Difference between Heaps and Sorted Array
1. Heap :
A heap is a tree based data structure in which tree should be almost complete. It is of two types i.e. max and min heap.
- Max heap In max heap if p is the parent and c is its child, then for every parent p the value of it is greater than or equal to the value of c
- Min heap In min heap if p is the parent and c is its child, then for every parent p value is less than or equal to the value of c.
Heap is also as priority queue. In which highest(in case of max heap) or lowest(in case of min heap) element is present at the root.
Heap is use in problems where we need to remove the highest or lowest priority element. A common implementation of heap is binary heap.
- As heap can be implemented as tree but in these lots of storage wasted for storing pointers. Due to property of heap as it is almost complete binary tree it can be easily stored in array.
- Where root element is stored at first index and its child index can be calculated as
- Left child index = 2×r where r is index is root and array starting index is 0.
- Right child index = 2×r+1.
- And parent index can be calculated as floor(i/2) where i is the index of its left or right child.
2. Sorted array :
A sorted array is a data structure in which elements are sorted in numerical, alphabetical, or by some other order and stored at contiguous memory locations.
- All data structures have their own pons and cons depending on the problems or algorithms they are used. For example heap is the best data structure in situations where we need optimality in finding(max or min), deleting(max or min) or inserting (max or min) element.
- And sorted array is used in situations in items need to stored in ascending or descending orders. For example in shortest-job-scheduling first algorithms where the processes(stored in array) need to be sorted according to burst time of the processes. So in case sorting array is required.
|Data structure||Insert||Search||Find min||Delete min|
|Sorted array||O(n)||O(log n)||O(1)||O(n)|
|Min heap||O(log n)||O(n)||O(1)||O(log n)|
Difference between Heaps and Sorted Array : Sorted array Heaps For a given set of n integers there can be multiple possible heaps(max or min) can be formed. Refer this article for more details
In sorted array, elements are sorted in numerical, alphabetical, or by some other order and stored at contiguous memory locations. A heap is almost complete binary tree, In case of max heap if p is the parent and c is its child, then the value of p is greater than or equal to the value of c and in min heap if p is the parent and c is its child, then the value p is less than or equal to the value of c. A sorted array can be act as heap when using array based heap implementation. Heap may or not be a sorted array when using array based heap implementation. For a given set of integers there can be two arrangements(i.e. ascending or descending) possible after sorting . Here the next element address can be accessed by incrementing the index of current element. Here the left child index can be accessed by calculating 2×r and right element index can be accessed by calculating 2×r+1, where r is the index of root and array is 0 index based. Searching can be performed (log n) time complexity in sorted array by using binary search. Heap is not optimal for searching operation but searching can be performed in O(n) complexity. Heap sort can be used for sorting an array, but for this first heap is build with array of n integers and then heap sort is applied Here O(n) time complexity is needed for building heap and O(n log n) is required for removing n (min or max) element from heap and placing at the end of array and decreasing the size of array) i.e. heap sort. Heap sort which is applied on heaps(min or max) and it is in-place sorting algorithm for performing sorting in O(n log n) time complexity. Sorting an array requires O(n log n) complexity which is best time complexity for sorting an array of n items in comparison based sorting algorithm. Building heap takes O(n) time complexity. Sorted array are used for performing efficient searching (i.e. binary search), SJFS scheduling algorithm and in the organizations where data is needed in sorted order etc. The heaps are used in heap sort, priority queue, in graph algorithms and K way merge etc.
For a given set of n integers there can be multiple possible heaps(max or min) can be formed.
Refer this article for more details
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