Found 210 Articles for Analysis of Algorithms

The insertion into Max HBLT, can be done using Max Meld operation. This operation is used to merge two Max HBLT into one Max HBLT. Suppose, we want to insert x into one max HBLT, called H. We will create a small HBLT using x, then meld this with H, then after melding, H will hold all elements including x. So melding operation is needed to perform the insertion operations for HBLT.

Here we will see what is the Height Balanced Leftist Trees (HBLT). Consider a binary tree where a special node, called an external node replaces each empty subtree. All other nodes are called Internal Nodes. When some external nodes are added with some binary tree, then that is called an extended binary tree.If we do not consider the leaf edges of this tree, then that is the actual binary tree. and this is the extended binary tree.Now suppose s(x) be the length of a shortest path from node x to an external node in its subtree. If x is an ... Read More

Here we will see the what is the Acyclic digraphs. The acyclic digraphs are directed graphs containing no directed cycles. The Directed Acyclic Graphs are abbreviated as DAG.Every finite DAG has at-least one node whose out-degree is 0.Example of DAG with one node −Example of DAG with two nodes −Example of DAG with three nodes −

In this section we will see what is the K-ary tree. The K-ary tree is a rooted tree, where each node can hold at most k number of children.If the value of k is 2, then this is known as binary tree. The binary tree, or ternary trees are some specialized k-ary trees. So k-ary trees re generalized.Example of K-ary Tree −In the above example, there is a root. The root has four children. Each child of root has some children also. The first child has three children, the second child has no child, the third one has two children, ... Read More

In this section we will see what are the differences between rooted and the unrooted trees. At first we will see some examples of Rooted, and Unrooted trees.Example of Rooted Tree −Example of Unrooted Tree −Basic Differences between rooted and Unrooted treesIn a rooted tree, each node with descendants represents the inferred most recent common ancestors of the descendants. In some trees, the edge lengths may be interpreted as time estimates.For the unrooted trees, there is no ancestral root. Unrooted trees represent the branching order, but do not indicate the root of the location of the last common ancestor.Read More

Here we will see the what is the unrooted binary tree. These trees are connected undirected graph with no cycle. The vertices with one neighbor are the leaves of the tree. Remaining vertices are internal nodes. The degree of the vertices is its number of neighbors. In a tree with more than one node, the leaves are the vertices of degree one.Free tree is one type of binary tree, where all internal nodes have exactly degree three. In Computer Science, binary trees are often rooted, and ordered, when they are used as data structures, but the applications of unrooted binary ... Read More

Here we will see the Tournament trees, Winner and Looser trees. The Tournament tree is a complete binary tree with n external nodes and n – 1 internal nodes. The external nodes represent the players, and the internal nodes are representing the winner of the match between the two players. This tree is also known as Selection tree.There are some properties of Tournament trees. These are like below −This tree is rooted. So the link in the tree and directed path from parent to children, and there is a unique element with no parentsThe parent value is less or equal ... Read More

The way to write arithmetic expression is known as a notation. An arithmetic expression can be written in three different but equivalent notations, i.e., without changing the essence or output of an expression. These notations are –InfixPrefixPostfixInfix notations are normal notations, that are used by us while write different mathematical expressions. The Prefix and Postfix notations are quite different.Prefix NotationIn this notation, operator is prefixed to operands, i.e. operator is written ahead of operands. For example, +ab. This is equivalent to its infix notation a + b. Prefix notation is also known as Polish Notation.Postfix NotationThis notation style is known ... Read More

Here we will see the R-Trees data structure. The R-Trees are used to store special data indexes in an efficient manner. This structure is very useful to hold special data queries and storages. This R-trees has some real life applications. These are like below −Indexing multidimensional informationHandling game dataHold geospatial coordinatesImplementation of virtual mapsOne example of R-Tree is like below.Corresponding R-tree is like below −Properties of R-TreesR-Trees are made of with single root, internal and leaf nodesThe root has a pointer to the largest region in the special domainThe parent nodes will hold child nodes where child nodes completely overlap ... Read More

Here we will see what are the B-Trees. The B-Trees are specialized m-way search tree. This can be widely used for disc access. A B-tree of order m, can have maximum m-1 keys and m children. This can store large number of elements in a single node. So the height is relatively small. This is one great advantage of B-Trees.B-Tree has all of the properties of one m-way tree. It has some other properties.Every node in B-Tree will hold maximum m childrenEvery node except root and leaves, can hold at least m/2 childrenThe root nodes must have at least two ... Read More