how can I convert this NFA to DFA 
In school we are told that, to do this conversion first we have to convert this NFA to TG (transition graph) and then find the RE (regular expression) of TG and then convert it into DFA.
The TG which I found is 
The RE of this TG, which I found, is $ r=(01)^*+1^*+(00(11+1))^*$
Now to find DFA I can use Kleene Theorem: $r_1=(01)^*,r_2=1^* , r_3=00(1+11)$ so $r$ becomes $r=r_1+r_2+r_3^*$
Is this solution correct?