<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 {
        typedef long long int i64;
        
        string myS;
        const char* s;
        i64 target;
        int slen;
        
    public:
      
        vector<string> addOperators(const string& num, int t) {
            myS = num;
            slen = myS.size();
            s = myS.c_str();
            target = t;
            
            vector<string> res;
            char buf[slen*2+1];
            
            int lmax = (s[0] == '0' ? 1 : slen);
            i64 v = 0;
            for (int l=1; l<=lmax; ++l) {
                int c = s[l-1];
                v = v*10 + (c-'0');
                buf[l-1] = c;
                processTail(0, v, l, buf, l, res);
            }
            return res;
        }
    
        void processTail(i64 prevsum, i64 last, int pos, char* buf, int bufpos, vector<string>& res) {
            if (pos == slen) {
                if (prevsum+last == target) {
                    buf[bufpos] = 0;
                    res.push_back(buf);
                }
                return;
            }
            
            int lmax = (s[pos] == '0' ? 1 : slen-pos);
            i64 v = 0;
            for (int l=1; l<=lmax; ++l) {
                int c = s[pos+l-1];
                v = v*10 + (c-'0');
    
                buf[bufpos] = '+';
                buf[bufpos+l] = c;
                processTail(prevsum+last, v, pos+l, buf, bufpos+l+1, res);
    
                buf[bufpos] = '-'; 
                processTail(prevsum+last, -v, pos+l, buf, bufpos+l+1, res);
    
                buf[bufpos] = '*'; 
                processTail(prevsum, last*v, pos+l, buf, bufpos+l+1, res);
            }
        }
    };
14896