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0298. Equation
| Имя входного файла: | equation.in |
| Имя выходного файла: | equation.out |
| Ограничение по времени: | 2 s |
| Ограничение по памяти: | 256 megabytes |
Write a program that can solve linear equations with one variable.
Input Specification
The input file will contain a number of equations, each one on a separate line. All equations are strings of less than 100 characters which strictly adhere to the following grammar (given in EBNF):
Equation := Expression '=' Expression
Expression := Term { ('+' | '-') Term }
Term := Factor { '*' Factor }
Factor := Number | 'x' | '(' Expression ')'
Number := Digit | Digit Number
Digit := '0' | '1' | ... | '9'
Although the grammar would allow to construct non-linear equations
like "x*x=25", we guarantee that all equations occuring
in the input file will be linear in x.
We further guarantee that all sub-expressions of an equation will be linear in x too.
That means, there won't be test cases like x*x-x*x+x=0 which is a linear equation
but contains non-linear sub-expressions (x*x).
Note that all numbers occuring in the input are non-negative integers, while the solution for x is a real number.
Output Specification
For each test case, print a line saying "Equation #i (where i is the number of the test case) and a line with one of the following answers:- If the equation has no solution, print "No solution.".
- If the equation has infinitely many solutions,
print "Infinitely many solutions.".
- If the equation has exactly one solution, print "x = solution" where solution is replaced by the appropriate real number (printed to six decimals).
Sample Input
x+x+x=10 4*x+2=19 3*x=3*x+1+2+3 (42-6*7)*x=2*5-10
Sample Output
Equation #1 x = 3.333333 Equation #2 x = 4.250000 Equation #3 No solution. Equation #4 Infinitely many solutions.
Источник: Ulm University Local Contest 1997
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