The final fate of the spherically symmetric collapse of a perfect fluid which follows the \gamma -law equation of state and adiabatic condition is investigated .
Full general relativistic hydrodynamics is solved numerically using a retarded time coordinate , the so-called observer time coordinate .
Thanks to this coordinate , the causal structure of the resultant space-time is automatically constructed .
Then , it is found that a globally naked , shell-focusing singularity can occur at the center from relativistically high-density , isentropic , and time symmetric initial data if \gamma \lesssim 1.01 within the numerical accuracy .
The result is free from the assumption of self-similarity .
The upper limit of \gamma with which a naked singularity can occur from generic initial data is consistent with the result of Ori and Piran based on the assumption of self-similarity .