<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:
    int target;
    string num;
    vector<string> addOperators(string num, int target) {
        vector<string> res;
        this->target = target;
        this->num = num;
        dfs(0, "", 0, 0, res);
        return res;
    }

    void dfs(int i, string path, long comp, int prevNum, vector<string>& res) {
        if (i == num.size() && comp == target) {
            res.push_back(path);
            return;
        }

        string numStr = "";
        long currNum = 0;
        for (int j = i ; j < num.size(); j++) {
            // ignore the rest j>i if the leading i-th digit is '0'.
            if (num[i] == '0' && j >i) break; 

            numStr.push_back(num[j]);
            currNum = currNum*10 + num[j] - '0';
            
            if (i==0) {
                dfs(j+1, numStr, currNum, currNum, res);
            } else {
                dfs(j+1, path+"+"+numStr, comp+currNum, currNum, res);
                dfs(j+1, path+"-"+numStr, comp-currNum, -currNum, res);
                dfs(j+1, path+"*"+numStr, comp-prevNum + (prevNum*currNum), prevNum*currNum, res);
            }
        }
    }
};


37859