Implementation a simple symbolic equation solver.
The equation should be stored in a binary tree. An equation consists of operands and operators.
Each operand or operator should be stored as a tuple of the form (TYPE, VALUE). Examples are (OPERAND, 5), (OPERAND, 7), (OPERAND, 34), (OPERATOR, ‘+’) or (OPERATOR, '*’').
Following operators should be supported: addition (+), subtraction (-), multiplication (), and exponentiation (^). Grouping of terms in the equation using brackets should be supported. However, nested brackets need not be supported. For example, the expression “1 + (2 * 3) + 3 ^ 2” should be supported but the expression “1 + ((2 * 3) + 3) ^ 2” need not be supported. In addition, the expressions will have a maximum of only one operator inside the brackets. For example, you do not have to consider expressions such as “1 + (2 * 3 + 7) + 3 ^ 2” which contains two operators ‘’ and ‘+’ inside the brackets.
Evaluation of terms should be done left-to-right subjected to precedence given by brackets. (i.e. all the operators have equal precedence except the brackets). For example, the expression “1 + (2 * 3) + 3 ^ 2” will result in 100.
Explanation: Total = 1 Total = 1 + (23) = 7 (23 is evaluated first since they are within brackets) Total = 7 + 3 = 10 Total = 10 ^ 2 = 100
Note that these are not our usual arithmetic operations where we follow the BODMAS order.
Sample binary tree for the expression “1 + (2 * 3) + 3 ^ 2”
Expression: 1 + (2 * 3) + 3 ^ 2
Use the insert method to add nodes
Begin with forming the root node for the tree.
root = Node(('OPERAND', 1))
Form the rest of the tree by inserting data to the root node.
root = root.insert(('OPERATOR', '+'), False)
root = root.insert(('OPERAND', 2), False)
root = root.insert(('OPERATOR', '*'), True)
root = root.insert(('OPERAND', 3), False)
root = root.insert(('OPERATOR', '+'), False)
root = root.insert(('OPERAND', 3), False)
root = root.insert(('OPERATOR', '^'), False)
root = root.insert(('OPERAND', 2), False)
Get the output.
root.get_output()
Should print 100