<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 {
private:
    string toStr(vector<string> expr) {
        string out = "";
        for (int i = 0; i < expr.size(); i++) {
            out += expr[i]; 
        }
        return out;
    }

    void calculate(string& num, int start, int target, long curr, long prevTerm, vector<string>& expr, vector<string>& result) {
        if (start >= num.length()) {
            if (curr == target)
                result.push_back(toStr(expr));
            return;
        }

        for (int end = start + 1; end <= num.length(); end++) {
            string nextTermStr = num.substr(start, end - start);
            long nextTerm = stol(nextTermStr);
            
            // cout << nextTerm << endl;

            // Already evaluated
            if (end > start + 1 && num[start] == '0')
                break;

            if (start == 0) {
                expr.push_back(nextTermStr);
                calculate(num, end, target, nextTerm, nextTerm, expr, result);
                expr.pop_back();
                continue;
            }

            expr.push_back("+");
            expr.push_back(nextTermStr);
            calculate(num, end, target, curr + nextTerm, nextTerm, expr, result);
            expr.pop_back();
            expr.pop_back();

            expr.push_back("-");
            expr.push_back(nextTermStr);
            calculate(num, end, target, curr - nextTerm, -nextTerm, expr, result);
            expr.pop_back();
            expr.pop_back();

            expr.push_back("*");
            expr.push_back(nextTermStr);
            calculate(num, end, target, curr - prevTerm + (prevTerm * nextTerm), prevTerm * nextTerm, expr, result);
            expr.pop_back();
            expr.pop_back();
        }
    }

public:
    vector<string> addOperators(string num, int target) {
        vector<string> expr;
        vector<string> result;
        calculate(num, 0, target, 0, 0, expr, result);
        return result;
    }
};
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