<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:
    void helper(vector<string>& res, const string& num, string expr, int pos, long prevOperand, long currentValue, int target) {
        if (pos == num.size()) {
            if (currentValue == target) {
                res.push_back(expr);
            }
            return;
        }
        for (int i = pos; i < num.size(); ++i) {
            // Avoid numbers with leading zeros
            if (i != pos && num[pos] == '0') {
                break;
            }
            string currStr = num.substr(pos, i - pos + 1);
            long currOperand = stol(currStr);
            if (pos == 0) {
                // First number, pick it without any operator
                helper(res, num, expr + currStr, i + 1, currOperand, currOperand, target);
            } else {
                // Addition
                helper(res, num, expr + '+' + currStr, i + 1, currOperand, currentValue + currOperand, target);
                // Subtraction
                helper(res, num, expr + '-' + currStr, i + 1, -currOperand, currentValue - currOperand, target);
                // Multiplication
                helper(res, num, expr + '*' + currStr, i + 1, prevOperand * currOperand,
                       currentValue - prevOperand + prevOperand * currOperand, target);
            }
        }
    }

    vector<string> addOperators(string num, int target) {
        vector<string> res;
        if (num.empty()) {
            return res;
        }
        helper(res, num, "", 0, 0, 0, target);
        return res;
    }
};
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