<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>

import operator 

class Solution:
    def addOperators(self, num: str, target: int) -> List[str]:
        expressions = []

        def generate_exp(nums: List[str], path: List[str]):
            if not nums:
                expressions.append("".join(path))
                return

            else:  
                for i in range(1, len(nums)+1):
                    next_num = nums[0:i]
                    if i == len(nums):
                        path.append(next_num)
                        generate_exp(nums[i:], path)
                        path.pop(-1)
                        
                    else:
                        for op in ['+', '-', '*']:
                            path.append(next_num)
                            path.append(op)
                            generate_exp(nums[i:], path)
                            path.pop(-1)
                            path.pop(-1)
        
        generate_exp(num, [])
        def infix(expression: str) -> str:
            stack = []
            infix = []
            i = 0
            prec = {'+': 1, '-': 1, '*': 2}
            while i < len(expression):
                if expression[i].isnumeric():
                    k = i
                    while k < len(expression) and expression[k].isnumeric():
                        k += 1
                    infix.append(expression[i:k])
                    i = k
                else:
                    if not stack or expression[i] == '*':
                        stack.append(expression[i])
                    else:
                        while stack:
                            infix.append(stack.pop(-1))
                        stack.append(expression[i])
                    i += 1
            while stack:
                infix.append(stack.pop(-1))
            return infix
        
        def evaluate(exp: list[str]) -> int:
            stack = []
            ops = {'*': operator.mul, '-': operator.sub, '+':operator.add}
            for x in exp:
                if x in ops:
                    v2 = stack.pop(-1)
                    v1 = stack.pop(-1)
                    stack.append(ops[x](v1, v2))
                else:
                    if x[0] == '0' and len(x) > 1:
                        return float('inf')
                    stack.append(int(x))
            return stack[-1]

        return [
            x for x in expressions if evaluate(infix(x)) == target
        ]





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