5 write a c program for heap sort
Heap Sort is a popular and efficient sorting algorithm in computer programming. Learning how to write the heap sort algorithm requires knowledge of two types of data structures - arrays and trees. The initial set of numbers that we want to sort is stored in an array e. Heap sort works by visualizing the elements of the array as a special kind of complete binary tree called a heap. As a prerequisite, you must know about a complete binary tree and heap data structure.
Heap Sort in C
Heap sort is a very fast sorting algorithm. It is kind of evolved selection sort, which uses a complete binary tree structure. This reduces the time to find the max element and thus makes the routine very efficient. The algorithm is unstable, because its structure could change the order of elements with equal keys.
One downside is that this sorting is not adaptive to nearly sorted input. Learn faster with deeper understanding! The "Computer programming for beginners" course is the perfect place to begin with programming. Start now! Aside from being very fast, heap sort has another major advantage.
Unlike bubble, selection and insertion sorts, explaining this method requires some preparation. For that reason we begin with explaining the basics. Heap or also binary heap is a special type of binary tree. A given tree could be a heap only if:. The first example has three elements, located on two levels.
This is a complete heap — all levels are filled to their capacity. The second and third examples are 3-level heaps. Their leaves 3rd level are incomplete, but they are filled left to right, so they are still correct heaps. Here are two examples of trees that violate the heap rules properties :. The graph on the left has incomplete levels 3 and 4. This violates the first property of the heap. This violates the second property.
The point of using heaps is to make some operations very quick. Such operations could be searching for an element with certain value, finding the maximum value and others.
For that purpose we need to arrange the data in a specific way. In max heap each node is greater than or equal to its children and smaller than or equal to its parent. Here are examples of max and min heap:. Usually the data that needs to be sorted is located in an array. It has the value 5. So, this is the element with index 1 value 2. Now we have completed the first two levels.
To map the third level, we need to find the children of the nodes of level 2. Left-to-right the nodes on level 3 have indices 3, 4, 5, 6 with values 6, 5, 10, 1. Now we have the heap representation of the array. What kind of heap is that? Heap sort uses min or max heap. You just saw that the heap representation of a random array is not a min or max heap.
Therefore we need to rearrange the elements in the array, so its tree representation is a max heap. Let's look at the implementation of this routine:. We start with the last leaf and go upwards until we reach the root. Our first step is to compare the current node to its "brother" and remember which one is bigger. Then we compare the bigger child with the parent. If the child is bigger we swap their places. This orders these three elements according to the max heap rules. If there was a swap in 2.
We will look more in the sift down algorithm in a moment. We go to the next pair of children and continue with until we reach the root element. It makes linear number of steps and each step takes logarithmic time, because of the Sift down procedure. This is used when we arrange our array to a correct max heap.
In "heapify", when we find that a child is bigger than its parent we swap their places. In this situation it is likely that the smaller element needs to go down even further and that is exactly what "sift down" does. We check if the current element has at least one child. If there are no children, the element is a leaf, it can't sink further and we are done.
We compare the children of the current element and remember which one is the bigger one. We compare the bigger child to the parent. If the parent is bigger then it doesn't need to sink further and we are done. Otherwise we make a swap and repeat the procedure with the same element, but one level lower. This algorithm makes at most O log n number of steps, because it goes only over one branch of the tree. The max depth that it could go is the number of level in the tree and that is O log n complexity.
Now that our array is a correct max heap we can start the sorting routine. We are going to repeat 2 for each element in the array:. Extract the max element from the heap.
Since we have a max heap this means we always take the first element the root. By "extract" we mean, swapping the first and the last element of the array and marking that we don't need to sort the last element anymore, since it is in its correct place.
Sink the root element to its correct place, so our array will be a correct max heap again. Note that extracted elements will not be moved.
Continue with step 1 until we extract all elements. At this point many of you will just discard this sorting as too complex. But guess what! Although the explanation is rather long, the typical implementation is about 60 lines of code. Do you learn better from video?
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scanf("%d", &no);. printf("\n Enter the nos: ");.
Heap sort is a very fast sorting algorithm. It is kind of evolved selection sort, which uses a complete binary tree structure. This reduces the time to find the max element and thus makes the routine very efficient. The algorithm is unstable, because its structure could change the order of elements with equal keys. One downside is that this sorting is not adaptive to nearly sorted input.
Sorting is a technique that is all about the ordering of elements based on different properties.
Sorting Algorithm This is a sorting algorithm. It may be applied to a set of data in order to sort it.
Program for Heap Sort in C
Edit Reply. Heap sort algorithm implementation, Heap sort pseudocode, time complexity, etc are also discussed in this article. Heap is a special kind of binary tree in which elements are stored in a hierarchical manner. Heap has some additional rules it must always have a heap structure, where all the levels of the binary tree are filled up from left to right. Second, it must either be ordered as a max heap or a min-heap. In Heap sort, we will be dealing with Max heap.
C Program For Heap Sort | C Programming
Heap sort is a comparison based sorting technique based on Binary Heap data structure. It is similar to selection sort where we first find the maximum element and place the maximum element at the end. We repeat the same process for remaining element. What is Binary Heap? Let us first define a Complete Binary Tree. A complete binary tree is a binary tree in which every level, except possibly the last, is completely filled, and all nodes are as far left as possible Source Wikipedia. A Binary Heap is a Complete Binary Tree where items are stored in a special order such that value in a parent node is greater or smaller than the values in its two children nodes. The former is called as max heap and the latter is called min heap. The heap can be represented by binary tree or array. Why array based representation for Binary Heap?
When we deal with a large set of data, we want that data to organize in a specific order, so whenever we want to search for a particular item, we could find it at no time.
Computers are really good at sorting things. They can complete complex sorting tasks in no time. The only thing left for us is to tell them the method to be used for the given sorting task. This article will tell your computer systems how to use Heap sort in C to sort your data.
