Final answer:
To create a binary expression tree for (7+(2-1))*8, we start with the root node as '*', build a left subtree for the expression (7+(2-1)) with '+' as the root, and have the right subtree be '8'. The binary expression tree represents the structure of the expression where operands are leaf nodes, and operators form internal nodes.
Step-by-step explanation:
To build a binary expression tree for the input (7+(2−1))∗8, we first need to understand the structure of binary expression trees. A binary expression tree is a specific kind of binary tree used to represent expressions. Each leaf node in the tree is an operand, such as a number, and each internal node is an operator that combines its child nodes, such as '+', '−' (minus), or '∗' (multiply).
The binary expression tree for the given expression (7+(2−1))∗8 is arranged as follows:
- The root node will have the last operator applied in the expression, which in this case is '∗' (multiply).
- The left subtree will represent the expression enclosed in the parentheses, (7+(2−1)), with '+' as the root of this subtree.
- The right subtree will be a single node tree with the operand '8', since it is only multiplied by the result of the left subtree.
The final expression tree looks like this, with each node containing either an operator ('+', '−', or '∗') or an operand (1, 2, 7, 8):
*
/ \
+ 8
/ \
7 -
/ \
2 1
The tree is created by continuing to break down each sub-expression in a similar binary structure until you reach the simplest elements of the expression (the operands).