Question

I was reading about linked list implementation of polynomials. It stated,

Compare this representation with storing the same
polynomial using an array structure.
In the array we have to have keep a slot for each exponent
of x, thus if we have a polynomial of order 50 but containing
just 6 terms, then a large number of entries will be zero in
the array.

I was wondering how do we represent a polynomial in an array? Please guide me.

Thanks

Answer 1

A complete Java implementation of array-based polynomials is here: https://cs.lmu.edu/~ray/classes/dsa/assignment/2/answers/

The basic idea is that if you have a polynomial like

4x^6-2x+5

then your array would look like

   0     1    2    3    4    5    6
+----+-----+----+----+----+----+----+
| 5  |  -2 |  0 |  0 |  0 |  0 |  4 |
+----+-----+----+----+----+----+----+

That is

• the coefficient 5 is in slot 0 of the array (representing 5x^0)
• the coefficient -2 is in slot 1 of the array (representing -2x^1)
• the coefficient 4 is in slot 6 of the array (representing 4x^6)

You can probably see how this represenation would be wasteful for polynomials like

3x^5000 + 2

In cases like this you want instead to use a sparse array representation. The simplest approach would be to use a map (dictionary) whose keys are the exponoents and whose values are the coefficients.