Description
Objective
● To learn about polymorphism by using function overloading and operator overloading in C++
Data Structure
Create a class in C++ to implement Polynomials. This class should support functionality to
add, subtract, and multiply using both functions as well as by overloading these operators:
+, -, *. The operands for these operations can be two Polynomials or a Polynomial and
a double. Also include the functionality to evaluate the result of a Polynomial at a given x.
The internal details of the implementation of the class are your choice.
Input Format
Each testcase will consist of n operations. Each operation is either an addition (‘a’),
subtraction (‘s’), multiplication (‘m’), or evaluation (‘e’). The first three operations take
two Polynomials as input and output a Polynomial. These operations can also take a
Polynomial and a double as input, however the double will also be given in the
polynomial format with one constant term. Polynomial evaluation takes a Polynomial and
a double as input and outputs a double.
The testcase format is as follows:
.
.
.
A Polynomial is represented in the following form in the testcase:
.
.
.
The exponent will be a non-negative integer. The coefficient will be a double. Note that the
exponents can be in any order.
Output Format
The output for addition, subtraction, multiplication is a Polynomial, while for evaluation it
is a double.
Polynomial:
– Each term of the Polynomial has to be printed in the format:
– The terms of the Polynomial have to be printed in increasing order of their
exponents.
– If there exists a constant term, print that with “x^0”.
– The format for the whole Polynomial is
– The sign will be ‘+’ or ‘-’ depending on the sign of the coefficient following it.
– Only terms with non-zero coefficients have to be printed.
– All coefficients should be printed with a fixed precision of 3 decimal digits (see note
at the end).
– An “empty” Polynomial should be printed as a blank line
Incorrect way to print Polynomial Corresponding correct representation
6x^4 + 3x^2 3.000x^2 + 6.000x^4
5.00 – 10.0x^3 5.000x^0 – 10.000x^3
5.000 + -6x^2 5.000x^0 – 6.000x^2
4x + 0x^2 4.000x^1
Double:
– Each double has to be printed with a fixed precision of 3 decimal digits (see note at
the the end).
Constraints
– There will be a maximum of 100 operations per testcase.
– The maximum degree of any Polynomial taken as input will be 10.
Sample Testcase
Input:
2 → Number of operations
a → Addition (first operation)
2 → Number of terms in the first polynomial
1 2 → 2x^1
3 4 → 4x^3
3 → Number of terms in the next (second) polynomial
5 -10 → -10x^5
2 7 → 7x^2
3 -6 → -6x^3
e → Evaluation (second operation)
3 → Number of terms in the polynomial
1 2 → 2x^1
3 4 → 4x^3
5 6 → 6x^5
10 → Value of x at which polynomial has to be evaluated
Output:
2.000x^1 + 7.000x^2 – 2.000x^3 – 10.000x^5
604020.000
Design Submission Format
For the design submission on Moodle, please submit a .tar.gz file named as your roll number.
Note
All doubles have to be printed with a fixed precision of 3 decimal digits. This includes the
coefficients of the Polynomials as well the result of the evaluation operation. Take a look
at the example below.
Number How it should be displayed
2 2.000
3.4 3.400
3.14159 3.142
This style of printing can be set by using the following statements before any “cout”. You
only need to write these statements once.
std::cout.precision(3);
std::cout << std::fixed;
Fun Challenge (not evaluated)
Extend the polynomial to support complex numbers.
