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20/12/2024 12:22:06
708. Equation
Задача
Аналитическое решение уравнений, неравенств, систем уравненийСтеки, очереди
Олимпиадные задачи на английском языке
| 05/12/2007 | Занятие 12 (задачи NEERC 2007) (E) |
| 10/07/2020 | Летние сборы - 6 (командное) (E) |
Ограничения: время – 2s/4s, память – 64MiB Ввод: input.txt или стандартный ввод Вывод: output.txt или стандартный вывод 
Послать решение Blockly Посылки Темы Где Обсудить (0)
Your task is to solve an equation of the form `f(x)\ =\ 0` where `f(x)` is written in postfix notation with
numbers, operations +, -, *, /, and at most one occurrence of a variable `x`.
For example, `f(x)` for an equation `(4x+2)/2\ =\ 0` is written as:
4 X * 2 + 2 /
The solution for `f(x)\ =\ 0` is `x\ =\ -1/2`.
Input
The input file consists of a single line with at most 30 tokens separated by spaces. Each token is either:
- a digit from 0 to 9;
- an operation +, -, *, or /;
- an uppercase letter X that denotes variable `x`.
The input file contains a correct representation of `f(x)` in postfix notation where token X occurs at most
once. There is no division by a constant zero in this equation, that is, there always exists a value of `x`,
such that `f(x)` can be evaluated without division by zero.
Output
Write to the output file:
- X = `p//q` if equation `f(x)\ =\ 0` has a single solution that can be represented with a simple fraction `p/q`, where `p` and `q` are coprime integer numbers and `q` is positive.
- NONE if equation `f(x)\ =\ 0` has no solution;
- MULTIPLE if equation `f(x)\ =\ 0` has multiple solutions.
Sample input 1
4 X * 2 + 2 /
Sample output 1
X = -1/2
Sample input 2
2 2 *
Sample output 2
NONE
Sample input 3
0 2 X / *
Sample output 3
MULTIPLE
