<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 calculate(self, s: str) -> int:
        def parse_number(i):
            res = 0
            while i < len(s) and s[i].isnumeric():
                res *= 10
                res += int(s[i])
                i += 1
            return i, res

        def compute(x, y, op):
            if op == "*":
                return x * y
            elif op == "/":
                return int(x / y)
    
        i = 0
        prev_op = "+"
        stack = []
        while i < len(s):
            if s[i].isnumeric():
                i, val = parse_number(i)
        
                if prev_op == "+":
                    stack.append(val)
                elif prev_op == "-":
                    stack.append(-val)
                else: # * or /
                    stack[-1] = compute(stack[-1], val, prev_op)
        
            elif s[i] in {"+", "-", "*", "/"}:
                prev_op = s[i]
                i += 1
            else:
                i += 1
        
        return sum(stack)

    def addOperators(self, num: str, target: int) -> List[str]:
        """
        at each index, we can add +, -, *, or nothing to space;

        * has precedence... how do we do this recursively...
        
        - just enumerate every possibility and calculate it once we
            reach the end of a recursion?
        """

        res = []
        acc = [num[0]]
        def recurse(idx, can_append_op, first_in_group):
            if idx == len(num):
                val = self.calculate("".join(acc))
                if val == target:
                    res.append("".join(acc))
                return

            if can_append_op:
                for op in ["+", "-", "*"]:
                    acc.append(op)
                    recurse(idx, False, None)
                    acc.pop()

            if first_in_group != "0":
                # skip
                acc.append(num[idx])
                recurse(idx+1, True, first_in_group or num[idx])
                acc.pop()

        recurse(1, True, num[0])
        return res
16800