<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> addOperators(string num, int target) {
        vector<string> exps;
        string exp = "";
        dfs(num, exps, exp, 0, 0, 0, target);
        return exps;
    }

private:
    void dfs(const string& num, vector<string>& exps, string& exp, int start, long prev_num, long res, int target) {
        if (start == num.length()) {
            if (res == target) {
                exps.push_back(exp);
            }
            return;
        }

        for (int i = start; i < num.length(); ++i) {
            if (num[start] == '0' && i > start) {
                break;
            }
            string new_num_s = num.substr(start, i - start + 1);
            long new_num = std::stol(new_num_s);
            if (start == 0) {
                exp = new_num_s;
                dfs(num, exps, exp, i + 1, new_num, new_num, target);
                exp = "";
            } else {
                int l = exp.length();
                exp += ("+" + new_num_s);
                dfs(num, exps, exp, i + 1, new_num, res + new_num, target);
                exp[l] = '-';
                dfs(num, exps, exp, i + 1, -1 * new_num, res - new_num, target);
                exp[l] = '*';
                dfs(num, exps, exp, i + 1, prev_num * new_num, res - prev_num + prev_num * new_num, target);
                exp = exp.substr(0, l);
            }
        }
    }
 


        


};
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