Heaps Definition

INTRO TO HEAP & Adding and Removing a NODE

Presented to: Sir AHSAN RAZA

Presented by: SHAH RUKH Roll # 07-22Semester BIT 3rd

Session 2007—2011

Department of Computer Science,B.Z.University Multan

Heaps DefinitionHeaps DefinitionA heap is a certain kind of complete binary tree.

Binary TREE

It has a Root and has two CHILDREN.

Left child or left subtree.

Right child or right subtree.

Every child has its two children (left & right) then this child is called a node.

If a node has no children then this node is said to be as a leaf.

HeapsHeapsA heap is a certain kind of complete binary tree.

When a completebinary tree is built,

its first node must bethe root.

When a completebinary tree is built,

its first node must bethe root.

Root

HeapsHeapsComplete binary tree.

Left childof theroot

The second node isalways the left child

of the root.

The second node isalways the left child

of the root.

HeapsHeapsComplete binary tree.

Right childof the

root

The third node isalways the right child

of the root.

The third node isalways the right child

of the root.

HeapsHeapsComplete binary tree.

The next nodesalways fill the next

level from left-to-right..

The next nodesalways fill the next

level from left-to-right..

HeapsHeapsComplete binary tree.

The next nodesalways fill the next

level from left-to-right.

The next nodesalways fill the next

level from left-to-right.

HeapsHeapsComplete binary tree.

The next nodesalways fill the next

level from left-to-right.

The next nodesalways fill the next

level from left-to-right.

HeapsHeapsComplete binary tree.

The next nodesalways fill the next

level from left-to-right.

The next nodesalways fill the next

level from left-to-right.

HeapsHeapsComplete binary tree.

HeapsHeapsA heap is a certain kind of complete binary tree.

Each node in a heapcontains a key thatcan be compared toother nodes' keys.

Each node in a heapcontains a key thatcan be compared toother nodes' keys.

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HeapsHeapsA heap is a certain kind of complete binary tree.

The "heap property"requires that each

node's key is >= thekeys of its children

The "heap property"requires that each

node's key is >= thekeys of its children

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What it is not: It is not a BSTIn a binary search tree, the entries of the nodes can be compared

with a strict weak ordering. Two rules are followed for every node n:The entry in node n is NEVER less than an entry in its left subtreeThe entry in the node n is less than every entry in its right

subtree.BST is not necessarily a complete tree

What it is: Heap DefinitionA heap is a binary tree where the entries of the nodes can be

compared with the less than operator of a strict weak ordering. In addition, two rules are followed:The entry contained by the node is NEVER less than the entries

of the node’s childrenThe tree is a COMPLETE tree.

Application : Priority QueuesA priority queue is a container class that allows entries to be

retrieved according to some specific priority levelsThe highest priority entry is removed firstIf there are several entries with equally high priorities, then the

priority queue’s implementation determines which will come out first (e.g. FIFO)

Heap is suitable for a priority queue

The Priority Queue ADT with HeapsThe entry with the highest priority is always at the root nodeFocus on two priority queue operations

adding a new entryremove the entry with the highest priority

In both cases, we must ensure the tree structure remains to be a heapwe are going to work on a conceptual heap without worrying about

the precise implementation

Adding a Node to a HeapAdding a Node to a HeapPut the new node in the next

available spot.Push the new node upward,

swapping with its parent until the new node reaches an acceptable location.

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Adding a Node to a HeapAdding a Node to a HeapPut the new node in the next

available spot.Push the new node upward,

swapping with its parent until the new node reaches an acceptable location.

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Adding a Node to a HeapAdding a Node to a HeapPut the new node in the next

available spot.Push the new node upward,

swapping with its parent until the new node reaches an acceptable location.

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Adding a Node to a HeapAdding a Node to a HeapThe parent has a key that is

>= new node, orThe node reaches the root.The process of pushing the

new node upward is called reheapification upward.

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Note: we need to easily go from child to parent as well as parent to child.

Removing the Top of a HeapRemoving the Top of a HeapMove the last node onto the

root.

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Removing the Top of a HeapRemoving the Top of a HeapMove the last node onto the

root.

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Removing the Top of a HeapRemoving the Top of a HeapMove the last node onto the

root.Push the out-of-place node

downward, swapping with its larger child until the new node reaches an acceptable location.

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Removing the Top of a HeapRemoving the Top of a HeapMove the last node onto the

root.Push the out-of-place node

downward, swapping with its larger child until the new node reaches an acceptable location.

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Removing the Top of a HeapRemoving the Top of a HeapMove the last node onto the

root.Push the out-of-place node

downward, swapping with its larger child until the new node reaches an acceptable location.

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Removing the Top of a HeapRemoving the Top of a HeapThe children all have keys

<= the out-of-place node, or

The node reaches the leaf.The process of pushing the

new node downward is called reheapification downward.

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Priority Queues RevisitedA priority queue is a container class that allows entries to be

retrieved according to some specific priority levelsThe highest priority entry is removed firstIf there are several entries with equally high priorities, then the priority

queue’s implementation determines which will come out first (e.g. FIFO)

Heap is suitable for a priority queue

Adding a Node: same priority Adding a Node: same priority Put the new node in the next

available spot.Push the new node upward,

swapping with its parent until the new node reaches an acceptable location.

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45*

Adding a Node : same priority Adding a Node : same priority Put the new node in the next

available spot.Push the new node upward,

swapping with its parent until the new node reaches an acceptable location.

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Adding a Node : same priority Adding a Node : same priority Put the new node in the next

available spot.Push the new node upward,

swapping with its parent until the new node reaches an acceptable location.

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