Question

Describe an algorithm for finding both the largest and the smallest integers in a finite sequence of integers.

Short answer

Algorithm that produces the minimum(smallest) and maximum(largest) integers in a finite sequence of integers$x_1,x_2,x_3$is:

proceduremin and max ($x_1,x_2,x_3$ : integers with$n\ge 1$ ).

role="math" localid="1668421689261" $$\begin{gathered} min:=x_1 \\ max:=x_1 \end{gathered}$$

for$i:=2$ to n

If$x_i<min$ then$min:=x_i$ .

for$i:=2$ to n

If$x_i>max$ then$max:=x_i$ .

returnmin, max

Step-by-step solution

algorithm

Algorithm is a finite sequence of precise instructions that are used for performing a computation or for a sequence of steps.

First, Assume the finite set of integers$x_1,x_2,.....x_n$ .

The algorithm calledmin and max and the input has finite integers$x_1,x_2,.....x_n$ .

Minimum and Maximum

proceduremin and max ($x_1,x_2,.....x_n$ : integers with$n\ge 1$ ).

Initially consider the minimum and maximum as the first term in the list, if the value is not minimum or maximum then the value will be adjusted later in algorithm.

$$\begin{gathered} min:=x_1 \\ max:=x_1 \end{gathered}$$

determine the minimum and maximum

In case the value for second term and term is smaller than the current minimum, then reassign the position of this term to the minimum.

for $i:=2$to n

If $x_i<min$then $min:=x_i$.

Also in case, if the value for second term and$n^{th}$ term is greater than the current maximum then reassigns the position of this term to the maximum.

for$i=2$ to n

If$x_i>max$ then$max:=x_i$ .

Combine above steps

Combine the above steps then the algorithm is:

proceduremin and max ($x_1,x_2,.....,x_n$ : integers with$n\ge 1$ ).

$$\begin{gathered} min:=x_1 \\ max:=x_1 \end{gathered}$$

for$i:=2$ to n

If$x_i<min$ then$min:=x_i$ .

for $i:=2$to n

If $x_i>max$then $max:=x_i$.

returnmin, max