Final answer:
A binary tree for the expression (A+B)*D/E-F+G/(H-I) is built by creating subtrees for each operation following the order of precedence and combining these subtrees to form the complete expression tree.
Step-by-step explanation:
To make a binary tree of the expression (A+B)*D/E-F+G/(H-I), you need to understand the order of operations and how binary trees represent these operations. The binary tree displays the hierarchy of operations, with each node representing an operation and each child node representing an operand. Here, we follow the operator precedence, which typically is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
Steps to create the binary tree:
Identify the primary operation, which is the last operation you would perform according to the order of operations. In this case, it is the addition of the subtraction result and the division result, corresponding to -F and +G/(H-I).
Construct left and right subtrees. The left subtree represents (A+B)*D/E and the right subtree represents G/(H-I).
Continue breaking down the subtrees into smaller operations until only single operands (letters or numbers) remain.
The resulting binary tree would have the primary root node representing '+', with the left child being another subtree for (A+B)*D/E and the right child being the subtree for G/(H-I). Continue this process for the subtrees, respecting the order of operations, until all operations have been represented in the tree.
Create a subtree for the expression within the first set of parentheses, (A+B), with '+' as the root and A and B as leaf nodes. Create subtrees for each division operation: '*D' and '/E' respectively, and link them to the root of (A+B) subtree.
Create a subtree for the second set of parentheses, (H-I), with '-' as the root and H and I as leaf nodes, followed by the division node '/' with G as the other leaf node.
Combine the subtrees with a root '+' node, adding in the remaining '-' operation, linked to 'F'. With each step, the expression's binary tree becomes more complete until we end with a single tree that represents the full expression.