Question

in the procedure mystery written below, the input to value is always a positive number
procedure mystery ()
{
value ←??
number ← value

repeat until (number = 0)
{
value ← value * -1
number ← number - 1
}

if (value > 0)
{
return (false)
}
else
{
return (true)
}
}
which of the following best describes the result of running the mystery procedure?
the result will always be true for any initial value of value
the result will be false whenever the initial value of value is even
the result will always be false for any initial value of value
the result will be false whenever the initial value of value is odd

Explanation:

Step1: Analyze the loop

The loop runs number times (where number is initially set to the input value). In each iteration, value is multiplied by - 1. So, if the initial value is positive, after an odd number of iterations, value will be negative; after an even number of iterations, value will be positive.

Step2: Analyze the return statement

The loop runs number (which is the initial value) times. If the initial value (let's call it \(n\)) is odd, then \(n\) (the number of loop - iterations) is odd. So, \(value = initial\ value\times(-1)^n\). Since \(n\) is odd, \(value\) is negative. If \(value<0\), the procedure returns true. If the initial value (\(n\)) is even, then \(n\) (the number of loop - iterations) is even. So, \(value = initial\ value\times(-1)^n\). Since \(n\) is even, \(value\) is positive. If \(value > 0\), the procedure returns false.

Answer:

The result will be false whenever the initial value of value is even