<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 {
    vector<string> output;
public:
    vector<string> addOperators(string num, int target) {
        string expression;
        expression.reserve(2 * num.size()); // 預分配空間
        DFS(num, (long long)target, 0, 0, 0, expression);
        return output;
    }
    
private:
    void DFS(const string& num, long long target, int index, long long curRes, long long lastNum, string& expression) {
        if (index == num.size()) {
            if (curRes == target) {
                output.push_back(expression);
            }
            return;
        }
        
        int expressionSize = expression.size();
        long long currentNum = 0;
        
        for (int i = index; i < num.size(); i++) {
            if (i != index && num[index] == '0') break; // 處理前導零
            
            currentNum = currentNum * 10 + (num[i] - '0');
            string currentStr = num.substr(index, i - index + 1);
            
            if (index == 0) {
                expression += currentStr;
                DFS(num, target, i + 1, currentNum, currentNum, expression);
                expression.resize(expressionSize);
            } else {
                // Addition
                expression += '+' + currentStr;
                DFS(num, target, i + 1, curRes + currentNum, currentNum, expression);
                expression.resize(expressionSize);
                
                // Subtraction
                expression += '-' + currentStr;
                DFS(num, target, i + 1, curRes - currentNum, -currentNum, expression);
                expression.resize(expressionSize);
                
                // Multiplication
                expression += '*' + currentStr;
                DFS(num, target, i + 1, curRes - lastNum + lastNum * currentNum, lastNum * currentNum, expression);
                expression.resize(expressionSize);
            }
            
            if (currentNum > INT_MAX / 10) break; // 防止溢出
        }
    }
};

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