<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]:
        output = []

        stack = [(0,0,0,'')] # (idx, currNum,prevnum, curr exp)

        cache = defaultdict(str)

        while stack:
            i,curr,prev,exp = stack.pop()

            if (i, curr, prev, exp) in cache:
                continue  

            if i==len(num): 
                if curr==target:
                    output.append(exp)
                continue
            j=i
            while j < len(num) and (j <= i or num[i] != '0'):
                n = int(num[i:j+1])
                stNum = str(n)
                if i==0:
                    stack.append((j+1, curr + n, n,  exp + stNum))
                else:
                    stack.append((j+1, curr + n, n, exp + '+' + stNum))
                    stack.append((j+1, curr- n, -n, exp + '-' + stNum))
                    stack.append((j+1, curr-prev + prev * n, prev * n, exp + '*' + stNum))
                cache[(i, curr, prev, exp)] = True  
                j+=1
                
        return output


        # @cache
        # def backtrack(i,path,curr,prev):
        #     if i == len(num):
        #         if curr==target:
        #             output.append(path)
        #         return

        #     for j in range(i, len(num)):
        #         if j > i and num[i]=='0':
        #             break
                
        #         n = int(num[i:j+1])
        #         if i == 0:
        #             backtrack(j+1, path + str(n), curr+n, n)
        #         else:
        #             backtrack(j+1,path+'+'+str(n), curr+n, n)
        #             backtrack(j+1,path+'-'+str(n), curr-n, -n)
        #             backtrack(j+1,path+'*'+str(n), curr-prev + prev*n, prev*n)



        # backtrack(0,'',0,0)
        # return output
43200