.

This happens when two or more information would collide on the same cell allocated for the hash table. Thus, a rehashing is needed. Then, the rehashing function is the method for finding the second or third or so on location for the information. One rehashing technique is the Linear Probing, where the rehashing is done by looking for the next empty space that it can occupy. The function for the rehashing is the following:. In this way, finding an empty space is easy and also the search for a stored item would be easier.

To test this algorithm, the use of the following example is needed. For example, we have a hash table that could accommodate 9 information, and the data to be stored were integers. Therefore, 27 is stored at 0. In this event, the need to rehash is needed. Since 1 is empty, 18 can be stored in it.

To retrieve data, the hash function and the rehash function were also useful. Using the example from above, retrieving 18 is done by using the hash function to find the key and check if the data would coincide to the data needed. If not, then the rehash would be needed.

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Until such time the correct location is found or an empty space is encountered that is the value of that space is -1which means that the data does not exist. This is authentic because, the path of the search function would be the same path that was used in storing the data. The use of the -2 value for deleted items is useful in such a way that in traversing the hash table, encountering a deleted cell would not end the traversal. For example, 5 spaces for integers. Input: 1,5,27,25 21, Delete 5.

Look for 25, Since 3 is -1, 25 can be stored here. Then, we assign a new value -2 location 0 to indicate this value have been deleted. To look for 25, we use the hash key, to find its location.

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And found 0, but then the value stored I n array[0] is not the same, therefore, the rehashing would be used. Then we traverse the hash table, until we found the right place.Linear probing is a scheme in computer programming for resolving hash collisions of values of hash functions by sequentially searching the hash table for a free location.

This is accomplished using two values - one as a starting value and one as an interval between successive values in modular arithmetic. The second value, which is the same for all keys and known as the stepsizeis repeatedly added to the starting value until a free space is found, or the entire table is traversed.

This algorithm, which is used in open-addressed hash tables, provides good memory caching if stepsize is equal to onethrough good locality of reference, but also results in clustering, an unfortunately high probability that where there has been one collision there will be more. The performance of linear probing is also more sensitive to input distribution when compared to double hashing. Given an ordinary hash function H xa linear probing function would be:.

Here H x is the starting value, n the size of the hash table, and the stepsize is i in this case. Data Structures Interview Questions. Data Structures Practice Tests. IT Skills. Management Skills. Communication Skills. Business Skills. Digital Marketing Skills. Human Resources Skills. Health Care Skills. Finance Skills.

## Quadratic Probing and Double Hashing

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Cuckoo Hashing. Adv Java Tutorial.Quadratic Probing and Double Hashing attempt to find ways to reduce the size of the clusters that are formed by linear probing. Quadratic Probing is similar to Linear probing. With linear probing we know that we will always find an open spot if one exists It might be a long search but we will find it. However, this is not the case with quadratic probing unless you take care in the choosing of the table size.

For example consider what would happen in the following situation:. In order to guarantee that your quadratic probes will hit every single available spots eventually, your table size must meet these requirements:.

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Double Hashing is works on a similar idea to linear and quadratic probing. Use a big table and hash into it. Whenever a collision occurs, choose another spot in table to put the value. The difference here is that instead of choosing next opening, a second hash function is used to determine the location of the next spot.

For example, given hash function H1 and H2 and key. Quadratic Probing and Double Hashing. Quadratic Probing and Double Hashing Quadratic Probing and Double Hashing attempt to find ways to reduce the size of the clusters that are formed by linear probing.

Quadratic Probing Quadratic Probing is similar to Linear probing. For example consider what would happen in the following situation: Table size is First 5 pieces of data that all hash to index 2 First piece goes to index 2. In order to guarantee that your quadratic probes will hit every single available spots eventually, your table size must meet these requirements: Be a prime number never be more than half full even by one element Double Hashing Double Hashing is works on a similar idea to linear and quadratic probing.

If it is empty, put record in it. If it is not empty calculate hash2 key. No results matching " ".