day18 - COP 3503 Computer Science II CLASS NOTES DAY#18...

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COP 3503 – Computer Science II CLASS NOTES - DAY #18 Expression Trees Expression trees are a useful technique for representing and evaluating expressions. The leaves of an expression tree represent the operands of the expression which may be either constants or variables. The internal nodes represent the operations embedded in the expression. Most operations are binary operations and thus most internal nodes will have two children, however, this is not always the case. Unary operators, such as unary minus, will have only a single child node representing the single operand of such an operator. Other operations may be tertiary, quadary, etc. and such operation nodes will have three or more child nodes. An expression tree T is evaluated by applying the operator in the root node to values obtained through recursive evaluation of the left and right subtrees. Shown below is an expression tree which represents the expression (a+b)*(c - d): Evaluation of the expression tree shown above produced the expression: ((a+b)*(c - d)). Note that this is an overly parenthesized infix expression as a result of the recursive production of a parenthesized left sub-expression followed by the operator in the root node followed by a recursively generated parenthesized right sub-expression. The traversal of the tree that produced this expression is called an inorder traversal and occurred by recursively traversing the left sub-tree followed by the root followed by the right sub-tree. Day 18 - 1 * + - a b c d Tree Traversal to Produce Infix Expressions Recursively produce the left sub-expression. Print out the root node. Recursively produce the right sub-expression.
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Specific Traversal Algorithms to Convert Expressions The following algorithms convert infix expressions to either prefix or postfix expressions. A preorder expression tree traversal generates a preorder expression if the
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day18 - COP 3503 Computer Science II CLASS NOTES DAY#18...

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