<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:
    Solution(){
        ios_base :: sync_with_stdio(false);
    }
    void solve(string num, int target, string helper, int index, long long curValue, long long prevValue, vector<string>& ans) {
        if (index == num.size()) {
            if (curValue == target) {
                ans.push_back(helper);
            }
            return;
        }

        for (int len = 1; len <= num.size() - index; ++len) {
            string part = num.substr(index, len);
            if (part.size() > 1 && part[0] == '0') break;  
            long long currentNum = stoll(part);
            if (index == 0) {
                solve(num, target, helper + part, index + len, currentNum, currentNum, ans);
            } else {
                solve(num, target, helper + '+' + part, index + len, curValue + currentNum, currentNum, ans);
                solve(num, target, helper + '-' + part, index + len, curValue - currentNum, -currentNum, ans);
                solve(num, target, helper + '*' + part, index + len, curValue - prevValue + prevValue * currentNum, prevValue * currentNum, ans);
            }
        }
    }

    vector<string> addOperators(string num, int target) {
        vector<string> ans;
        solve(num, target, "", 0, 0, 0, ans);
        return ans;
    }
};

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