<p>Given a string <code>num</code> that contains only digits and an integer <code>target</code>, return <em><strong>all possibilities</strong> to insert the binary operators </em><code>&#39;+&#39;</code><em>, </em><code>&#39;-&#39;</code><em>, and/or </em><code>&#39;*&#39;</code><em> between the digits of </em><code>num</code><em> so that the resultant expression evaluates to the </em><code>target</code><em> value</em>.</p>

<p>Note that operands in the returned expressions <strong>should not</strong> contain leading zeros.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> num = &quot;123&quot;, target = 6
<strong>Output:</strong> [&quot;1*2*3&quot;,&quot;1+2+3&quot;]
<strong>Explanation:</strong> Both &quot;1*2*3&quot; and &quot;1+2+3&quot; evaluate to 6.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> num = &quot;232&quot;, target = 8
<strong>Output:</strong> [&quot;2*3+2&quot;,&quot;2+3*2&quot;]
<strong>Explanation:</strong> Both &quot;2*3+2&quot; and &quot;2+3*2&quot; evaluate to 8.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> num = &quot;3456237490&quot;, target = 9191
<strong>Output:</strong> []
<strong>Explanation:</strong> There are no expressions that can be created from &quot;3456237490&quot; to evaluate to 9191.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= num.length &lt;= 10</code></li>
	<li><code>num</code> consists of only digits.</li>
	<li><code>-2<sup>31</sup> &lt;= target &lt;= 2<sup>31</sup> - 1</code></li>
</ul>

from typing import List

class Solution:
    def addOperators(self, num: str, target: int) -> List[str]:
        def calculate_expression(exp):
            i = 0 
            stack = []
            operation = "+"
            number = 0 

            while i < len(exp):
                char = exp[i]
                if char.isdigit():
                    number = number * 10 + int(char)
                else:
                    if operation == "+":
                        stack.append(number)
                    elif operation == "-":
                        stack.append(-number)
                    else:
                        num2 = stack.pop()
                        stack.append(number * num2)
                    
                    number = 0 
                    operation = char 
                
                i += 1 
            
            return sum(stack)
        
        expressions = []
        n = len(num)
        m = 2 * n - 1
        options = ["+", "-", "*", " "]
        def gen(i, temp):
            if i == m:
                result = []
                for char in temp:
                    if char != " ":
                        result.append(char)

                result = "".join(result)
                expressions.append(result)

                return 
            
            for option in options:
                original_option = temp[i]
                temp[i] = option 
                gen(i + 2, temp)
                temp[i] = original_option
        
        def validate(exp):
            number = ""
            for char in exp:
                if char.isdigit():
                    number += char 
                else:
                    if len(number) >= 2 and number[0] == "0":
                        return False 
                    
                    number = ""
            
            if len(number) >= 2 and number[0] == "0":
                return False 

            return True 
            
        temp = [0 for _ in range(m)]
        for i, digit in enumerate(num):
            temp[i * 2] = digit 
        
        gen(1, temp)

        answer = []
        for exp in expressions:
            if not validate(exp):
                continue 

            result = calculate_expression(exp + "+")
            if result == target:
                answer.append(exp)
        
        return answer
        

if __name__ == '__main__':
    sol = Solution()
    num = "232"
    target = 46
    result = sol.addOperators(num, target)
    print(result)

118900