Rajat,

It seems that I confused lines and did not express in the code what I wrote 
above:
You have to add that additional index also when initializing the sparsity 
pattern, i.e.
  std::cout << " constraints printed " <<std::endl;
  DynamicSparsityPattern dsp (locally_relevant_dofs);
should become
  std::cout << " constraints printed " <<std::endl;
  locally_relevant_dofs.add_index(the_dof);
  DynamicSparsityPattern dsp (locally_relevant_dofs);

Best,
Daniel

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