Before revision:  In this paper, we achieve the desired optimal bounds by presenting a simple algorithm that does not use any complex data structures  ]  .
After revision:  In this paper, we achieve the desired optimal bounds by presenting a simple algorithm that does not use any complex data structures ] for a special case of the All Pairs Suffix Prefix (APSP) problem from O(||P||+n^2) time to optimal O(||P||) time, which may be of independent interest .