<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:
    void solve(vector<string>& ans, string& path, string& num, int target,
               int pos, long long curr, long long prev) {
        if (pos == num.size()) {
            if (curr == target) {
                ans.push_back(path);
            }
            return;
        }

        for (int i = pos; i < num.size(); ++i) {
            if (i != pos && num[pos] == '0')
                break;

            string part = num.substr(pos, i - pos + 1);
            long long n = stoll(part);

            if (pos == 0) {
                path += part;
                solve(ans, path, num, target, i + 1, n, n);
                path.erase(path.size() - part.size());
            } else {
                path += '+' + part;
                solve(ans, path, num, target, i + 1, curr + n, n);
                path.erase(path.size() - part.size() - 1);

                path += '-' + part;
                solve(ans, path, num, target, i + 1, curr - n, -n);
                path.erase(path.size() - part.size() - 1);

                path += '*' + part;
                solve(ans, path, num, target, i + 1, curr - prev + prev * n,
                      prev * n);
                path.erase(path.size() - part.size() - 1);
            }
        }
    }

    vector<string> addOperators(string num, int target) {
        vector<string> ans;
        if (num.empty())
            return ans;

        string path;
        solve(ans, path, num, target, 0, 0, 0);
        return ans;
    }
};
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