I have a question about heap sort. It state in an Algorithms book that <code>A.heap-size<= A.length</code> I don’t understand the difference between the two. If an array represents a heap, why is there a possibility that <code>A.heap-size</code> is less than <code>A.length</code>. I know that <code>A.heap-size</code> represents the number of elements inside a heap, so why is it not completely only equal to the number of items inside an array?

Just to expand an answer. Read further that book. <code>A.heap_size</code> of an array, is that place where heap (max_heap or min_heap) structure elements will be placed. It makes sense in scope of sorting or queuing. You are right: this is the number of elements inside a heap, but it's equal to <code>A.length</code> only at first iteration of heap sort. At next iteration, after exchanging root of the max_heap tree (<code>A[1]</code>) with <code>A[i] = A[A.length]</code> (last element inside array A), the <code>A[1]</code> element will be the last element of the A, and <code>A.heap_sort</code> value will be decreased by 1 and max_heap structure should be max_heapified: <code>A[Parent(i)] >= A[i]</code>, where <code>Parent(i)</code> returns i/2 of heap tree.

What is the difference between A.length and A.heap-size?

Q: What is a heap size?

The heap size value is determined by the amount of memory available in the computer. Initial heap size is 1/64th of the computer's physical memory or reasonable minimum based on platform (whichever is larger) by default. The initial heap size can be overridden using -Xms.

Q: What is a heap in simple terms?

1 : a collection of things thrown one on another : pile. 2 : a great number or large quantity : lot. heap. verb. heaped; heaping; heaps.

Q: What is heap size array?

The tree is completely filled on all levels except possibly the lowest, which is filled from the left up to a point. An array A that represents a heap is an object with two attributes: length[A], which is the number of elements in the array, and heap-size[A], the number of elements in the heap stored within array A.

Q: What is heap size data structure?

In computer science, a heap is a specialized tree-based data structure which is essentially an almost complete tree that satisfies the heap property: in a max heap, for any given node C, if P is a parent node of C, then the key (the value) of P is greater than or equal to the key of C.

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arrays

algorithm

data-structures

heap

I have a question about heap sort. It state in an Algorithms book that A.heap-size<= A.length I don’t understand the difference between the two. If an array represents a heap, why is there a possibility that A.heap-size is less than A.length. I know that A.heap-size represents the number of elements inside a heap, so why is it not completely only equal to the number of items inside an array?

333

asked Sep 27 '13 20:09

monkey doodle

1 Answers

Just to expand an answer. Read further that book.

A.heap_size of an array, is that place where heap (max_heap or min_heap) structure elements will be placed. It makes sense in scope of sorting or queuing. You are right: this is the number of elements inside a heap, but it's equal to A.length only at first iteration of heap sort.

At next iteration, after exchanging root of the max_heap tree (A[1]) with A[i] = A[A.length] (last element inside array A), the A[1] element will be the last element of the A, and A.heap_sort value will be decreased by 1 and max_heap structure should be max_heapified: A[Parent(i)] >= A[i], where Parent(i) returns i/2 of heap tree.

139

answered Oct 11 '22 13:10

pryg_skok

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