Hash Table and Heaps

Still With Tree Traversalvoid BST::levelOrder(){

Queue<node*> q;

q.enqueue(root);

while(!q.isEmpty()){

node *p = q.dequeue();

cout<<p->item<<“ “;

if(p->left!=NULL)

q.enqueue(p->left);

if(p->right!=NULL)

q.enqueue(p->right);

}

}

Still On Search

Through the AVL, search was improved to log n. But we perform better?

Hash TableHash function/ HashingAn array of some fixed containing the keysEach key is mapped into some number in

range 0 to H_SIZE-1This mapping is called a hash function

Hash Table10

2

4

8

Hash Table

Hash Functionsitem % H_SIZEProblematic

Might run out of space (array)An item might already exist (collision)Solutions

Closed hashing (linear probing)Open hashing

Hash Table10

12

34

4

14

74

8

18

Hash Table

Closed hashingpos = x % H_SIZE;

while(??){

pos++;

}

Items[pos] = x;

Hash Table

The keys of the hash table are normally strings

Hash functionsSum up the ASCII codes of the characters

before performing %(st[0] + 27*st[1] + 729*st[2]) % H_SIZE

Hash Table

Open hashing Array of linked-lists

Priority Queue (Heap)A data structure allows at least the

following two operationsinsert – similar to enqueuedeleteMin/deleteMax – heap’s equivalent of

dequeueImplementation

Represent as a binary tree that is completely filled, with the exception of the bottom level

Completely filled from left to right

Simplest way is to use an array

Heap

Heap

Heap order propertyEvery node X, the key in the parent of X is

smaller (or equal to) the key in XWith the exception of the root (which has no

parent)min-heap

Heap

Heap

Insertion (refer to board)

Heapbool Heap::insert(int x){

if(isFull())

return false;

else{

int i = size++;

while(items[i/2]>x){

items[i] = items[i/2];

i/=2;

}

items[i] = x;

}

Heap

deleteMin (refer to board)

Heapbool Heap::deleteMin(){

if(isEmpty())

return false;

else{

last = items[size--];

for(int i=1; i*2<=size; i=child){

child = i*2;

if(child!=size && items[child+1] < items[child])

child++;

if(last > items[child])

items[i] = items[child];

else

break;

}

return true;

}

}