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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
Boolean indexing helps us to select the data from the DataFrames using a boolean vector. We need a DataFrame with a boolean index to use the boolean indexing. Let's see how to achieve the boolean indexing.Create a dictionary of data.Convert it into a DataFrame object with a boolean index as a vector.Now, access the data using boolean indexing.See the example below to get an idea.Exampleimport pandas as pd # data data = { 'Name': ['Hafeez', 'Srikanth', 'Rakesh'], 'Age': [19, 20, 19] } # creating a DataFrame with boolean index vector data_frame = pd.DataFrame(data, index = [True, False, True]) ... 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
We can perform the calendar operations using the calendar module in Python. Here, we are going to learn about the different methods of calendar class instance.calendar.calendar(year)The calendar class instance returns the calendar of the year. Let's see one example.Example Live Demo# importing the calendar module import calendar # initializing year year = 2019 # printing the calendar print(calendar.calendar(year))OutputIf you run the above code, you will get the following results.calendar.firstweekday()The method calendar.firstweekday() returns the first weekday in the week i.e.., MONDAY.Example Live Demo# importing the calendar import calendar # getting firstweekday of the year print(calendar.firstweekday())OutputIf you run the above program, you will get ... 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
We are going to explore different methods of calendar module in this tutorial. Let's see one by one.calendar.monthrange(year, month)The method calendar.monthrange(year, month) returns starting weekday number and number of days of the given month. It returns two values in a tuple. Let's see one example.Example Live Demo# importing the calendar module import calendar # initializing year and month year = 2019 month = 1 # getting the tuple of weekday and no. of days weekday, no_of_days = calendar.monthrange(year, month) print(f'Weekday number: {weekday}') print(f'No. of days: {no_of_days}')OutputIf you run the above code, you will get the following results.Weekday number: 1 No. of ... Read More
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
The print and echo are both language constructs to display strings. The echo has a void return type, whereas print has a return value of 1 so it can be used in expressions. The print_r is used to display human-readable information about a variable.ExampleLet us now see an example that displays output using echo, print, and print_r: Live DemoOutputThis will produce the following output−Array... Value = John Value = Jacob Value = Tom Value = Tim Displaying Array Values using print... Value = John Value = Jacob Value = Tom Value = Tim Displaying Array Values using print_r... Array ( [0] => John [1] => Jacob [2] => Tom [3] => Tim )