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

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

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

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.