Quicksort (sometimes called partition-exchange sort) is an efficient and very fast sorting algorithm for internal sorting, serving as a systematic method for placing the elements of an array in order. When implemented well, it can be about two or three times faster than its main competitors, merge sort and heapsort. In efficient implementations it is not a stable sort, meaning that the relative order of equal sort items is not preserved. Quicksort can operate in-place on an array, requiring small additional amounts of memory to perform the sorting. Continue reading “Quick Sort using C”
Bubble sort is one of the most popular sorting methods. It can be treated as a selection sort because it is based on successively selecting the smallest element, second smallest element and so on. In order to find the successive smallest elements this process relies heavily on the exchange of the adjacent elements and swaps them if they are in the wrong order.
Bubble sort has worst-case and average complexity both О(n2), where n is the number of items being sorted.
Selection sorting refers to a class of algorithms for sorting a list of items using comparisons. These algorithms select successively smaller or larger items from the list and add them to the output sequence. This is an improvement of the Simple Selection Sort and instead of replacing the selected element by a unique value in the i-th pass (as happens in Simple Selection Sort), the selected element is exchanged with the i-th element. Let’s assume an array “a” with “n” elements. Thus, at the beginning of the i-th pass, the first (i-1) elements of the array are those that have been selected in the previous passes. The smallest element is now searched in the remaining (n-i+1) elements. After (n-1) passes, the sorted array is completely developed in the space occupied by the original array.
The simplest possible technique based on the principle of repeated selection makes use of “n” passes over an array elements. In the i-th pass, the i-th smallest element is selected from the given array and it is placed in the i-th position of a separate output array. The already selected element is not selected next time and in order to ensure it, a unique value is put in place of the selected element in the original array.
This method makes repeated use of straight insertion or shuttle sort. An array with n elements, in each pass, an increment is chosen. The increment must be less than n and the increment progressively should be smaller and the last increment must be equal to 1.
Please find detail information on Shell Sort https://en.wikipedia.org/wiki/Shellsort
Insertion sort is a simple sorting algorithm that builds the final sorted array (or list) one item at a time. More details can be found here at https://en.wikipedia.org/wiki/Insertion_sort
Let’s say we have an array a, so at each i-th pass, a[i] is successively compared with a[i-1], a[i-2], etc. until an element smaller than a[i] is found or the beginning of the array is reached. Elements that are found to be greater than a[i], are moved right by one position each to make room for a[i].
The time complexity of this algorithm is O(n^2). Continue reading “Straight Insertion Sort using C”
In Shuttle Sort technique for n elements in an array a, it requires n-1 passes. When i-th pass(1<=i<=n) begins, the first i elements, i.e., elements a to a[i-1] have been sorted and these occupy the first i positions of the array. To insert (i+1)th element, a[i] is compared with a[i-1] and if the value of a[i] is smaller than a[i-1] then they are exchanged. In the same way the process continues until either no exchange is required or the beginning of the array is reached.
This example shows how Binary Search Algorithm works.
Binary search algorithm is better when an array is sorted because it makes comparison between the search key “k” and middle element of the array. Since the array is sorted, the comparison results either in a match between “k” and the middle element of the array or identifying the left half or right half of the array to which the desired element may belong. This process continues on the half in which the desired element may be present in case “k” is not equal to the middle element. In this way, either the element is detected or the final division leads to a half, where the array does not contain the desired element “k”.
This is very efficient method of searching algorithm because the comparison enables one to eliminate half of the elements from further consideration.
This example shows how Sequential Search algorithm works.
Simple way to search for a key value
k in an array
a is to compare the values of the elements in
k. The process starts with the first element of the array and
k and comparison continues as long as either the comparison does not result in a success or the list of elements in the array are exhausted. This method of searching is known as sequential search or linear search.
The following code example will return the index of the array when a successful search is found for the given key value and when the search is unsuccessful, the function returns
Binary tree is an important class of tree in data structure. A node in binary tree can have at most two children, which are called sub-trees. Children of a node in binary tree are ordered. One child is called left child and another child is called right child.
A binary tree can be defined as
- an empty tree is a binary tree
- a binary tree consists of a node is called root, a left and right sub-tree both of which are binary trees once again.