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.
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Sorting refers to arranging data in a particular format. Sorting algorithm specifies the way to arrange data in a particular order. Most common orders are in numerical or lexicographical order. The importance of sorting lies in the fact that data searching can be optimized to a very high level, if data is stored in a sorted manner. Sorting is also used to represent data in more readable formats. Sorting algorithms may require some extra space for comparison and temporary storage of few data elements. These algorithms do not require any extra space and sorting is said to happen in-place, or for example, within the array itself.
This is called in-place sorting.
Bubble sort is an example of in-place sorting. However, in some sorting algorithms, the program requires space which is more than or equal to the elements being sorted.
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Sorting which uses equal or more space is called not-in-place sorting. Merge-sort is an example of not-in-place sorting. If a sorting algorithm, after sorting the contents, does not change the sequence of similar content in which they appear, it is called stable sorting. If a sorting algorithm, after sorting the contents, changes the sequence of similar content in which they appear, it is called unstable sorting. Stability of an algorithm matters when we wish to maintain the sequence of original elements, like in a tuple for example. A sorting algorithm is said to be adaptive, if it takes advantage of already 'sorted' elements in the list that is to be sorted.
That is, while sorting if the source list has some element already sorted, adaptive algorithms will take this into account and will try not to re-order them.
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A non-adaptive algorithm is one which does not take into account the elements which are already sorted. They try to force every single element to be re-ordered to confirm their sortedness. A sequence of values is said to be in increasing order , if the successive element is greater than the previous one. For example, 1, 3, 4, 6, 8, 9 are in increasing order, as every next element is greater than the previous element. A sequence of values is said to be in decreasing order , if the successive element is less than the current one. For example, 9, 8, 6, 4, 3, 1 are in decreasing order, as every next element is less than the previous element.
A sequence of values is said to be in non-increasing order , if the successive element is less than or equal to its previous element in the sequence. This order occurs when the sequence contains duplicate values. For example, 9, 8, 6, 3, 3, 1 are in non-increasing order, as every next element is less than or equal to in case of 3 but not greater than any previous element.
A sequence of values is said to be in non-decreasing order , if the successive element is greater than or equal to its previous element in the sequence. For example, 1, 3, 3, 6, 8, 9 are in non-decreasing order, as every next element is greater than or equal to in case of 3 but not less than the previous one. Bubble sort is a simple sorting algorithm. This sorting algorithm is comparison-based algorithm in which each pair of adjacent elements is compared and the elements are swapped if they are not in order.
We take an unsorted array for our example. In this case, value 33 is greater than 14, so it is already in sorted locations. Next, we compare 33 with We swap these values. We find that we have reached the end of the array.
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To be precise, we are now showing how an array should look like after each iteration. We assume list is an array of n elements. We further assume that swap function swaps the values of the given array elements. We observe in algorithm that Bubble Sort compares each pair of array element unless the whole array is completely sorted in an ascending order.
This may cause a few complexity issues like what if the array needs no more swapping as all the elements are already ascending. To ease-out the issue, we use one flag variable swapped which will help us see if any swap has happened or not. If no swap has occurred, i. One more issue we did not address in our original algorithm and its improvised pseudocode, is that, after every iteration the highest values settles down at the end of the array.
Hence, the next iteration need not include already sorted elements. For this purpose, in our implementation, we restrict the inner loop to avoid already sorted values. To know about bubble sort implementation in C programming language, please click here.
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This is an in-place comparison-based sorting algorithm. Here, a sub-list is maintained which is always sorted. For example, the lower part of an array is maintained to be sorted. An element which is to be 'insert'ed in this sorted sub-list, has to find its appropriate place and then it has to be inserted there.
Hence the name, insertion sort. The array is searched sequentially and unsorted items are moved and inserted into the sorted sub-list in the same array. It swaps 33 with It also checks with all the elements of sorted sub-list. Here we see that the sorted sub-list has only one element 14, and 27 is greater than Hence, the sorted sub-list remains sorted after swapping.
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This process goes on until all the unsorted values are covered in a sorted sub-list. Now we shall see some programming aspects of insertion sort. Now we have a bigger picture of how this sorting technique works, so we can derive simple steps by which we can achieve insertion sort. To know about insertion sort implementation in C programming language, please click here. Selection sort is a simple sorting algorithm. This sorting algorithm is an in-place comparison-based algorithm in which 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. The smallest element is selected from the unsorted array and swapped with the leftmost element, and that element becomes a part of the sorted array. This process continues moving unsorted array boundary by one element to the right. For the first position in the sorted list, the whole list is scanned sequentially.
The first position where 14 is stored presently, we search the whole list and find that 10 is the lowest value.