Created Dijkstra's Two Stack Algorithm

data_structures/stacks/dijkstras_two_stack_algorithm.py

@@ -0,0 +1,83 @@
+"""
+Author: Alexander Joslin
+GitHub: github.com/echoaj
+
+Explanation:  https://medium.com/@haleesammar/implemented-in-js-dijkstras-2-stack-
+              algorithm-for-evaluating-mathematical-expressions-fc0837dae1ea
+
+We can use Dijkstra's two stack algorithm to solve an equation
+such as: (5 + ((4 * 2) * (2 + 3)))
+
+THESE ARE THE ALGORITHM'S RULES:
+RULE 1: Scan the expression from left to right. When an operand is encountered,
+        push it onto the the operand stack.
+
+RULE 2: When an operator is encountered in the expression,
+        push it onto the operator stack.
+
+RULE 3: When a left parenthesis is encountered in the expression, ignore it.
+
+RULE 4: When a right parenthesis is encountered in the expression,
+        pop an operator off the operator stack.  The two operands it must
+        operate on must be the last two operands pushed onto the operand stack.
+        We therefore pop the operand stack twice, perform the operation,
+        and push the result back onto the operand stack so it will be available
+        for use as an operand of the next operator popped off the operator stack.
+
+RULE 5: When the entire infix expression has been scanned, the value left on
+        the operand stack represents the value of the expression.
+
+NOTE:   It only works with whole numbers.
+"""
+__author__ = "Alexander Joslin"
+
+from .stack import Stack
+
+import operator as op
+
+
+def dijkstras_two_stack_algorithm(equation: str) -> int:
+    """
+    DocTests
+    >>> dijkstras_two_stack_algorithm("(5 + 3)")
+    8
+    >>> dijkstras_two_stack_algorithm("((9 - (2 + 9)) + (8 - 1))")
+    5
+    >>> dijkstras_two_stack_algorithm("((((3 - 2) - (2 + 3)) + (2 - 4)) + 3)")
+    -3
+
+    :param equation: a string
+    :return: result: an integer
+    """
+    operators = {"*": op.mul, "/": op.truediv, "+": op.add, "-": op.sub}
+
+    operand_stack = Stack()
+    operator_stack = Stack()
+
+    for i in equation:
+        if i.isdigit():
+            # RULE 1
+            operand_stack.push(int(i))
+        elif i in operators:
+            # RULE 2
+            operator_stack.push(i)
+        elif i == ")":
+            # RULE 4
+            opr = operator_stack.peek()
+            operator_stack.pop()
+            num1 = operand_stack.peek()
+            operand_stack.pop()
+            num2 = operand_stack.peek()
+            operand_stack.pop()
+
+            total = operators[opr](num2, num1)
+            operand_stack.push(total)
+
+    # RULE 5
+    return operand_stack.peek()
+
+
+if __name__ == "__main__":
+    equation = "(5 + ((4 * 2) * (2 + 3)))"
+    # answer = 45
+    print(f"{equation} = {dijkstras_two_stack_algorithm(equation)}")