Delete from a binary heap

This is the process of removing the highest priority value from the binary heap. The way that the Heap is set up, the node with the highest priority is at the root. Finding it is easy but the removal process must ensure that both the complete binary tree structure along with the heap order property is maintained wo just removing the root would be a bad idea.

In order for the complete binary tree property to be maintained we will be removing the right most node at the bottom level. Note that a complete binary tree with n nodes can only have 1 shape, so the shape is pretty much determined by the fact that removing a value creates a tree with one fewer node.

The empty spot that had been created by the removal of the value at root must be filled and the value that had been in the rightmost node must go back into the heap. We can accomplish this by doing the following:

• If the value could be placed into the empty node (remember, this starts at root) without violating the Heap Order Property, put it in and we are done
• otherwise move the child with the higher priority up (the empty spot moves down).
• Repeat until value is placed

The process of moving the empty spot down the heap is called percolate down

Illustrated example: