<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> ans;

     void helper(string s, int target,int i, const  string  path, long eval, long residual) {
        // bc
        if(i==s.length()){
            if(eval==target){
                ans.push_back(path);
                return;
            }
        } 
        string currStr;
        long num=0;
        // backtracking loop
        for(int j=i;j<s.length();j++){
            // handle 0
            if(j>i && s[i]=='0') return;
            currStr+= s[j]; 
            num= num*10 + s[j]- '0';
            if(i==0){
                helper(s,target, j+1,path+ currStr,num, num);
            }
            else{
                helper(s,target,j+1,path + "+" + currStr, eval + num, num);
                helper(s,target,j+1,path + "-" + currStr, eval - num, -num);
                helper(s,target,j+1,path + "*" + currStr, eval -residual + residual*num , residual*num);


            }
        }
        
        
    }
    
    vector<string> addOperators(string s, int target) {
        string path="";
        helper(s,target, 0, path, 0, 0);
        return ans;
    }
   
};
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