Serial and binary search program in c using function
OpenMP provides a high level of abstraction and allows compiler directives to be embedded in the source code. Ease of use and flexibility are the amongst the main advantages of OpenMP. In OpenMP, you do not see how each and every thread is created, initialized, managed and terminated. You will not see a function declaration for the code each thread executes. You will not see how the threads are synchronized or how reduction will be performed to procure the final result.
You will not see exactly how the data is divided between the threads or how the threads are scheduled. This, however, does not mean that you have no control. OpenMP has a wide array of compiler directives that allows you to decide each and every aspect of parallelization; how you want to split the data, static scheduling or dynamic scheduling, locks, nested locks, subroutines to set multiple levels of parallelism etc.
Another important advantage of OpenMP is that, it is very easy to convert a serial implementation into a parallel one. In many cases, serial code can be made to run in parallel without having to change the source code at all. This makes OpenMP a great option whilst converting a pre-written serial program into a parallel serial and binary search program in c using function. Further, it is still possible to run the program in serial, all the programmer has to do is to remove the OpenMP directives.
OpenMP consists of a set of compiler directives, library routines, and environment variables that influence run-time behavior. So basically when we use OpenMP, we use directives to tell the compiler details of how our code shuld be run in parallel. Programmers do not have to write or cannot write implicit parallelization code, they just have to inform the compiler to do so. It is imperative to note that the compiler does not check if the given code is parallelizable or if there is any racing, it is the responsibility of the programmer to do the required checks for parallelism.
OpenMP programs accomplish parallelism exclusively through the use of threads. The master plays the role of a manager. All the threads exist within a single process. By default, each thread executes the parallelized section of code independently. Work-sharing constructs can be used to divide a task among the threads so that each thread executes its allocated part of the code.
Therefore, both task parallelism serial and binary search program in c using function data parallelism can be achieved using OpenMP. Linear search or sequential search is a method for finding a target value within a serial and binary search program in c using function. It sequentially checks each element of the list for the target value until a match is found or until all the elements have been searched. Linear search is one of the simplest algorithms to implement and has the worst case complexity of O nie.
By parallelizing the implementation, we make the multiple threads split the data amongst themselves and then search for the element independently on their part of the list. All the directives start with pragma omp In the above serial implementation, there is a window to parallelize the for loop. To parallelize the for loop, the openMP directive is: This directive tells the compiler to parallelize the for loop below.
Whilst parallelizing the loop, it is not possible to return from within the if statement if the element is found. This is due to the fact that returning from the if will result in an invalid branch from OpenMP structured block. Hence we will have change the implementation a bit. The above snippet will keep on scanning the the input till the end regardless of a match, it does not have any invalid branches from OpenMP block.
It is as simple as thisall that had to be done serial and binary search program in c using function adding the comipler directive and it gets taken care of, completely. Also, the code will run in serial after the OpenMP directives have been removed, albeit with the modification.
It is noteworthy to mention that with the parallel implementation, each and every element will be checked regardless of a match, though, parallely. This is due to the fact that no thread can directly return after finding the element. Further, if there are more than one instances of the required element present in the array, there is no guarantee that the parallel linear search will return the first match.
The order of threads running and termination is non-deterministic. There is no way of which which thread will return first or last. To preserve the order of the matched results, another attribute index has to be added to the results. You can find the complete code of Parallel Linear Search here. Selection sort is serial and binary search program in c using function in-place comparison sorting algorithm. Selection sort is noted for its simplicity, and it has performance advantages over more complicated algorithms in certain situations, particularly where auxiliary memory is limited.
In selection sort, the list is divided into two parts, the sorted part at the left end and the unsorted part at the right end. Initially, the sorted part is empty and the unsorted part is the entire list. This process continues moving unsorted array boundary by one element to the right. Selection Sort has the time complexity of O n 2making it unsuitable for large lists.
By parallelizing the implementation, we make the multiple threads split the data amongst themselves and then search for the largest element independently on their part of the list.
Each thread locally stores it own smallest element. The outer loop is not parallelizable owing to the fact that there are frequent changes made to the array and that every i th iteration needs the i-1 th to be completed. In selection sort, the parallelizable region is the inner loop, where we can spawn multiple threads to look for the maximum element in the unsorted array division. Then we can reduce each local maximum into one final maximum. However, in the implementation, we are not looking for the maximum element, instead we are looking for the index of the maximum element.
For this we need to declare a new custom reduction. The ability to describe our own custom reduction is a testament to the flexibility that OpenMP provides. The declared reduction clause receives a struct. So, our custom maximum index reduction will look something like this:. For that, we can have a simple verify function that checks if the array is sorted. So, the parallel implementation is equivalent to the serial implementation and produces the required output. You can find the complete code of Parallel Selection sort here.
Mergesort is one of the most popular sorting techniques. It is the typical example for demonstrating the divide-and-conquer paradigm. Merge sort also commonly spelled mergesort is an efficient, general-purpose, comparison-based sorting algorithm. If a given array A has zero or one element, simply return; it is already sorted.
That is, q is the halfway point of A[p. Combine the elements back in A[p. We need to make sure that the left and the right sub-arrays are sorted simuntaneously. We need to serial and binary search program in c using function both left and right sections in parallel. For that, we can use the verify function that we used for our selection sort example.
Great, so the parallel implementation works. You can find the parallel implementation here.
Searching a list of values is a common task. An application program might retrieve a student record, bank account record, credit record, or any other type of record using a search algorithm. Some of the most common search algorithms are serial searchbinary search and search by hashing. The tool for comparing the performance between the different algorithms is called run-time analysis.
Here, we present search by hashingand discuss serial and binary search program in c using function performance of this method. But first, we present a simple search method, the serial search and its run-time analysis.
In a serial search, we step through an array or list one item at a time looking for a desired item. The search stops when the item is found or when the search has examined each item without success. This technique is probably the easiest to implement and is applicable to many situations.
The running-time of serial search is easy to analyze. We will count the number of operations required by the algorithm, rather than measuring the actual time. For searching an array, a common approach is to count one operation each time that the algorithm accesses an element of the array.
Usually, when we discuss running times, we consider the "hardest" inputs, for example, a search that requires the algorithm to access the largest number of array elements. This is called the worst-case running time. For serial searchthe worst-case running time occurs when the desired item is not in the array.
In this case, the algorithm accesses every element. Thus, for an array of n elements, the worst-case time for serial search requires n array accesses. An alternative to worst-case running time, is the average-case running time, which is obtained by averaging the different running times for all inputs of a particular kind. For example, if our array contains ten elements, then if we are searching for the target that occurs at the first location, then there is just one array access.
If we are searching serial and binary search program in c using function the target that occurs at the second location, then there are two array accesses. And so on through the final target, which requires ten accesses. The average of all these searches is:. Both worst-case time and average-case time are O nbut nevertheless, the average case is about half the time of the worst-case.
A third way to measure running time is called best-caseand as the name suggests, it takes the most optimistic view. The best-case running time is defined as the smallest of all the running times on inputs of a particular size. For serial search, the best-case occurs when the target is found at the front of the array, requiring only one array access. Thus, for an array of n elements, the best-case time for serial search requires just 1 array access.
Unless the best-case behavior occurs with high probability, the best-case running time is generally not used during analysis. Hashing has a worst-case behavior that is linear for finding a target, but with some care, hashing can be dramatically fast in the average-case.
Hashing also makes it easy to add and delete elements from the collection that is being searched. To be specific, suppose the information about each student is an object of the following form, with the student ID stored in the key field:.
We call each of these objects a record. Of course, there might be other information in each student record. If student IDs are all in the range The record for student ID k can be retrieved immediately since we know serial and binary search program in c using function is in data[k]. What, serial and binary search program in c using function, if the student IDs do not form a neat range like Suppose that we only know that there will be a hundred or fewer and that they will be distributed in the range We could then use an array with 10, components, but that seems wasteful since only a small fraction of the array will be used.
It appears that we have to store the records in an array with elements and to use a serial search serial and binary search program in c using function this array whenever we wish to find a particular student ID. If we are clever, we can store the records in a relatively small array and still retrieve students by ID much faster than we could by serial search.
In this case, we can store the records in an array called data with only components. We'll store the record with student ID k at location:. The record for student ID is stored in array component data. This general technique is called hashing. Each record requires serial and binary search program in c using function unique value called its key. In our example the student ID is the key, but other, more complex keys are sometimes used. A function called the hash function serial and binary search program in c using function, maps keys to array indices.
Suppose we name our hash function hash. If a record has a key of kthen we will try to store that record at location data[hash k ]. Using the hash function to compute the correct array index is called hashing the key to an array index. The hash function must be chosen so that its return value is always a valid index for the serial and binary search program in c using function. Given this hash function and keys that are multiples ofevery key produces a different index when it was hashed.
Thus, hash is a perfect hash function. Unfortunately, a perfect hash function cannot always be found. Suppose we no longer have a student IDbut we have instead. The record with student ID will be stored in data as before, but where will student ID be placed? So there are now two different records that belong in data. This situation is known as a collision. In this case, we could redefine our hash function to avoid the collision, but in practice you do not know the exact numbers that will occur as keys, and therefore, you cannot design a hash function that is guaranteed to be free of collisions.
Typically, though, you do know an upper bound on how many keys there will be. The usual approach is to use an array size that is larger than needed. The extra array positions make the collisions less likely. A good hash function will distribute the keys uniformly throughout the locations of the array. If the array indices range from 0 to 99, then you might use the following hash function to produce an array index for a record with a given key:. One way to resolve collisions is to place the colliding record in another location that is still open.
This storage algorithm is called open-addressing. Open addressing requires that the array be initialized so that the program can test if an array position already contains a record. With this serial and binary search program in c using function of resolving collisions, we still serial and binary search program in c using function decide how to choose the locations to search for an open position when a collision occurs There are 2 main ways to do so.
There is a problem with linear probing. When several different keys hash to the same location, the result is a cluster of elements, one after another. As the table approaches its capacity, these clusters tend to merge into larger and larger clusters.
This is the problem of clustering. Clustering makes insertions take longer because the insert function must step all the way through a cluster to find a vacant location. Searches require more time for the same reason. The most common technique to avoid clustering is called double hashing. With double hashing, we could return to our starting position before we have examined every available location.
An easy way to avoid this problem is serial and binary search program in c using function make sure that the array size is relatively prime with respect to the value returned by hash2 in other words, these two numbers must not have any common factor, apart from 1.
Two possible implementations are:. In open addressing, each array element can hold just one entry. When the array is full, no more records can be added to the table.
One possible solution is to resize the array and rehash all the entries. This would require a careful choice of new size and probably require each entry to have a new hash value computed. A better approach is to use a different collision resolution method called chained hashingor simply chainingin which each component of the hash table's array can hold more than one entry.
We still hash the key of each entry, but upon collision, we simply place the new entry in its proper array component along with other entries that happened to hash to the same array index. The most common way to implement chaining is to have each array element be a linked list. The nodes in a particular linked list will each have a key that hashes to the same value.
The worst-case for hashing occurs when every key hashes to the same array index. In this case, we may end up searching through all the records to find the target just as in serial search. The average-case performance of hashing is complex, particularly if deletions are allowed.
We will give three different formulas for the three versions of hashing: The three formulas depend on how many records are in the table. When the table has many records, there are many collisions and the average time for a search is longer.
We define the load factor alpha as follows:. For open address hashing, each array element holds at most one item, so the load factor can never exceed 1.
But with chaining, each array position can hold many records, and the load factor might be higher than 1. In the following table, we give formulas for the average-case performance of the three hashing schemes along with numerical examples. You are given a template implementation of a hash table using open addressing with linear probing.
Here is the source code:.
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