fixes #8673; Add operator's associativity check for stacks/infix_to_p… (#8674)

* fixes #8673; Add operator's associativity check for stacks/infix_to_postfix_conversion.py

* fix ruff N806 in stacks/infix_to_postfix_conversion.py

* Update data_structures/stacks/infix_to_postfix_conversion.py

Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>

* Update data_structures/stacks/infix_to_postfix_conversion.py

Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>

---------

Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>

Author: amirsoroush

data_structures/stacks/infix_to_postfix_conversion.py

@@ -4,17 +4,42 @@
 https://en.wikipedia.org/wiki/Shunting-yard_algorithm
 """
 
+from typing import Literal
+
 from .balanced_parentheses import balanced_parentheses
 from .stack import Stack
 
+PRECEDENCES: dict[str, int] = {
+    "+": 1,
+    "-": 1,
+    "*": 2,
+    "/": 2,
+    "^": 3,
+}
+ASSOCIATIVITIES: dict[str, Literal["LR", "RL"]] = {
+    "+": "LR",
+    "-": "LR",
+    "*": "LR",
+    "/": "LR",
+    "^": "RL",
+}
+
 
 def precedence(char: str) -> int:
     """
     Return integer value representing an operator's precedence, or
     order of operation.
     https://en.wikipedia.org/wiki/Order_of_operations
     """
-    return {"+": 1, "-": 1, "*": 2, "/": 2, "^": 3}.get(char, -1)
+    return PRECEDENCES.get(char, -1)
+
+
+def associativity(char: str) -> Literal["LR", "RL"]:
+    """
+    Return the associativity of the operator `char`.
+    https://en.wikipedia.org/wiki/Operator_associativity
+    """
+    return ASSOCIATIVITIES[char]
 
 
 def infix_to_postfix(expression_str: str) -> str:
@@ -35,6 +60,8 @@ def infix_to_postfix(expression_str: str) -> str:
     'a b c * + d e * f + g * +'
     >>> infix_to_postfix("x^y/(5*z)+2")
     'x y ^ 5 z * / 2 +'
+    >>> infix_to_postfix("2^3^2")
+    '2 3 2 ^ ^'
     """
     if not balanced_parentheses(expression_str):
         raise ValueError("Mismatched parentheses")
@@ -50,9 +77,26 @@ def infix_to_postfix(expression_str: str) -> str:
                 postfix.append(stack.pop())
             stack.pop()
         else:
-            while not stack.is_empty() and precedence(char) <= precedence(stack.peek()):
+            while True:
+                if stack.is_empty():
+                    stack.push(char)
+                    break
+
+                char_precedence = precedence(char)
+                tos_precedence = precedence(stack.peek())
+
+                if char_precedence > tos_precedence:
+                    stack.push(char)
+                    break
+                if char_precedence < tos_precedence:
+                    postfix.append(stack.pop())
+                    continue
+                # Precedences are equal
+                if associativity(char) == "RL":
+                    stack.push(char)
+                    break
                 postfix.append(stack.pop())
-            stack.push(char)
+
     while not stack.is_empty():
         postfix.append(stack.pop())
     return " ".join(postfix)