<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>

class Solution:
    from collections import deque
    def addOperators(self, num: str, target: int) -> List[str]:
        def creation(arr): 
            if len(arr) == 1: 
                return arr
            st_1 = arr[0] + '+'
            st_2 = arr[0] + '-'
            st_3 = arr[0] + '*'
            st_4 = arr[0]
            ret_val = creation(arr[1:])
            final_vals = []
            for val in ret_val: 
                new_val_1 = st_1 + val
                new_val_2 = st_2 + val
                new_val_3 = st_3 + val
                new_val_4 = st_4 + val
                final_vals.append(new_val_1)
                final_vals.append(new_val_2)
                final_vals.append(new_val_3)
                final_vals.append(new_val_4)
            return final_vals

        def evaluation(s): #returns True if equals target
            #multiply first then do the rest
            #return 
            eval_stack = deque()
            s_point = 0
            e_point = 0
            while e_point < len(s): 
                while e_point < len(s) and s[e_point].isdigit(): 
                    e_point += 1
                letter = s[s_point:e_point]
                if len(letter) > 1 and letter[0] == '0':
                    return False
                if letter.isdigit() and len(eval_stack) > 1 and eval_stack[0] == '*': 
                    mult = eval_stack.popleft()
                    num = eval_stack.popleft()
                    eval_stack.appendleft(str(int(num)*int(letter)))
                else: 
                    eval_stack.appendleft(letter)
                if e_point < len(s): 
                    eval_stack.appendleft(s[e_point])

                s_point = e_point + 1
                e_point = e_point + 1

            #should be only additions and subtractions
            final_value = 0
            stick = 1
            while eval_stack: 
                curr = eval_stack.pop()
                if curr == '+': 
                    stick = 1
                if curr == '-': 
                    stick = -1
                
                if curr.isdigit(): 
                    final_value += stick*int(curr)
                    stick = 1
            
            return (final_value == target)    

        output = []
        possible_outputs = creation(num)

        for possible in possible_outputs: 
            if evaluation(possible): 
                output.append(possible)
        
        return output
        

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