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What is binomial expansion?

Updated: 8/11/2023
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15y ago

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Sounds pretty sexy, eh? See link. http://en.wikipedia.org/wiki/Binomial_expansion

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Is the binomial expansion.

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What is binomial array in antenna?

Binomial array is an array in which the amplitudes of the antenna elements in the array are arranged according to the coefficients of the binomial series... The need for a binomial array is i) In uniform linear array as the array length is increased to increase the directivity, the secondary lobes also occurs. ii) For certain applications, it is highly desirable that secondary lobes should be eliminated completely or reduced to minimum desirable level compared to main lobes. Suman Kalyan...


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Difference between Fibonacci heap and binomial heap?

Both Binomial Heap and Fibonacci Heap are types of priority queues, but they have some differences in their structure and performance characteristics. Here's a comparison between the two: Structure: Binomial Heap: Binomial Heap is a collection of Binomial Trees. A Binomial Tree is a specific type of tree with a recursive structure. Each Binomial Tree in a Binomial Heap has a root node and may have children, where each child is also a root of a Binomial Tree of smaller size. Fibonacci Heap: Fibonacci Heap is a collection of trees, similar to Binomial Heap, but with more flexible tree structures. It allows nodes to have any number of children, not just two as in the Binomial Heap. The trees in a Fibonacci Heap are not strictly binomial trees. Operations Complexity: Binomial Heap: Binomial Heap supports the following operations with the given time complexities (n is the number of elements in the heap): Insertion: O(log n) Find minimum: O(log n) Union (merge): O(log n) Decrease key: O(log n) Deletion (extract minimum): O(log n) Fibonacci Heap: Fibonacci Heap generally has better time complexities for most operations (amortized time complexity). The amortized analysis takes into account the combined cost of a sequence of operations. For Fibonacci Heap (n is the number of elements in the heap): Insertion: O(1) Find minimum: O(1) Union (merge): O(1) Decrease key: O(1) Deletion (extract minimum): O(log n) Potential Advantage: Fibonacci Heap: The main advantage of Fibonacci Heap is that it allows constant-time insertion, decrease key, and deletion operations in the amortized sense. This makes it particularly useful in certain algorithms, such as Dijkstra's algorithm for finding the shortest path in a graph, where these operations are frequently used. Space Complexity: Binomial Heap: Binomial Heap usually requires more memory due to the strict structure of Binomial Trees. Fibonacci Heap: Fibonacci Heap can have better space complexity due to its more flexible structure, but this can vary depending on the specific implementation. Real-world Use: Binomial Heap: Binomial Heap is simpler to implement and may be preferred when ease of implementation is a concern. Fibonacci Heap: Fibonacci Heap's advantage in amortized time complexity makes it a better choice in scenarios where frequent insertions, deletions, and decrease key operations are expected. In summary, Binomial Heap and Fibonacci Heap are both priority queue data structures, but Fibonacci Heap offers better amortized time complexity for certain operations. However, Fibonacci Heap can be more complex to implement and may require more memory than Binomial Heap in some cases. The choice between the two depends on the specific use case and the performance requirements of the application.


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Related questions

What is the relationship between the binomial expansion and binomial distribution?

First i will explain the binomial expansion


What is a binominal theorem?

The binomial theorem describes the algebraic expansion of powers of a binomial, hence it is referred to as binomial expansion.


What is The expansion of a binomial that involves a coefficient found by combinations?

Binomial Theorum


Validity of binomial expansion for n less than 0?

The binomial expansion is valid for n less than 1.


What is a binomial coefficient?

A binomial coefficient is a coefficient of any of the terms in the expansion of the binomial (x+y)^n.


What is meant by the first two non-zero terms in an binomial expansion?

The first two terms in a binomial expansion that aren't 0


The expansion of a binomial that involves a coefficient found by combinations. The expansion will contain the same number of terms as the exponent of the original binomial. For each term the exponents?

Not true. The expansion will have one more term.


What does an binomial expansion do?

Binomial Expansion makes it easier to solve an equation. It brings an equation of something raised to a power down to a solveable equation without parentheses.


Define binomial theorem?

The binomial theorem describes the algebraic expansion of powers of a binomial: that is, the expansion of an expression of the form (x + y)^n where x and y are variables and n is the power to which the binomial is raised. When first encountered, n is a positive integer, but the binomial theorem can be extended to cover values of n which are fractional or negative (or both).


What does pascals triangle relate the coefficients to?

Expansion of the Binomial a+b


What are the applications of pascal's triangle?

For binomial expansions. (When you have to multiply out many brackets, binomial expansion speeds things up greatly).


What is universal binomial raised to power n?

universal binomial raised to power n means the is multiplied to itself n number of times and its expansion is given by binomial theorem