Question

Devise an algorithm for generating all the r-permutations of a finite set when repetition is allowed.

Short answer

Device an algorithm for generating all the \(r - \)permutation of a finite set when repetition is allowed.

Step-by-step solution

Step 1:

\({a_1},{a_2},.............,{a_n}\)and each\({a_i} < n\)

\(i = r\)

When\({r_i} = n\)

\(\left\{ \begin{array}{l}{a_i} = 1\\i:i - 1\end{array} \right\}\)

\(\left\{ {{a_i} = {a_i} + 1} \right\}\)

Step 2:

Given:

Repetition is allowed.

Concept used.

\(r\)Permutation of n element when repetition is allowed\({n_{{p_r}}} = \frac{{n!}}{{r!}}\)

Calculation:

\({a_1},{a_2},{a_3}.............,{a_n}\) be positive integer, \({a_i} < n\) procedure

\(i = r\)

While\({a_i} = n\)

\(\begin{array}{l}{a_i} = 1\\i:i - 1\end{array}\)

So, the result will be

\({a_1},{a_2},.............,{a_r}\) Is the next permutation in lexicographic order.