Techniques of representing polynomials using arrays, Data Structure & Algorithms

Assignment Help:

Q. Explain any three methods or techniques of representing polynomials using arrays. Write which method is most efficient or effective for representing the following polynomials.

 

8x100+10x+6

8x3-7x2+5x+15

 

Ans.

The three methods or techniques of representing polynomials using arrays is given as follows

(1) if maximum value of exponent of a polynomial is m then describe an array of size m+1 and store coefficient in corresponding index position or location as exponent. Ex:

2x2 +1 is stored as

829_array.png

(2) The one-dimensional  array  is  used  to  store  exponent  and  coefficient alternatively. Ex: 2x2 +1 is stored as

2005_array1.png

The  size  of  array  needed  is  2*n  where  n  is  the  number  of  elements  in

polynomial.

(3) Use  two dimensional arrays  or  one-dimensional  array  of  structures  one  for  storing exponents and other for co-efficient.

Ex: 2x2 +1 is stored as

525_array2.png

The size of arrays is 2*n where n is the number of the elements in polynomial. (i)  The second and third methods or techniques are the efficient methods.

For saving 8x100+10x+6  , as in method 1 there is a requirement of 101 integer locations.

(ii) 8x3-7x2+5x+15 for this polynomial any one of the representations can be used, but method or technique 1 will be best as there is only coefficients required to be stored. There are no gaps in the exponents; hence the complete array will be filled with the coefficients.


Related Discussions:- Techniques of representing polynomials using arrays

The complexity ladder, The complexity Ladder: T(n) = O(1). It is ca...

The complexity Ladder: T(n) = O(1). It is called constant growth. T(n) does not raise at all as a function of n, it is a constant. For illustration, array access has this c

Generate a single sorted list of all n elements, Q. Assume that we have sep...

Q. Assume that we have separated n elements in to m sorted lists. Explain how to generate a single sorted list of all n elements in time O (n log m )?

Basic concept of the primitive data structures, Q. Explain the basic concep...

Q. Explain the basic concept of the primitive data structures.                                             Ans. The concept of P r i m i t i ve Data

Sort the Sequence Using Merge Sort, Q. Sort the sequence written below of k...

Q. Sort the sequence written below of keys using merge sort. 66, 77, 11, 88, 99, 22, 33, 44, 55                                                                      Ans:

Splaying steps - splay trees, Readjusting for tree modification calls for r...

Readjusting for tree modification calls for rotations in the binary search tree. Single rotations are possible in the left or right direction for moving a node to the root position

Best case, Best Case: If the list is sorted already then A[i] T (n) = ...

Best Case: If the list is sorted already then A[i] T (n) = c1n + c2 (n -1) + c3(n -1) + c4 (n -1)  = O (n), which indicates that the time complexity is linear. Worst Case:

Define rule-based expert system, 1. Define the following terms in a rule-ba...

1. Define the following terms in a rule-based expert system? a) Knowledge base b) Inference engine 2. What is a fuzzy rule? Explain the difference between classical and fuzzy

Tower of hanoi problem., Write an algorithm for getting solution to the Tow...

Write an algorithm for getting solution to the Tower's of Hanoi problem. Explain the working of your algorithm (with 4 disks) with appropriate diagrams. Ans: void Hanoi(int

Project, human resource management project work in c++

human resource management project work in c++

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd