What are the step to create a binary expression tree from the given infix expression ? Also, create the binary expression tree for the expression A+B*C

To create a binary expression tree from an infix expression, you can follow these steps:

1. Tokenization: Break the infix expression into individual tokens (operands, operators, parentheses, etc.).
2. Conversion to Postfix: Convert the infix expression into its equivalent postfix notation using the shunting-yard algorithm or a similar method. This step ensures that the expression’s operator precedence is maintained.
3. Construction of Expression Tree: Use the postfix expression to construct the binary expression tree recursively.
   • Start with an empty stack.
   • Iterate through each token in the postfix expression.
   • If the token is an operand, create a leaf node for it and push it onto the stack.
   • If the token is an operator, pop the top two nodes from the stack, create a new node with the operator as the root, and make the popped nodes its children. Push this new node onto the stack.
   • Repeat until all tokens are processed.
   • The final node remaining on the stack will be the root of the binary expression tree.

Now, let’s create the binary expression tree for the expression A+B*C:

1. Infix expression: A+B*C
2. Convert to postfix: ABC*+
3. Construct expression tree:
   • Start with an empty stack.
   • Process each token from left to right.
   • When encountering operands, push them onto the stack.
   • When encountering operators:
     • Pop the top two operands from the stack.
     • Create a new node with the operator as the root, and make the popped operands its left and right children.
     • Push this new node onto the stack.
   • At the end, the root of the tree will be the only element left in the stack.

   Steps:

   • Token: A Stack: A
   • Token: B Stack: A, B
   • Token: C Stack: A, B, C
   • Token: * Pop: C, B Create: * with left child B and right child C Stack: A, (B * C)
   • Token: + Pop: (B * C), A Create: + with left child A and right child (B * C) Stack: (A + (B * C))

The final binary expression tree for the expression A+B*C: