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

Explain decision tree, Decision Tree A decision tree is a diagram that ...

Decision Tree A decision tree is a diagram that shows conditions and actions sequentially and therefore shows which condition is to be considered first, second and so on. It is

What do you mean by hash clash, What do you mean by hash clash? Hashing...

What do you mean by hash clash? Hashing is not perfect. Occasionally, a collision occurs when two different keys hash into the same hash value and are assigned to the same arra

Road transport booking system, what algorithms can i use for the above titl...

what algorithms can i use for the above title in my project desing and implmentation of road transport booking system

Write an algorithm for binary search., Write an algorithm for binary search...

Write an algorithm for binary search. Algorithm for Binary Search 1.  if (low> high) 2.  return (-1) 3.  Mid = (low + high)/2 4.  if ( X = = a[mid]) 5.  return (mid); 6.

Explain the method of overlapping and intersecting, Overlapping or Interse...

Overlapping or Intersecting A polygon overlaps or intersects the current background if any of its sides cuts the edges of the viewport as depicted at the top right corner of th

Explain optimal binary search trees, Explain Optimal Binary Search Trees ...

Explain Optimal Binary Search Trees One of the principal application of Binary Search Tree is to execute the operation of searching. If probabilities of searching for elements

Calculation of time complexity, Example: Assume the following of code: ...

Example: Assume the following of code: x = 4y + 3 z = z + 1 p = 1 As we have been seen, x, y, z and p are all scalar variables & the running time is constant irrespective

Illustrate the intervals in mathematics, Illustrate the intervals in mathem...

Illustrate the intervals in mathematics Carrier set of a Range of T is the set of all sets of values v ∈ T such that for some start value s ∈ T and end value e ∈ T, either s ≤

Program segment for quick sort, Illustrates the program segment for Quick s...

Illustrates the program segment for Quick sort. It uses recursion. Program 1: Quick Sort Quicksort(A,m,n) int A[ ],m,n { int i, j, k; if m { i=m; j=n+1; k

Relation of time and space complexities of an algorithm, What is complexity...

What is complexity of an algorithm? What is the basic relation between the time and space complexities of an algorithm? Justify your answer by giving an example.

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