Question

Describe an algorithm that puts the first three terms of a sequence of integers of arbitrary length in increasing order.

Short answer

Algorithm that that puts the first three terms of a sequence of integers of arbitrary length in increasing order is:

procedureorder first three($x_1,x_2,x_3,...,x_n$: integers with$n\le 3$ ).

If $x_1<x_2$

then interchange$x_1$and$x_2$i.e.,$x_1<x_2$

If $x_2<x_3$

Then interchange $x_2$and$x_3$i.e.,$x_2<x_3$

return $x_1<x_2<x_3$

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 sequence of integers $x_1,x_2,x_3,...,x_n$.

The algorithm called order first three and the input has finite integers $x_1,x_2,x_3,...,x_n$.

Interchange for first and second term

procedureorder first three($x_1,x_2,x_3,...,x_n$ : integers with$n\le 3$ ).

Use the variable to interchange variables.

First check if the integer$x_1$ and$x_2$ are in increasing order, if$x_1$ and$x_2$ are not in increasing order then interchange the variables.

If $x_1>x_2$

then interchange$x_1$ and$x_2$ i.e.,$x_1<x_2$

Interchange for second and third term

Now check if the integer$x_2$ and$x_3$ are in increasing order, if$x_2$ and$x_3$ are not in increasing order then interchange the variables.

If$x_2>x_3$

Then interchange$x_2$ and$x_3$ i.e.,$x_2<x_3$

Combine the above steps

Combine the above steps, the algorithm is:

procedureorder first three($x_1,x_2,x_3,...,x_n$ : integers with$n\le 3$ ).

If $x_1>x_2$

then interchange$x_1$ and$x_{2_{}}$ i.e.,$x_1>x_2$

If$x_2>x_3$

Then interchange$x_2$ and$x_3$ i.e.,$x_2>x_3$

return$x_1<x_2<x_3$