<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> result;
        string expression;
        backtrack(num,target,0,0,0,expression,result);
        return result;
    }
private:
    void backtrack(const string& num,int target,int index,long long prev,long long current,string& expression,vector<string>& result){
        if(index==num.length()){
            if(current==target){
                result.push_back(expression);
            }
            return;
        }
        int start=expression.length();
        if(index>0){
            expression.push_back(0);
        }
        long long n=0;
        for(int i=index;i<num.length();i++){
            if(i!=index&& num[index]=='0') break;
            n=n*10+(num[i]-'0');
            expression.push_back(num[i]);

            if(index==0){
                backtrack(num,target,i+1,n,n,expression,result);
            } else{
                expression[start]='+';
                backtrack(num,target,i+1,n,current+n,expression,result);

                expression[start]='-';
                backtrack(num,target,i+1,-n,current-n,expression,result);

                expression[start]='*';
                backtrack(num,target,i+1,prev*n,(current-prev)+(prev*n),expression,result);
            }
        }
        expression.resize(start);
    }
};
13853