<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 {
public:

  string join(vector<string>& vs) {
    string res = "";
    for (int i = 1; i < vs.size(); i++) res += vs[i];
    return res;
  }

  void recurse(string& num, int index, int target, vector<string>& curr, long long value, long long currOperand, long long lastOperand, vector<string>& result) {
    if (index >= num.size()) {
      if (value == target && currOperand == 0) {
        result.push_back(join(curr));
      }
      return;
    }

    currOperand = currOperand * 10 + num[index] - '0';
    string currStr = to_string(currOperand);

    // Move forward
    if (currOperand > 0) {
      recurse(num, index + 1, target, curr, value, currOperand, lastOperand, result);
    }

    // Add a plus
    curr.push_back("+");
    curr.push_back(currStr);
    recurse(num, index + 1, target, curr, value + currOperand, 0, currOperand, result);
    curr.pop_back();
    curr.pop_back();

    if (curr.size() > 0) {
      curr.push_back("-");
      curr.push_back(currStr);
      recurse(num, index + 1, target, curr, value - currOperand, 0, -currOperand, result);
      curr.pop_back();
      curr.pop_back();

      curr.push_back("*");
      curr.push_back(currStr);
      recurse(num, index + 1, target, curr, value - lastOperand + currOperand * lastOperand, 0, currOperand * lastOperand, result);
      curr.pop_back();
      curr.pop_back();
    }
  }

  vector<string> addOperators(string num, int target) {
    vector<string> result;
    vector<string> curr;

    recurse(num, 0, target, curr, 0, 0, 0, result);

    return result;
  }
};
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