<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]:
        n = len(num)
        dp = {}
        ops = {'+':lambda x,y:x+y,'-':lambda x,y:x-y,'*':lambda x,y:x*y}
        def helper(i):
            # All possible expressions for 0:i
            if i in dp:
                return dp[i]
            dp[i] = []
            for j in range(1,i):
                n1 = int(num[j:i])
                if num[j]=='0' and j<i-1:
                    continue
                temp = helper(j)
                if temp:
                    for a,op,b,exp in temp:
                        dp[i].append((op(a,b),ops['+'],n1,exp+"+"+num[j:i]))
                        dp[i].append((op(a,b),ops['-'],n1,exp+"-"+num[j:i]))
                        dp[i].append((a,op,ops['*'](b,n1),exp+"*"+num[j:i]))
            if num[0]!='0' or i==1:
                dp[i].append((0,ops['+'],int(num[:i]),num[:i]))
            return dp[i]
        temp = helper(n)
        out = []
        for a,op,b,exp in temp:
            if op(a,b)==target:
                out.append(exp)
        return out
96500