<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:
    vector<string> answer;
public:
    void dfs(string num, int target, int idx, long long curr_val, long long prev_val, string path) {
        if(idx == num.size()) {
            if(curr_val == target) {
                answer.push_back(path);
            }
            return;
        }

        for(int i = idx ; i < num.size() ; i++) {
            if(i > idx && num[idx] == '0') {
                break;
            }
            string str = num.substr(idx, i - idx + 1);
            long long val = stoll(str);

            if(idx == 0) {
                dfs(num, target, i+1, val, val, path + str);
            }
            else {
                dfs(num, target, i+1, curr_val + val, val, path + '+' + str);
                dfs(num, target, i+1, curr_val - val, -val, path + '-' + str);
                dfs(num, target, i+1, (curr_val - prev_val) + (prev_val * val), prev_val * val, path + '*' + str);
            }
        }
    }
    vector<string> addOperators(string num, int target) {
        string path = "";
        int idx = 0;
        dfs(num, target, idx, 0, 0, path);
        return answer;
    }
};
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