Question

Describe an algorithm that takes as input a list of integers and finds the location of the last even integer in the list or returns 0 if there are no even integers in the list.

Short answer

The algorithm is as follows:

$$\begin{gathered} procedurelasteven\left(a_1,a_2,....,a_n:integerswithn\ge 1\right) \\ k:=0 \\ fori=1ton \\ if{a}_{i}iseventhenk:=1 \\ returnk \end{gathered}$$

Step-by-step solution

Describing the steps needed to write the required algorithm

We can call the algorithm as ‘lasteven’ and input is a list of k integers

$procedurelasteven\left(a_1,a_2,....,a_n:integerswithn\ge 1\right)$

We initially define the variable k as 0 ( k will determine the last even number).

k : = 0

For every integer between 1 and n ,$a_i$ if is even, then we replace the current value of variablewith.

$$\begin{gathered} fori=1ton \\ if{a}_{i}iseventhenk:=1 \end{gathered}$$

Finally, we return the k which at the end of the loop contains the last even integer in the list

return k

Combining all the steps to form an algorithm

The algorithm is as follows:

$$\begin{gathered} procedurelasteven\left(a_1,a_2,....,a_n:integerswithn\ge 1\right) \\ k:=0 \\ fori=1ton \\ if{a}_{i}iseventhenk:=1 \\ returnk \end{gathered}$$

Therefore, the required algorithm is designed for the given conditions.