<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:
    vector<string> expressions;

    void generateExpressions(int index, int n, string path, string currentNumStr, long processedValue, long currentNum, string num, int target) {
        // Base case: All digits have been processed
        if (index == n) {
            // If the expression evaluates to the target, add it to the list
            if (processedValue + currentNum == target) {
                expressions.push_back(path + currentNumStr);
            }
            return;
        }

        for (int i = index; i < n; i++) {
            // Extract the current chunk of digits
            string chunkStr = num.substr(index, i - index + 1);
            long chunkValue = stol(chunkStr);

            // Check if the extracted chunk is a valid number (ex 1*05 = 5 cases).
            if (to_string(chunkValue) != chunkStr) {
                return;
            }

            if (index == 0) {
                // First number in the expression
                generateExpressions(i + 1, n, path, chunkStr, 0, chunkValue, num, target);
            } else {
                // Addition operation
                generateExpressions(i + 1, n, path + currentNumStr + "+", chunkStr, processedValue + currentNum, chunkValue, num, target);
                // Subtraction operation
                generateExpressions(i + 1, n, path + currentNumStr + "-", chunkStr, processedValue + currentNum, -chunkValue, num, target);
                // Multiplication operation
                generateExpressions(i + 1, n, path, currentNumStr + "*" + chunkStr, processedValue, currentNum * chunkValue, num, target);
            }
        }
    }

    vector<string> addOperators(string num, int target) {
        int n = num.size();
        generateExpressions(0, n, "", "", 0, 0, num, target);
        return expressions;
    }
};
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