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18/02/2014

Binary Trees:
The binary tree is a fundamental data structure used in computer science. The binary tree is a useful data structure for rapidly storing sorted data and rapidly retrieving stored data. A binary tree is composed of parent nodes, or leaves, each of which stores data and also links to up to two other child nodes (leaves) which can be visualized spatially as below the first node with one placed to the left and with one placed to the right. It is the relationship between the leaves linked to and the linking leaf, also known as the parent node, which makes the binary tree such an efficient data structure. It is the leaf on the left which has a lesser key value (i.e., the value used to search for a leaf in the tree), and it is the leaf on the right which has an equal or greater key value. As a result, the leaves on the farthest left of the tree have the lowest values, whereas the leaves on the right of the tree have the greatest values. More importantly, as each leaf connects to two other leaves, it is the beginning of a new, smaller, binary tree. Due to this nature, it is possible to easily access and insert data in a binary tree using search and insert functions recursively called on successive leaves.

18/02/2014

Heap:
A heap is a partially sorted binary tree. Although a heap is not completely in order, it conforms to a sorting principle: every node has a value less (for the sake of simplicity, we will assume that all orderings are from least to greatest) than either of its children. Additionally, a heap is a "complete tree" -- a complete tree is one in which there are no gaps between leaves. For instance, a tree with a root node that has only one child must have its child as the left node. More precisely, a complete tree is one that has every level filled in before adding a node to the next level, and one that has the nodes in a given level.

18/02/2014

HASHING:
Hash tables are an efficient implementation of a keyed array data structure, a structure sometimes known as an associative array or map.
Keyed Arrays vs. Indexed Arrays
In C/C++ array (also called an indexed array), the only way to access an element would be through its index number. To find element 50 of an array named "employees" you have to access like this:
1 employees[50];
In a keyed array, however, you would be able to associate each element with a "key," which can be anything from a name to a product model number. So, if you have a keyed array of employee records, you could access the record of employee "John Brown" like this:
1 employees["Brown, John"];
One basic form of a keyed array is called the hash table. In a hash table, a key is used to find an element instead of an index number. Since the hash table has to be coded using an indexed array, there has to be some way of transforming a key to an index number. That way is called the hashing function.
Collisions
When inserting items into a hash table, it sometimes happens that an item to be inserted in table has a hash value that points to an already existing location in table. The new item typically is inserted somewhere else, though we must be sure that there is still a way to look up the item.

One of the simplest ways to overcome collisions is to use a rehash function:
rehash(id) = (id+1)%size;

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Maping????

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