<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 evaluate(self, arr):
        stack = []
        op = "+"
        num = 0
        nums = set(list('0123456789'))
        for idx, item in enumerate(arr):
            if len(item) > 1 or item in nums:
                num = int(item)
            if item in "+-*" or idx == len(arr) - 1:
                if op == '+':
                    stack.append(num)
                if op == '-':
                    stack.append(-num)
                if op == '*':
                    stack.append(stack.pop() * num)
                op = item
                num = 0
        res = 0
        while len(stack) > 0:
            res += stack.pop()
        return res

    def addOperators(self, num: str, target: int) -> List[str]:
        n = len(num)
        res = []
        def dfs(text, pos, buf, res):
            if pos == len(text):
                value = self.evaluate(buf)
                # print("evalute: {0} = {1}".format(buf, value))
                if target == value:
                    res.append([x for x in buf])
                return
            if buf[-1] != '0':
                buf[-1] = buf[-1] + text[pos]
                dfs(text, pos + 1, buf, res)
                buf[-1] = buf[-1][:-1]

            buf.append('-')
            buf.append(text[pos])
            dfs(text, pos + 1, buf, res)
            buf.pop()
            buf.pop()

            buf.append('+')
            buf.append(text[pos])
            dfs(text, pos + 1, buf, res)
            buf.pop()
            buf.pop()

            buf.append('*')
            buf.append(text[pos])
            dfs(text, pos + 1, buf, res)
            buf.pop()
            buf.pop()


        dfs(num, 1, [num[0]], res)
        res = [''.join(x) for x in res]
        return res
        
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