<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:
    
    // recursion
    
    vector<string> res;
    
    void dfs(string num, int target, int ind, string path, long prev, long cur) {
        if(ind == num.size() && cur + prev == target) {
            res.push_back(path);
        }
        
        for(int i=1; ind+i<=num.size(); i++) {
            string s = num.substr(ind, i);
            long n = stol(s);
            if (to_string(n).size() != s.size()) return;
            if(ind == 0) {
                dfs(num, target, i, path+s, 0, n);
            } else {
                dfs(num, target, ind+i, path + "+" + s, prev+cur, n);
                dfs(num, target, ind+i, path + "-" + s, prev+cur, -n);
                dfs(num, target, ind+i, path + "*" + s, prev, cur*n);
            }
        }
    }
        
        
    vector<string> addOperators(string num, int target) {
        dfs(num, target, 0, "", 0, 0);
        return res;
    }
};
68128