堆和排序数组的区别

1. 堆：
堆是一种基于树的数据结构，其中树应该几乎是完整的。它有两种类型，即最大堆和最小堆。

• 最大堆在最大堆中，如果 p 是父级，c 是其子级，那么对于每个父级 p，它的值大于或等于 c 的值
• 最小堆在最小堆中，如果 p 是父级，c 是其子级，则对于每个父级，p 值都小于或等于 c 的值。

堆也作为优先队列。其中最高（在最大堆的情况下）或最低（在最小堆的情况下）元素存在于根处。
堆用于我们需要删除最高或最低优先级元素的问题。堆的一个常见实现是二叉堆。

执行

• 由于堆可以实现为树，但是在这些大量存储空间中浪费了存储指针。由于堆的特性，因为它几乎是完整的二叉树，所以可以很容易地存储在数组中。
• 其中根元素存储在第一个索引处，其子索引可以计算为
• 左子索引 = 2×r 其中 r 是索引是根，数组起始索引是 0。
• 右子索引 = 2×r+1。
• 并且父索引可以计算为 floor(i/2) ，其中 i 是其左孩子或右孩子的索引。

例子 ：

最大堆示例

2. 排序数组：
排序数组是一种数据结构，其中元素按数字、字母或其他顺序排序并存储在连续的内存位置。

排序数组示例

• 所有数据结构都有自己的优缺点，具体取决于它们使用的问题或算法。例如，在我们需要寻找（最大或最小）、删除（最大或最小）或插入（最大或最小）元素的最优性的情况下，堆是最好的数据结构。
• 排序数组用于需要按升序或降序存储项目的情况。例如，在最短作业调度优先算法中，需要根据进程的突发时间对进程（存储在数组中）进行排序。因此，如果需要排序数组。

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)

堆和排序数组的区别：

Sorted array	Heaps
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 .	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
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.