<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:


long long calc(string& s){
    long long ans = 0;
    long long ls = 1;
    long long nu = 0;
    for(int i=0; i<s.size(); i++){
        if(s[i]>='0' && s[i]<='9'){
            nu *= 10;
            nu += s[i] - '0';
        } else if (s[i] == '*') {
            ls *= nu;
            nu = 0;
        } else {
            ls *= nu;
            nu = 0;
            ans += ls;
            ls = s[i] == '-' ? -1 : 1;
        }
    }
    ans += nu*ls;
    return ans;
}

    vector<string> addOperators(string num, int target) {
        int n4 = 1;
        vector<string> ans;
        for(int i = 0 ; i+1<num.size(); i++) n4 <<= 2;
        for(int i=0; i< n4; i++){
            int r = i;
            string ss = string{num[0]};
            string  op;
            bool ok = true;
            int run = 1;
            for(int i=1; i<num.size(); i++){
                int tmp = r % 4;
                r /= 4;
                if(tmp==0) ss.push_back('-');
                else if(tmp==1) ss.push_back('+');
                else if(tmp==2) ss.push_back('*');
                if (tmp != 3) run = 0;
                if (ss.back() == '0' and run == 1) {
                    ok = false;
                    break;
                }
                ss.push_back(num[i]);
                run++;
            }
            if(ok and calc(ss)==target){
                ans.push_back(ss);
            }
        }
        return ans;
    }
};
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