<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 {
    string s;
    int target;
    vector<string>res;

    void helper(int idx = 0, long long score = 0, string curr = "", long long prev_num = -1) {
        if (idx == s.length()) {
            if (score == target) res.push_back(curr);
            return;
        }
        long long num = 0;
        for (int i=idx; i<s.length(); i++) {
            if (i > idx && s[idx] == '0')   break;
            num = num*10 + (s[i] - '0');
            if (idx == 0)   helper(i+1, score + num, to_string(num), num);
            else {
                helper(i+1, score + num, curr + "+" + to_string(num), num);
                helper(i+1, score - num, curr + "-" + to_string(num), -num);
                helper(i+1, score - prev_num + num*prev_num, curr + "*" + to_string(num), num*prev_num);
            }
        }
    }

public:
    vector<string> addOperators(string num, int target) {
        this->s = num;
        this->target = target;
        helper();
        return res;
    }
};
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