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Such trees do not necessarily need to be implemented using data structures conventionally used for trees. Instead, tokens can be stored in flat structures, such as tables, by simultaneously building a priority list which states what elements to process in which order.
Another approach is to first fully parenthesize the expression, inserting a number of parentheses around each operator, such that they lead to the correct precedence even when parsed with a linear, left-to-right parser. This algorithm was used in the early [[Fortran#FORTRAN|FORTRAN I]] compiler:<ref name="Padua2000">{{cite journal |last1=Padua |first1=David |title=The Fortran I Compiler |year=2000
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