<p>Given a string <code>s</code> which represents an expression, <em>evaluate this expression and return its value</em>.&nbsp;</p>

<p>The integer division should truncate toward zero.</p>

<p>You may assume that the given expression is always valid. All intermediate results will be in the range of <code>[-2<sup>31</sup>, 2<sup>31</sup> - 1]</code>.</p>

<p><strong>Note:</strong> You are not allowed to use any built-in function which evaluates strings as mathematical expressions, such as <code>eval()</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> s = "3+2*2"
<strong>Output:</strong> 7
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> s = " 3/2 "
<strong>Output:</strong> 1
</pre><p><strong class="example">Example 3:</strong></p>
<pre><strong>Input:</strong> s = " 3+5 / 2 "
<strong>Output:</strong> 5
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= s.length &lt;= 3 * 10<sup>5</sup></code></li>
	<li><code>s</code> consists of integers and operators <code>(&#39;+&#39;, &#39;-&#39;, &#39;*&#39;, &#39;/&#39;)</code> separated by some number of spaces.</li>
	<li><code>s</code> represents <strong>a valid expression</strong>.</li>
	<li>All the integers in the expression are non-negative integers in the range <code>[0, 2<sup>31</sup> - 1]</code>.</li>
	<li>The answer is <strong>guaranteed</strong> to fit in a <strong>32-bit integer</strong>.</li>
</ul>

class Solution:

    def infix_to_postfix(self, s:str) -> List[str]:
        priorities = {
            "+":0,
            "-":0,
            "*":1,
            "/":1
        }

        stack = []
        last_num = ""
        postfix = []

        for char in s:
            if not char.isdigit() and char not in priorities:
                continue
            
            if char.isdigit():
                last_num += char
            else:
                if last_num != "":
                    postfix.append(last_num)
                    last_num = ""
                
                if char in priorities:
                    while stack and priorities[stack[-1]] >= priorities[char]:
                        postfix.append(stack.pop())
                    stack.append(char)
        
        if last_num != "":
            postfix.append(last_num)
        
        while stack:
            postfix.append(stack.pop())

        return postfix

            

    def calculate(self, s: str) -> int:
        postfix = self.infix_to_postfix(s)
        print(postfix)
        stack = []
        for item in postfix:
            if item.isdigit():
                stack.append(int(item))
            else:
                num1, num2 = stack.pop(), stack.pop()
                if item == "+":
                    stack.append(num1 + num2)
                elif item == "-":
                    stack.append(num2 - num1)
                elif item == "*":
                    stack.append(num1*num2)
                else:
                    stack.append(int(num2/num1))
        
        return stack[0]
        
"""
We can solve this problem by first converting the string to postfix notation, then iterating through it and calculating it.

For example, we can evaluate 3 + 2 * 2 as 32+2*

then we can iterate through the string in postfix notation, simply popping 2 elements every time we see an operand

this appraoch takes O(N) time and O(N) space
"""
25100