Found 349 Articles for Data Structure Algorithms

Pairing heaps are implemented for a perfect use of a priority queue. A priority queue maintains track of the minimum of a set of objects, so every time we take something eliminate from the queue it is always the minimum value. Priority queues are mostly implemented when using Dijkstra’s Algorithm to calculate the shortest path in a graph.Pairing heaps are perfect because they are easy to use and operate well in real applications. Specifically, they operate excellent in amortized time . Meaning that while an individual operation consumes a longer time, the sum of all the operations over the whole ... Read More

Calculating the amortized cost of meld operation is a difficult task. The major difficulty is in accumulating for the wide variations in the costs of an operation performed at different points in a random sequence of operations. Although our design goal is affected by the costs of sequence of operations, defining the notion of amortized cost of an operation in terms of the costs of sequences of operations leads nothing. Implementing a potential function to off set the variations in the actual costs is a perfect way of handling the situation.In the next topic we discuss the notion of amortized ... Read More

A pairing heap can be either an empty heap, or a pairing tree containing of a root element and a possibly empty list of pairing trees.The heap ordering property needs that parent of any node is no greater than the node itself.The following description considers a purely functional heap that does not support the decrease-key operation.type PairingTree[Element] = Heap(element: Element, subheaps: List[PairingTree[Element]])type PairingHeap[Element] = Empty | PairingTree[Element]Pairing heaps exist in two varieties--min pairing heaps and max pairing heaps. Min pairing heaps are implemented when we wish to represent a min priority queue, and max pairing heaps are implemented for max ... Read More

A pairing heap is defined as a type of heap data structure with relatively easy implementation and superb practical amortized performance.Pairing heaps are heap-ordered multiway tree structures, and can be denoted as simplified Fibonacci heaps.They are considered a "robust choice" for implementing such Algorithms like Prim's MST Algorithm, and support the following operations (assuming a min-heap) −find-min − This function is responsible to return the top element of the heap.meld −This function is responsible to compare the two root elements, the smaller remains the root of the result, the larger element and its subtree is added as a child of ... Read More

Meldable Priority QueuesDefinitionA randomized meldable heap (also Meldable Heap or Randomized Meldable Priority Queue) is defined as a priority queue based data structure in which the underlying structure is also a heap-ordered binary tree. However, there are no hard and fast rules on the shape of the underlying binary tree.AdvantagesThis approach has a number of facilities i.e. advantages over similar data structures.It offers simpler approach than other data structures.All operations for the randomized meldable heap are easy to apply and the constant factors in their complexity bounds are small.There is also no requirement to preserve balance conditions and no satellite ... Read More

Spanning TreeOne simple definition is that a tree is a connected graph associated with no cycles, where a cycle let's us go from a node to itself without repeating an edge.A spanning tree for a connected graph G is defined as a tree containing all the vertices of G.Spanning trees are often implemented for Internet routing Algorithms. In the Internet, computers (nodes) are often connected with many redundant physical connections.Total number of Spanning Trees in a Graph. If a graph is a complete graph with n no. of vertices, then total number of spanning trees is n(n-2)where n is denoted ... Read More

An m-ary tree in computer science is defined as a collection of nodes normally represented hierarchically in the following manner.The tree is started at the root node.Each node of the tree maintains a list of pointers to its child nodes.The number of child nodes is less than or equal to m.A typical representation of m-ary tree implements an array of m references (or pointers) to store children (Note that m is an upper bound on number of children).An m-way search treea. is empty orb. consists of a root containing b (1

According to computational complexity theory, the potential method is defined as a method implemented to analyze the amortized time and space complexity of a data structure, a measure of its performance over sequences of operations that eliminates the cost of infrequent but expensive operations.In the potential method, a function Φ is selected that converts states of the data structure to non-negative numbers. If S is treated as state of the data structure, Φ(S) denotes work that has been accounted in the amortized analysis but not yet performed. Thus, Φ(S) may be imagined as calculating the amount of potential energy stored ... Read More

Left-Child Right-Sibling Representation is a different representation of an n-ary tree where instead of maintaining a pointer to each and every child node, a node holds just two pointers, first a pointer to its first child, and the other pointer to its immediate next sibling. This new transformation not only eliminates the need of prior knowledge of the number of children a node has, but also restricts the number of pointers to a maximum of two, so making it so much simpler to code.At each node, link or connect children of same parent from left to right.Parent should be linked ... Read More

The randomized meldable heap(also called as Meldable Priority Queue) supports a number of common operations. These are known as insertion, deletion, and a searching operation, findMin. The insertion and deletion operations are implemented in terms of an additional operation specific to the meldable heap, Meld(A1, A2).MeldThe basic target of the meld (also called as merge) operation is to take two heaps (by taking each heaps root nodes), A1 and A2, and merges them, returning a single heap node as a result. This heap node is the root node of a heap containing all elements from the two subtrees rooted at ... Read More