Added postfix_to_infix_conversion.py (#10607)

* Added postfix_to_infix_conversion.py

* Added wikipedia link in postfix_to_infix_conversion.py

* updating DIRECTORY.md

---------

Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: cclauss <cclauss@users.noreply.github.com>

Author: bhorsujal

DIRECTORY.md

@@ -385,6 +385,7 @@
     * [Lexicographical Numbers](data_structures/stacks/lexicographical_numbers.py)
     * [Next Greater Element](data_structures/stacks/next_greater_element.py)
     * [Postfix Evaluation](data_structures/stacks/postfix_evaluation.py)
+    * [Postfix To Infix Conversion](data_structures/stacks/postfix_to_infix_conversion.py)
     * [Prefix Evaluation](data_structures/stacks/prefix_evaluation.py)
     * [Stack](data_structures/stacks/stack.py)
     * [Stack Tracking Min Max](data_structures/stacks/stack_tracking_min_max.py)

data_structures/stacks/postfix_to_infix_conversion.py

@@ -0,0 +1,63 @@
+"""
+https://math.oxford.emory.edu/site/cs171/postfixExpressions/
+https://en.wikipedia.org/wiki/Shunting_yard_algorithm
+"""
+
+
+def postfix_to_infix(postfix_expression: str) -> str:
+    """
+    Returns the infix expression for the given postfix expression as an argument
+    >>> postfix_to_infix("")
+    Traceback (most recent call last):
+        ...
+    ValueError: Invalid postfix expression.
+    >>> postfix_to_infix("123+*4+")
+    '((1*(2+3))+4)'
+    >>> postfix_to_infix("abc*+de*f+g*+")
+    '((a+(b*c))+(((d*e)+f)*g))'
+    >>> postfix_to_infix("xy^5z*/2+")
+    '(((x^y)/(5*z))+2)'
+    >>> postfix_to_infix("232^^")
+    '(2^(3^2))'
+    >>> postfix_to_infix("32+")
+    '(3+2)'
+    """
+
+    # Check for invalid input.
+    if postfix_expression is None or postfix_expression == "":
+        raise ValueError("Invalid postfix expression.")
+
+    # Create a stack to store the operands and operators.
+    stack = []
+
+    # Iterate over the postfix expression.
+    for item in postfix_expression:
+        # If the item is an operand, push it onto the stack.
+        if item not in ["+", "-", "*", "/", "^"]:
+            stack.append(item)
+        else:
+            # If the item is an operator, pop the top two operands from the stack
+            # and concatenate the operator between them.
+            operand_2 = stack.pop()
+            operand_1 = stack.pop()
+            infix_expression = "(" + operand_1 + item + operand_2 + ")"
+
+            # Push the resulting infix expression onto the stack.
+            stack.append(infix_expression)
+
+    # The top element of the stack is the final infix expression.
+    return stack.pop()
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()
+    # Enter the posfix expression with no whitespaces.
+    postfix_expression = "512+4*+3-"
+
+    try:
+        infix_expression = postfix_to_infix(postfix_expression)
+        print("Infix expression: " + infix_expression)
+    except ValueError as e:
+        print(e)