<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 ll;
    void dfs(int pos, string &num, string &curr, ll tar, ll last_mul, ll last_num, vector<string> &ans) {
        if(pos == num.size()) {
            if(last_mul == tar) ans.push_back(curr);
            return;
        }

        auto ncurr = curr;
        if(pos != 0) ncurr += "+";
        ncurr += num[pos];
        dfs(pos + 1, num, ncurr, tar - last_mul, num[pos] - '0', num[pos] - '0', ans);
        
        if(pos != 0){
            ncurr = curr;
            ncurr += "-";
            ncurr += num[pos];
            dfs(pos + 1, num, ncurr, tar - last_mul, -(num[pos] - '0'), num[pos] - '0', ans);
        }
        // continue
        if(pos != 0) {
            ncurr = curr;
            ncurr += "*";
            ncurr += num[pos];
            dfs(pos + 1, num, ncurr, tar, last_mul * (num[pos] - '0'), num[pos] - '0', ans);

            if(last_num != 0){
                ncurr = curr;
                ncurr += num[pos];
                auto nmul = last_mul / last_num;
                auto nnum = last_num * 10 + num[pos] - '0';
                dfs(pos + 1, num, ncurr, tar, nmul * nnum, nnum, ans);
            }
        }
    }
public:
    vector<string> addOperators(string num, int target) {
        auto ans = vector(0, string{});
        string curr;
        dfs(0, num, curr, target, 0, 0, ans);

        return ans;
    }
};
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