3. Polynomial#

Implement a class called Polynomial, which holds a polynomial (eg. $a{x}^2+b{x}^1$), and satisfies the following invariants,

• No similar term.

  • Users shouldn't observe similar terms in the polynomial. That is, $3+3x^2+5+2x^2$ should be observed as $8+5x^2$.

• Sorted by ascending power order.

  • Users should observe an ascendingly sorted polynomial. That is, $2x^2+3+x$ should be observed as $3+x+2x^2$.

• For terms with 0 as coefficient, the observable state shows as if the term dosen't exsit. That is, $0x^2+x^3$ should be observed as $x^3$.

You should implement the following functions for it,

• auto operator+=(Polynomial const& other) -> Polynomial&

  • Add *this and other, store the result in *this.

• friend auto operator+(Polynomial const& lhs, Polynomial const& rhs) -> Polynomial

  • Add lhs and rhs, store the result in a new Polynomial.

• friend auto operator<<(std::ostream& ostream, Polynomial const& polynomial) -> std::ostream&

  • Output the polynomial with the format 3 + 5x^2 + 1x^3 + 1x^5.

After that, write a main function to test all your public functions.

1struct Pair {
2 public:
3  int const first;
4  int second;
5};