<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:
    def addOperators(self, num: str, target: int) -> List[str]:
        def eval_expr(expr: str):
            s = ''
            m = 1
            part_expr = ''
            for c in expr:
                if c.isdigit(): 
                    s += c
                elif c == '+':
                    part_expr = part_expr + str(int(s)*m) + '+'
                    s = ''
                    m = 1
                elif c == '-': 
                    part_expr = part_expr + str(int(s)*m) + '-'                    
                    s = ''
                    m = 1
                elif c == '*':
                    m = m * int(s)
                    s = ''
                    
            if s: part_expr = part_expr + str(int(s)*m)
            
            i = 0
            v = 0
            s = ''
            last_sign = ''
            for i in range(len(part_expr)+1):
                if i < len(part_expr) and part_expr[i].isdigit(): 
                    s += part_expr[i]
                else: 
                    if not last_sign: 
                        v = int(s)
                        s = ''
                    elif last_sign == '+':
                        v += int(s)
                        s = ''
                    else:
                        v -= int(s)
                        s = ''
                    if i < len(part_expr):
                        last_sign = part_expr[i]
            return v
        
        def validate(expr):
            prev = ''
            check = False
            cnt = 0
            for v in expr:
                if not prev.isdigit():
                    if v == '0': check = True
                    else: 
                        check = False
                        cnt = 0
                if v.isdigit() and check: cnt += 1
                else:
                    check = False
                    cnt = 0
                if cnt == 2: return False
                prev = v
            return True
        
        def find_expressions(available):
            if not available: return ''
            if len(available) == 1: return available[0]
            exps = []
            c = available.pop()
            for expr in find_expressions(available):
                exps.append(expr + c)
                exps.append(expr + '+' + c)
                exps.append(expr + '-' + c)
                exps.append(expr + '*' + c)
            return exps

        ret = []
        available = list(num)
        for expr in find_expressions(available):
            if eval_expr(expr) == target and validate(expr): ret.append(expr)

        return ret

43900