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.
8x^{100}+10x+6
8x^{3}-7x^{2}+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:
2x^{2} +1 is stored as
(2) The one-dimensional array is used to store exponent and coefficient alternatively. Ex: 2x^{2} +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 8x^{100}+10x+6 , as in method 1 there is a requirement of 101 integer locations.
(ii) 8x^{3}-7x^{2}+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.