<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) {
        vector<string> ans;
        long long dig = 0;
        for (int i = 0; i < num.size(); i++) {
            dig = dig * 10 + num[i]-'0';
            addOpHelper(num, i+1, dig, to_string(dig), target, ans, dig, 1);
            if (num[0] == '0') break;
        }
        return ans;
    }
    
    void addOpHelper(string &num, int pos, long long cur, string val, int target, vector<string> &ans, long long contMul, bool sym) {
        if (pos == num.length()) {
            if (cur == target) {
                ans.push_back(val);
            }
            return;
        }
        long long digit = 0;
        for (int i = pos; i < num.length(); i++) {
            digit = digit * 10 + (num[i]-'0');
            long long nex = cur + (sym?(contMul * digit - contMul):(contMul-contMul*digit));
            addOpHelper(num, i+1, nex, val+"*"+to_string(digit), target, ans, contMul * digit, sym);
            nex = cur + digit;
            addOpHelper(num, i+1, nex, val+"+"+to_string(digit), target, ans, digit, 1);
            nex = cur - digit;
            addOpHelper(num, i+1, nex, val+"-"+to_string(digit), target, ans, digit, 0);
            if (num[pos] == '0') break;
        }
    }
};
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