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28/01/2023 16:14:01

# Рабочее место участника

## Задачи

708. Equation

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

Source: ACM ICPC NEERC 2007 