documentclass{article}
usepackage[table,dvipsnames]{xcolor}
usepackage{algorithm,algpseudocode,float}

%-----------
makeatletter
newenvironment{breakablealgorithm}
  {% begin{breakablealgorithm}
   begin{center}
     refstepcounter{algorithm}% New algorithm
     hrule height.8pt depth0pt kern2pt% @fs@pre for @fs@ruled
     renewcommand{caption}[2][relax]{% Make a new caption
       {raggedrighttextbf{ALG@name~thealgorithm} ##2par}%
       ifxrelax##1relax % #1 is relax
         addcontentsline{loa}{algorithm}{protectnumberline{thealgorithm}##2}%
       else % #1 is not relax
         addcontentsline{loa}{algorithm}{protectnumberline{thealgorithm}##1}%
       fi
       kern2pthrulekern2pt
     }
  }{% end{breakablealgorithm}
     kern2pthrulerelax% @fs@post for @fs@ruled
   end{center}
  }
makeatother

begin{document}

begin{breakablealgorithm}
  caption{PPPPPPPPPPPPP}
  begin{algorithmic}[1]
  makeatlettersetcounter{ALG@line}{0}makeatother
  If { $phi < 10^circ$}
        State{$A = aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa$} Comment{ where textbf{a} is aaaaaaaaaa   constant.}
        Else
           State{$B =  bbbbbbbbb$ }
        EndIf
end{algorithmic}
end{breakablealgorithm}


end{document}