Exam & Solution - A Concise and Practical Introduction to Programming Algorithms in Java - page 236

- Given a signal s , we first wish to invert it: that is, to obtain its logical
negation. For example, the invert of signal1 is:

true

false

t=0 t=1 t=3 t=4

Write a function static Signal invert (Signal s) performing this process.
Your function shall not modify the original signal. That is, you need
to create a new Signal . The time complexity of this function should
not depend on the length of the transition states in s .

- Given a signal s and time tick t ,wewanttocompute s ( t ) that
is the value ( true or false ) of the signal s at time t . Write an it-
erative function static boolean valueAt(Signal s, int time) performing
this task. You shall not modify signal s , and the time complexity
should be proportional to the number of transition states in s .

- We would like a function that displays a signal as a sequence of
intervals with respective values. For example,

− inf −> +inf : false

means that the signal uniformly takes value false .For signal1 ,the
display function shall produce the output:

− inf −> 1.0 : false
1.0 −> 3.0 : true
3.0 −> 4.0 : false
4.0 −> +inf : true

Write such an iterative function static void print(Signal s) .

- Given a signal s , we would like to produce another signal identical
to s but shifted in time by a step δ> 0. That is, we want a signal
with the same initial value but with transition states ( τ i ) defined by
τ i = τ i + δ, ∀ i ∈{ 1 ,...,n } .

To illustrate this operation, the shifted signal of signal1 with δ =3
produces the following result: