Binary expression tree

A binary expression tree is a specific kind of binary tree used to represent expressions, most commonly algebraic and boolean expressions, including those that contain both unary and binary operators. Like any binary tree, each node has zero, one or two children, a restricted structure that simplifies the processing of expression trees. In an algebraic expression tree the operators sit in the internal nodes and the numbers and variables in the leaf nodes, with binary operators taking two child nodes and unary operators one. Boolean expressions are represented in the same way, using true and false as constant values and operators such as AND, OR and NOT. A tree is constructed from an expression in postfix notation by reading its symbols one at a time: operands become one-node trees whose pointers are pushed onto a stack, and each operator pops the top two tree pointers and merges them under a new root, leaving one pointer to the finished tree.