Heaps By JJ Shepherd.

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Presentation transcript:

Heaps By JJ Shepherd

Introduction Heaps are another type of binary tree Each node has to have some comparable value Think of each of these values as a priority

Introduction Is always balanced as each node is put in via breadth order Each node is comparable to its parent Either greater than or less than depending on the type of heap

Introduction 2 common versions versions Min Heap Max Heap

Insertion Add the new node to the first available child in breath order Next “bubble up” that node so it’s in the correct position If the node above it is less than the node’s value then swap those values Continue to do this until that’s not true or the root is reached

Insertion Insert 7 to the max heap 20 16 6 8 11 4 5 1 2 3 10 - - - -

Insertion Check breath order to find the first empty (-) value 20 16 6 8 11 4 5 1 2 3 10 - - - -

Insertion Add the new value 7 20 16 6 8 11 4 5 1 2 3 10 7 - - -

Insertion “Bubble up” that value until the parent is greater than that value 20 16 6 8 11 4 5 1 2 3 10 7 - - -

Insertion 7 > 4 SWAP 20 16 6 8 11 7 5 1 2 3 10 4 - - -

Insertion 7 > 6 SWAP 20 16 7 8 11 6 5 1 2 3 10 4 - - -

Insertion 7 < 20 DONE! 20 16 7 8 11 6 5 1 2 3 10 4 - - -

Deletion You always remove the node at the root Get the last node via breadth order and place that node at the root Finally take that node and “bubble down” First see which of the two children are larger If the larger child is larger then SWAP Otherwise it is sorted

Deletion Remove and return the node at the root 20 16 7 8 11 6 5 1 2 3 10 4 - - -

Deletion Take the last node in breadth order and place it at the root - 16 7 8 11 6 5 1 2 3 10 4 - - -

Deletion Bubble that value down. Pick the larger of the two children. If it is larger then swap 4 16 7 8 11 6 5 1 2 3 10 - - - -

Deletion 16 > 4 SWAP 16 4 7 8 11 6 5 1 2 3 10 - - - -

Deletion 11 > 4 SWAP 16 11 7 8 4 6 5 1 2 3 10 - - - -

Deletion 10 > 4 SWAP 16 11 7 8 10 6 5 1 2 3 4 - - - -

Deletion There are no more children. DONE! 16 11 7 8 10 6 5 1 2 3 4 -

Heap Sort If a heap is constructed if every element is removed it is returned in that order Max Heap returns everything largest to smallest Min Heap return everything smallest to largest This is due to the value of the root is either the largest or smallest value always

Heap Sort 20 20 16 7 8 11 6 5 1 2 3 10 4 - - -

Heap Sort 20 16 16 11 7 8 10 6 5 1 2 3 4 - - - -

Heap Sort 20 16 11 11 10 7 8 4 6 5 1 2 3 - - - - -

Heap Sort 20 16 11 10 10 8 7 3 4 6 5 1 2 - - - - - -

Heap Sort 20 16 11 10 8 8 4 7 3 2 6 5 1 - - - - - - -

Heap Sort 20 16 11 10 8 7 7 4 6 3 2 1 5 - - - - - - - -

Heap Sort 20 16 11 10 8 7 6 6 4 5 3 2 1 - - - - - - - - -

Heap Sort 20 16 11 10 8 7 6 5 5 4 1 3 2 - - - - - - - - - -

Heap Sort 20 16 11 10 8 7 6 5 4 4 3 1 2 - - - - - - - - - - -

Heap Sort 20 16 11 10 8 7 6 5 4 3 3 2 1 - - - - - - - - - - - -

Heap Sort 20 16 11 10 8 7 6 5 4 3 2 2 1 - - - - - - - - - - - - -

Heap Sort 20 16 11 10 8 7 6 5 4 3 2 1 1 - - - - - - - - - - - - - -

Heap Sort 20 16 11 10 8 7 6 5 4 3 2 1 DONE! - - - - - - - - - - - - -