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84 lines
2.6 KiB
Python
84 lines
2.6 KiB
Python
"""
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Author: Alexander Joslin
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GitHub: github.com/echoaj
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Explanation: https://medium.com/@haleesammar/implemented-in-js-dijkstras-2-stack-
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algorithm-for-evaluating-mathematical-expressions-fc0837dae1ea
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We can use Dijkstra's two stack algorithm to solve an equation
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such as: (5 + ((4 * 2) * (2 + 3)))
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THESE ARE THE ALGORITHM'S RULES:
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RULE 1: Scan the expression from left to right. When an operand is encountered,
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push it onto the operand stack.
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RULE 2: When an operator is encountered in the expression,
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push it onto the operator stack.
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RULE 3: When a left parenthesis is encountered in the expression, ignore it.
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RULE 4: When a right parenthesis is encountered in the expression,
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pop an operator off the operator stack. The two operands it must
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operate on must be the last two operands pushed onto the operand stack.
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We therefore pop the operand stack twice, perform the operation,
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and push the result back onto the operand stack so it will be available
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for use as an operand of the next operator popped off the operator stack.
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RULE 5: When the entire infix expression has been scanned, the value left on
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the operand stack represents the value of the expression.
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NOTE: It only works with whole numbers.
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"""
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__author__ = "Alexander Joslin"
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import operator as op
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from .stack import Stack
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def dijkstras_two_stack_algorithm(equation: str) -> int:
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"""
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DocTests
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>>> dijkstras_two_stack_algorithm("(5 + 3)")
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8
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>>> dijkstras_two_stack_algorithm("((9 - (2 + 9)) + (8 - 1))")
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5
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>>> dijkstras_two_stack_algorithm("((((3 - 2) - (2 + 3)) + (2 - 4)) + 3)")
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-3
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:param equation: a string
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:return: result: an integer
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"""
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operators = {"*": op.mul, "/": op.truediv, "+": op.add, "-": op.sub}
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operand_stack: Stack[int] = Stack()
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operator_stack: Stack[str] = Stack()
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for i in equation:
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if i.isdigit():
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# RULE 1
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operand_stack.push(int(i))
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elif i in operators:
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# RULE 2
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operator_stack.push(i)
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elif i == ")":
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# RULE 4
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opr = operator_stack.peek()
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operator_stack.pop()
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num1 = operand_stack.peek()
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operand_stack.pop()
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num2 = operand_stack.peek()
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operand_stack.pop()
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total = operators[opr](num2, num1)
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operand_stack.push(total)
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# RULE 5
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return operand_stack.peek()
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if __name__ == "__main__":
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equation = "(5 + ((4 * 2) * (2 + 3)))"
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# answer = 45
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print(f"{equation} = {dijkstras_two_stack_algorithm(equation)}")
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