Polynomial Showdown
Given the coefficients of a polynomial from degree 8 down to 0, you are to format the polynomial in a readable format with unnecessary characters removed. For instance, given the coefficients 0, 0, 0, 1, 22, -333, 0, 1, and -1, you should generate an output line which displays x^5 + 22x^4 - 333x^3 + x - 1.
The formatting rules which must be adhered to are as follows:
- Terms must appear in decreasing order of degree.
- Exponents should appear after a caret “^”.
- The constant term appears as only the constant.
- Only terms with nonzero coefficients should appear, unless all terms have zero coefficients in which case the constant term should appear.
- The only spaces should be a single space on either side of the binary + and − operators.
- If the leading term is positive then no sign should precede it; a negative leading term should be
preceded by a minus sign, as in -7x^2 + 30x + 66.
- Negated terms should appear as a subtracted unnegated term (with the exception of a negative leading term which should appear as described above). That is, rather than x^2 + -3x, the output should be x^2 - 3x.
- The constants 1 and -1 should appear only as the constant term. That is, rather than -1x^3 + 1x^2 + 3x^1 - 1, the output should appear as -x^3 + x^2 + 3x - 1.
Input
The input file will contain one or more lines of coefficients delimited by one or more spaces. There are nine coefficients per line, each coefficient being an integer with a magnitude of less than 1000.
Output
The output file should contain the formatted polynomials, one per line.
Sample Input
0 0 0 1 22-333 0 1 -1 0 0 0 0 0 0 -55 5 0
Sample Output
x^5 + 22x^4 - 333x^3 + x - 1
-55x^2 + 5x