Create a class polynomial that is used to evaluate a polynomial function of x:
P(x) = a0 + a1x + a2x + ⋯ + an−1xn−1 + anxn
The coefficients ai are floating-point numbers, the exponents of x are integers, and the largest exponent n—called the degree of the polynomial—is greater than or equal to 0. The class has the attributes
■ degree —the value of the largest exponent n
■ coefficients —an array of the coefficients ai
and the following methods:
- Polynomial (max) —a constructor that creates a polynomial of degree max whose coefficients are all 0
- setConatant (i, value) —Sets the Coefficient ai to value
- evaluate (x) — returns the value of the polynomial for the given value x
For example, the polynomial
P(x) = 3 + 5x + 2x3
is of degree 3 and has coefficients a0 = 3, a1 = 5, a2 = 0, and a3 = 2. The invocation evaluate (7) computes 3 + 5 × 7 + 0 × 7 + 2 = 73, which is 3 + 35 + 0 + 686, and returns the result 724.
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