<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]:
        res = []
        currPath = []
        def dfs(startIdx, currRes, prevNum):
            # Base case: we've reached the end of num
            if startIdx >= len(num):
                if currRes == target:
                    res.append("".join([str(i) for i in currPath]))

            for endIdx in range(startIdx, len(num)):
                # Can't start a new number with 0
                if endIdx != startIdx and num[startIdx] == "0":
                    break

                currNum = int(num[startIdx:endIdx + 1])
                print(startIdx, endIdx)
                if startIdx == 0:
                    currPath.append(currNum)
                    dfs(endIdx + 1, currNum, currNum)
                    currPath.pop()
                else:
                    currPath.append("+")
                    currPath.append(currNum)
                    dfs(endIdx + 1, currRes + currNum, currNum)
                    currPath.pop()
                    currPath.pop()

                    currPath.append("-")
                    currPath.append(currNum)
                    dfs(endIdx + 1, currRes - currNum, -1 * currNum)
                    currPath.pop()
                    currPath.pop()

                    currPath.append("*")
                    currPath.append(currNum)
                    dfs(endIdx + 1, currRes - prevNum + (prevNum * currNum), prevNum * currNum)
                    currPath.pop()
                    currPath.pop()

            return

        dfs(0, 0, 0)
        return res

        # 4^n different possibilities (+, -, *, noop)
        # Try inserting +, -, and * between every digit. Backtrack. Keep track of value/calculate once we reach the end

        # res = []
        # currStr = []
        # currRes = 0
        # # Inserting operator *after* currIdx
        # # TODO: do we need prevNum and currNum?
        # def dfs(currIdx, prevNum, currNum, prevOp):
        #     nonlocal currRes
        #     print(currRes)
        #     originalRes = currRes

        #     currDigit = int(num[currIdx])
        #     currStr.append(currDigit)

        #     # Case: Do not insert an operator
        #     if currIdx + 1 < len(num):
        #         dfs(currIdx + 1, prevNum, currNum * 10 + currDigit, prevOp)

        #     # Case: Insert an operator
        #     if prevOp == "+":
        #         currRes += prevNum
        #     elif prevOp == "-":
        #         currRes -= prevNum
        #     # "*"
        #     else:
        #         # 2-3*2
        #         currRes = currRes - prevNum + (prevNum * currNum)

        #     if currIdx + 1 < len(num):
        #         dfs(currIdx + 1, currNum, int(num[currIdx + 1]), "+")
        #         dfs(currIdx + 1, -1 * currNum, int(num[currIdx + 1]), "-")
        #         dfs(currIdx + 1, currNum, int(num[currIdx + 1]), "*")
        #     # Base case: we've reached the end of the string
        #     elif currRes == target:
        #         res.append("".join(currStr))

        #     currStr.pop()
        #     currRes = originalRes
        #     return

        # dfs(0, 0, int(num[0]), "+")
        # return res
17500