<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 {

    void help(string num, int target, int i, long sum, string temp, vector<string> &ans, long prevNo){
        if(i == num.size()){
            if(sum == target){
                ans.push_back(temp);
                return;
            }
        }
        for(int j = i; j<num.size(); j++){
            string no = num.substr(i, j-i+1);
            long number = stol(no);
            if(j > i && num[i] == '0') break;
            if(i == 0) help(num, target, j+1, number, no, ans, number);

            else {
                help(num, target, j+1, sum + number, temp +"+"+ no, ans, number);
                help(num, target, j+1, sum - number, temp + "-" + no, ans, -1*number);
                help(num, target, j+1, (sum - prevNo) + (prevNo*number), temp + "*" + no, ans, prevNo*number);
            }
        }
    }
public:
    vector<string> addOperators(string num, int target) {
        vector<string> ans;
        string temp = "";
        help(num, target, 0, 0, temp, ans, 0);
        return ans;
        // string, target, index, sumtillnow, temp, ans, prevNo
    }
};
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