How to check whether an array represents max heap

In summary, the given arrays do represent a binary max heap, as they satisfy the required heap property. However, the statement of the problem may be unclear and should be revised for better understanding.
  • #1
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Homework Statement


Does the following array represents the binary max heap
99,98,97,55,49,49,48,13,54
99,98,97,55,54,49,49,48,13

Homework Equations

The Attempt at a Solution


I've tried to construct the tree structure and all the above array representation satisfies the binary max heap property. But ans is given as no (i.e non of them represents the binary max heap)
 
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  • #2
After glancing at the method or representing heaps as arrays and looking up the definition of a max heap, I think your answer is correct (i.e. each array does represent a max heap).

However, the grammer in the statement of the problem is peculiar. I think the problem should say "Do the following arrays represent a binary max heap?". That version is still not clear. It would be clear if it said "For each of the following arrays, tell whether the array represents a binary max heap." Is it possible that there is only supposed to be a single array and that a comma was omitted after "54"?
 

1. How do I check if an array represents a max heap?

To check if an array represents a max heap, you can follow these steps:

  • Start by checking the root element of the array. It should be the largest element in the array.
  • Next, check the left and right child of the root element. If they exist, they should be smaller than the root.
  • Repeat this process for each level of the heap, checking the parent and its children.
  • If at any point, the above conditions are not met, then the array does not represent a max heap.
  • If all elements pass the above checks, then the array represents a max heap.

2. What is a max heap?

A max heap is a type of binary tree data structure where the parent node is always larger than its children. This means that the root node will always contain the largest element in the heap. Max heaps are commonly used in sorting algorithms.

3. How do I build a max heap from an array?

To build a max heap from an array, you can follow these steps:

  • Start by inserting all elements from the array into a binary tree data structure, maintaining the heap property (parent node is larger than its children).
  • Next, starting from the last parent node (array.length/2 - 1), check the parent and its children and swap them if necessary to maintain the heap property.
  • Repeat this process for each parent node until you reach the root node.
  • Once all parent nodes have been checked and swapped if necessary, the resulting binary tree will be a max heap.

4. How can I efficiently check if an array represents a max heap?

To efficiently check if an array represents a max heap, you can use a bottom-up approach. This means starting from the last parent node and working your way up to the root, checking each parent and its children. If at any point the heap property is violated, you can immediately return false. This approach has a time complexity of O(n) since all parent nodes are checked only once.

5. Can an array represent both a min and max heap?

No, an array can only represent either a min or max heap. This is because a min heap has the opposite heap property of a max heap, where the parent node is always smaller than its children. Therefore, an array can only represent one type of heap at a time.

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