DCFL with prefix property have LR(0) grammar?
Your grammar is $\mathrm{LR}(0)$ by adding a $\mathrm{\$}$ symbol to the alphabet and a starting deduction rule $S'\rightarrow S\$$ when constructing the $\mathrm{LR}(0)$ automaton (and it is a standard construction).

Omitting syntactical purposes, every DCFL $\mathrm{L}$ can be parsed by an $\mathrm{LR}(0)$ grammar for $\mathrm{L}\$$. What makes $\mathrm{LR}(k)$ ($k&gt;0$) more practical is that it may include more syntactical information which is very important in compiler design. Otherwise, all these techniques would never be used in practice. In that case, $\mathrm{LL}(k)$ with local manipulation for expressions would be used instead, even with prohibitive cost of time and space.