<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:
    typedef long long ll;

    void f(int idx, string& num, int& target, ll val, ll pv, string ds, vector<string>& res) {
        if (idx == num.size()) {
            if (val == target) {
                res.push_back(ds);
            }
            return;
        }

        string t;
        ll v = 0;

        for (int j = idx; j < num.size(); j++) {
            if (j > idx && num[idx] == '0') {
                break;
            }
            v = v * 10 + (num[j] - '0');
            t += num[j];
            if (idx == 0) {
                f(j + 1, num, target, v, v, t, res);
            } else {
                f(j + 1, num, target, val + v, v, ds + "+" + t, res);
                f(j + 1, num, target, val - v, -v, ds + "-" + t, res);
                f(j + 1, num, target, (val - pv) + (v * pv), pv * v, ds + "*" + t, res);
            }
        }
    }

    vector<string> addOperators(string num, int target) {
        ios_base::sync_with_stdio(false);
        cin.tie(0);

        vector<string> res;
        f(0, num, target, 0LL, 0LL, "", res);
        return res;
    }
};
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