<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:
    void solve(int ind, long long cur, string &num, int target, vector<string> &ans, string &temp, long long last) {
        if (ind == num.size()) {
            if (cur == target) {
                ans.push_back(temp);
            }
            return;
        }
        
        for (int i = ind; i < num.size(); ++i) {
            string str = num.substr(ind, i - ind + 1);
            long long val = stoll(str);
            
            if (to_string(val).size() != str.size()) break;
            
            if (ind == 0) {
                solve(i + 1, val, num, target, ans, str, val);
            } else {
                temp.push_back('+');
                temp.append(str);
                solve(i + 1, cur + val, num, target, ans, temp, val);
                temp.resize(temp.size() - str.size() - 1); 
                
                temp.push_back('-');
                temp.append(str);
                solve(i + 1, cur - val, num, target, ans, temp, -val);
                temp.resize(temp.size() - str.size() - 1);
                
                temp.push_back('*');
                temp.append(str);
                solve(i + 1, cur - last + last * val, num, target, ans, temp, last * val);
                temp.resize(temp.size() - str.size() - 1); 
            }
        }
    }
    
    vector<string> addOperators(string num, int target) {
        vector<string> ans;
        string temp;
        solve(0, 0, num, target, ans, temp, 0);
        return ans;
    }
};

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