To execute an algorithm, we follow its instructions until we reach return. At return, we leave the algorithm. The values after return are the algorithm’s output. These values must have the properties listed under Output. If an algorithm returns several values, we separate them with commas (see Algorithm 2.2.3 below, for example). We give some examples.
In these simple examples, the stated Output and the expression after return are almost the same, so one may seem unnecessary. Later examples make the difference clearer. Under Output, we state what we are computing. The instructions state how we compute it.
return\(a+b\text{:}\) The value of the variable \(a\) is 57 and the value of the variable \(b\) is 8. We compute \(a+b=57+8=65\text{.}\) So the value after return is 65, it is the output of the algorithm.
Algorithm 2.2.3 below has four output values. The input of the algorithm is an integer \(c\text{;}\) its output are the powers \(c\text{,}\)\(c^2\text{,}\)\(c^3\text{,}\) and \(c^4\text{.}\)
Before returning \(c\text{,}\)\(c\cdot c\text{,}\)\(c\cdot c\cdot c\text{,}\)\(c\cdot c\cdot c\cdot c\) the values of the expressions have to be computed. Because \(c\) is equal to \(-3\) we compute
\begin{align*}
c\cdot c \amp = (-3)\cdot(-3)=9\\
c\cdot c\cdot c \amp =(-3)\cdot(-3)\cdot(-3)=-27\\
c\cdot c\cdot c\cdot c\amp =(-3)\cdot(-3)\cdot(-3)\cdot (-3)=81
\end{align*}
Thus the algorithms returns the values \(-3\text{,}\)\(9\text{,}\)\(-27\text{,}\) and \(81\text{.}\)
