Question

Помогите с информатикой 1.Найдите такие x,y,z чтобы выполнялось: 2.Дана постфиксная (обратная польская) запись арифметического выражения: xy + xz +*a*b-c*x+. Запишите в инфиксном виде, вычислите значение этого выражения при x=5, y=2, a=1, b=1, c=1, z=3

Answer 1

Задание 1

Для начала отметим, что так как числа состоят из одних и тех же цифр, то эти цифры должны подходить под ограничения системы счисления с самым низким основанием, то есть x,y,z ∈ [0, 1, 2].

Приводим все части уравнения к десятичной системе счисления.

$(x \cdot 3^2 + y \cdot 3 + z) +( y \cdot 5^2 + x \cdot 5 + z) = 2 \cdot 7 + 0$

$9x + 3y + z +25y + 5x + z = 14$

$14x + 28y + 2z = 14$

$7x + 14y + z = 7$

Вспоминаем про ограничения x,y,z ∈ [0, 1, 2].

Переменная $y$ не может быть больше 0, так как мы сразу "перепрыгиваем" ответ.

Если $x = 1$, то выражение сразу становится = 7, увеличивать x мы больше не можем, остальные переменные должны быть равны 0. - первый ответ x = 1, y = 0, z = 0.

Если x = 0 и y = 0, то максимальное значение получаемое изменением z = 2, что не подходит по условию.

Ответ:  x = 1, y = 0, z = 0

Задание 2

xy + = x+y

xz + = x+z

(xy +) (xz +) * = (x+y)*(x+z)

(xy + xz +*) (a) * = (x+y)*(x+z)*a

(xy + xz +*a*) (b) - = (x+y)*(x+z)*a - b

(xy + xz +*a*b-) (c) * = ((x+y)*(x+z)*a - b) * c

(xy + xz +*a*b-c*) (x) + = ((x+y)*(x+z)*a - b) * c + x

$((5+2)*(5+3)*1 - 1) * 1 + 5 = 7*8 - 1 + 5 = 56 + 4 = 60$ - ответ.

Answer 2

1. Найдите такие x, y, z, чтобы выполнялось:

To find the values of x, y, and z that satisfy the given condition, we need more information about the condition itself. Please provide additional details or clarify the condition so that I can help you find the values of x, y, and z.

2. Дана постфиксная (обратная польская) запись арифметического выражения: xy xz * a b * c x - +. Запишите в инфиксном виде, вычислите значение этого выражения при x=5, y=2, a=1, b=1, c=1, z=3

To convert the given expression from postfix notation to infix notation, we will use a stack data structure. The steps are as follows:

1. Create an empty stack. 2. Read the expression from left to right. 3. If the character is an operand (variable or number), push it onto the stack. 4. If the character is an operator, pop the top two elements from the stack, concatenate them with the operator in between, and push the resulting string back onto the stack. 5. Repeat steps 3 and 4 until all characters in the expression have been processed. 6. The final element in the stack will be the infix expression.

Let's apply these steps to the given expression:

Expression: xy xz * a b * c x - +

1. Read the first character 'x'. It is an operand, so push it onto the stack: x 2. Read the next character 'y'. It is also an operand, so push it onto the stack: y 3. Read the next character 'x'. It is an operand, so push it onto the stack: x x 4. Read the next character 'z'. It is also an operand, so push it onto the stack: x x z 5. Read the next character '*'. It is an operator, so pop the top two elements from the stack (z and x), concatenate them with the operator in between, and push the resulting string back onto the stack: x (x*z) 6. Read the next character 'a'. It is an operand, so push it onto the stack: x (x*z) a 7. Read the next character 'b'. It is also an operand, so push it onto the stack: x (x*z) a b 8. Read the next character '*'. It is an operator, so pop the top two elements from the stack (b and a), concatenate them with the operator in between, and push the resulting string back onto the stack: x (x*z) (a*b) 9. Read the next character 'c'. It is an operand, so push it onto the stack: x (x*z) (a*b) c 10. Read the next character 'x'. It is an operand, so push it onto the stack: x (x*z) (a*b) c x 11. Read the next character '-'. It is an operator, so pop the top two elements from the stack (x and c), concatenate them with the operator in between, and push the resulting string back onto the stack: x (x*z) (a*b) (c-x) 12. Read the next character '+'. It is an operator, so pop the top two elements from the stack ((c-x) and (a*b)), concatenate them with the operator in between, and push the resulting string back onto the stack: x (x*z) ((a*b)+(c-x)) 13. The final element in the stack is the infix expression: x (x*z) ((a*b)+(c-x))

Now, let's calculate the value of this expression when x=5, y=2, a=1, b=1, c=1, and z=3:

Substituting the values: x (x*z) ((a*b)+(c-x)) 5 (5*3) ((1*1)+(1-5))

Calculating the multiplications and subtractions: 5 15 ((1)+(1-5))

Calculating the additions and subtractions: 5 15 (-4)

Final result: 5 -4

Therefore, the value of the expression is -4 when x=5, y=2, a=1, b=1, c=1, and z=3.