<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 generate_exprs(num):
            num_len = len(num)
            splits = []
            for enc in range(4 ** (num_len - 1)):
                split = [0]
                for _ in range(num_len - 1):
                    split.append(enc % 4)
                    enc //= 4
                splits.append(split)
            enc_to_op = dict(zip(range(4), ['', '+', '-', '*']))
            exprs = []
            for split in splits:
                expr = ''
                valid_expr = True
                for idx in range(num_len):
                    op = enc_to_op[split[idx]]
                    expr += op
                    if (op != '' or idx == 0) and num[idx] == '0' and idx != num_len - 1 and split[idx + 1] == 0:
                        valid_expr = False
                        break
                    expr += num[idx]
                if valid_expr:
                    exprs.append(expr)
            return exprs

        exprs = generate_exprs(num)

        def eval_expr(expr):
            items = []
            prev_idx = 0
            expr_len = len(expr)
            for idx in range(expr_len):
                if expr[idx] in '+-*':
                    items.append(int(expr[prev_idx: idx]))
                    items.append(expr[idx])
                    prev_idx = idx + 1
            items.append(int(expr[prev_idx:]))
            items_after_mul = [items[0]]
            num_items = len(items)
            for idx in range(1, num_items, 2):
                if items[idx] == '*':
                    items_after_mul[-1] *= items[idx + 1]
                else:
                    items_after_mul.extend(items[idx: idx + 2])
            val = items_after_mul[0]
            num_items_after_mul = len(items_after_mul)
            for idx in range(1, num_items_after_mul, 2):
                if items_after_mul[idx] == '+':
                    val += items_after_mul[idx + 1]
                else:
                    val -= items_after_mul[idx + 1]
            return val

        return [expr for expr in exprs if eval_expr(expr) == target]
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