<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 {
    
private:
    int target;
    string num;
    void dfs(int pos, long last, long sum, string path, vector<string>& res){
        
        if (pos == num.size())
        {
            if (sum == target)
            {
                res.push_back(path);
            }
            
            return;
        }
        
        long curVal = 0;
        string cur = "";
        for(auto i = pos; i < num.size(); ++i)
        {
            curVal = curVal * 10 + num[i] - '0';
            cur += num[i];
            
            if (pos == 0)
            {
                dfs(i + 1, curVal, curVal, path + cur, res);
            }
            else
            {
                dfs(i + 1, curVal, sum + curVal , path + "+" + cur, res);
                dfs(i + 1, -curVal, sum - curVal , path + "-" + cur, res);
                dfs(i + 1, curVal * last, sum - last + curVal * last , path + "*" + cur, res);
            }
            
            if (num[pos] == '0') {
                break;
            }
        }
    }
public:
    vector<string> addOperators(string num, int target) {
        if (num.size() == 0)
        {
            return vector<string>();
        }
        
        this->target = target;
        this->num = num;
        
        vector<string> res;
        dfs(0, 0, 0, "", res);
        return res;
    }
};
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