<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) {
        // DFS
        // accumulated num, cur num
        vector<string> res;
        for(int i = 1; i <= num.size(); i++) {
            if (num[0] == '0' && i > 1) break;
            recur(res, 0, atol(num.substr(0, i).c_str()), target, num.substr(i), num.substr(0, i));
        }
        return res;
    }

    void recur(vector<string>& res, long resNum, long curNum, int target, string num, string cur) {
        if (num.size() == 0) {
            if (resNum + curNum == target) {
                res.push_back(cur);
                return ;
            }
        }

        for(int i = 1; i <= num.size(); i++) {
            if (num[0] == '0' && i > 1) break;
            // +
            long n = atol(num.substr(0, i).c_str());
            recur(res, resNum + curNum, n, target, num.substr(i), cur + "+" + num.substr(0, i));
            // -
            recur(res, resNum + curNum, -n, target, num.substr(i), cur + "-" + num.substr(0, i));
            // *
            recur(res, resNum, curNum*n, target, num.substr(i), cur + "*" + num.substr(0, i));
        }
    }
};
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