Baum Sweet Sequence in C Program?


Here we will see the Baum Sweet Sequence. This sequence is one binary sequence. If a number n has an odd number of contiguous 0s, then nth bit will be 0, otherwise nth bit will be 1.

We have a natural number n. Our task is to find the n-th term of Baum Sweet sequence. So we have to check whether it has any consecutive block of zeros of odd length.

If the number is 4 then the term will be 1, because 4 is 100. So it has two (even) number of zeros.

Algorithm

BaumSweetSeqTerm (G, s) −

begin
   define bit sequence seq of size n
   baum := 1
   len := number of bits in binary of n
   for i in range 0 to len, do
      j := i + 1
      count := 1
      if seq[i] = 0, then
         for j in range i + 1 to len, do
            if seq[j] = 0, then
               increase count
            else
               break
            end if
         done
         if count is odd, then
            baum := 0
         end if
      end if
   done
   return baum
end

Example

#include <bits/stdc++.h>
using namespace std;
int BaumSweetSeqTerm(int n) {
   bitset<32> sequence(n); //store bit-wise representation
   int len = 32 - __builtin_clz(n);
   //builtin_clz() function gives number of zeroes present before the first 1
   int baum = 1; // nth term of baum sequence
   for (int i = 0; i < len;) {
      int j = i + 1;
      if (sequence[i] == 0) {
         int count = 1;
         for (j = i + 1; j < len; j++) {
            if (sequence[j] == 0) // counts consecutive zeroes
               count++;
            else
               break;
         }
         if (count % 2 == 1) //check odd or even
            baum = 0;
      }
      i = j;
   }
   return baum;
}
int main() {
   int n = 4;
   cout << BaumSweetSeqTerm(n);
}

Output

1
raja
Published on 20-Aug-2019 16:33:07
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