Question

(a) Generate all sequences of n digits 0, 1 and 2 that do not contain a substring of type XX. (E.g., the sequence 210102 is prohibited because it contains 1010.)

(b) Repeat the previous problem for binary strings of length n that do not contain a substring of type XXX.

Answer 1

a. Pseudo code to generate sequences of n digits 0, 1 and 2 that do not contain a substring of type XX is given below, here it first generate random number of n length by randno() function, then the generated sequence check to meet the condition.

Numseq : 12001

Output: 121

The "12001" is reduced to "121".

Main program :

Function Seqnum(n)

{

Input: n as the length of string

Output: sequence of string

Numseq =randno(n);

for i=1 to i<n

{

if (Numseq[i-1]!= Numseq[i])

(Numseq[k++]= Numseq[i-1])

else

While (Numseq[i-1]== Numseq[i])

I++;

}

Numseq[k++]= Numseq[i-1];

Numseq[k]=’\0’;

If(k!=n)

Seqnum(Numseq ,k)

}

Function randno(n){

For i=1 to i<=n

{

return Numseq[i]= rand()%2 // for digit 0, 1 and 2

}

}

b. The code for the binay string of 0 and 1 character.

Function Seqnum(n)

{

Input: n as the length of string

Output: sequence of string

Numseq =randno(n);

for i=1 to i<n

{

if (Numseq[i-1]!= Numseq[i])

(Numseq[k++]= Numseq[i-1])

else

While (Numseq[i-1]== Numseq[i])

I++;

}

Numseq[k++]= Numseq[i-1];

Numseq[k]=’\0’;

If(k!=n)

Seqnum(Numseq ,k)

}

Function randno(n){

For i=1 to i<=n

{

return Numseq[i]= rand()%1 // for binary 0 and 1

}

}