<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> res;
        if (num.empty()) return res;

        for (int i = 1; i <= num.size(); i++) {
            string s = num.substr(0, i);
            long cur = stol(s);
            if (to_string(cur).size() != s.size()) continue;
            dfs(res, num, target, s, i, cur, cur); 
        }

        return res;
    }

private:
    void dfs(vector<string>& res, const string& num,
            const int target, string cur, int pos,
            const long cv, const long pv) { // current value, previous value
        if (pos == num.size()) {
            if (cv == target) {
                res.push_back(cur);
            }
            return;
        }

        for (int i = pos + 1; i <= num.size(); i++) {
            string t = num.substr(pos, i - pos);
            long now = stol(t);
            if (to_string(now).size() != t.size()) continue;

            dfs(res, num, target, cur + '+' + t, i, cv + now, now);
            dfs(res, num, target, cur + '-' + t, i, cv - now, -now);
            dfs(res, num, target, cur + '*' + t, i, cv - pv + pv * now, pv * now);
        }
    }
};

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