Deletion Operation in Max Heap

Deletion Operation in Max Heap

In a max heap, deleting last node is very simple as it is not disturbing max heap properties.

Deleting root node from a max heap is title difficult as it disturbing the max heap properties. We use the following steps to delete root node from a max heap...

• Step 1: Swap the root node with last node in max heap
• Step 2: Delete last node.
• Step 3: Now, compare root value with its left child value.
• Step 4: If root value is smaller than its left child, then compare left child with its right sibling. Else goto Step 6
• Step 5: If left child value is larger than its right sibling, then swap root with left child. otherwise swap root with its right child.
• Step 6: If root value is larger than its left child, then compare root value with its right child value.
• Step 7: If root value is smaller than its right child, then swap root with rith child. otherwise stop the process.
• Step 8: Repeat the same until root node is fixed at its exact position.

Example
Consider the above max heap. Delete root node (90) from the max heap.

• Step 1: Swap the root node (90) with last node 75 in max heap After swapping max heap is as follows...
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• Step 2: Delete last node. Here node with value 90. After deleting node with value 90 from heap, max heap is as follows...
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• Step 3: Compare root node (75) with its left child (89).
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• Here, root value (75) is smaller than its left child value (89). So, compare left child (89) with its right sibling (70).
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• Step 4: Here, left child value (89) is larger than its right sibling (70), So, swap root (75) with left child (89).
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• Step 5: Now, again compare 75 with its left child (36).
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• Here, node with value 75 is larger than its left child. So, we compare node with value 75 is compared with its right child 85.
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• Step 6: Here, node with value 75 is smaller than its right child (85). So, we swap both of them. After swapping max heap is as follows...
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• Step 7: Now, compare node with value 75 with its left child (15).
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• Here, node with value 75 is larger than its left child (15) and it does not have right child. So we stop the process.
  
  Finally, max heap after deleting root node (90) is as follows...
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Insertion Operation in Max Heap

Finding Maximum Value Operation in Max Heap

It's easy to find the node in a max heap with the highest value. The root node in the max heap has the highest value of all the other nodes in the max heap. As a result, we can display the value of the root node as the maximum value in the max heap.

Insertion Operation in Max Heap

Insertion Operation in max heap is performed as follows...

• Step 1: Insert the newNode as last leaf from left to right.
• Step 2: Compare newNode value with its Parent node.
• Step 3: If newNode value is greater than its parent, then swap both of them.
• Step 4: Repeat step 2 and step 3 until newNode value is less than its parent nede (or) newNode reached to root.

Example
Consider the above max heap. Insert a new node with value 85.

• Step 1: Insert the newNode with value 85 as last leaf from left to right. That means newNode is added as a right child of node with value 75. After adding max heap is as follows.
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• Step 2: Compare newNode value (85) with its Parent node value (75). That means 85 > 75
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• Step 3: Here newNode value (85) is greater than its parent value (75), then swap both of them. After swapping, the max heap is as follows...
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• Step 4: Now, again compare the newNode value (85) with its parent node value (89).
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• Here, the newNode value (85) is smaller than its parent node value (89). So, we stop the insertion process. Finally, the max heap after insertion of a new node with value 85 is as follows...
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