<p>You are given a <strong>0-indexed</strong> string <code>expression</code> of the form <code>&quot;&lt;num1&gt;+&lt;num2&gt;&quot;</code> where <code>&lt;num1&gt;</code> and <code>&lt;num2&gt;</code> represent positive integers.</p>

<p>Add a pair of parentheses to <code>expression</code> such that after the addition of parentheses, <code>expression</code> is a <strong>valid</strong> mathematical expression and evaluates to the <strong>smallest</strong> possible value. The left parenthesis <strong>must</strong> be added to the left of <code>&#39;+&#39;</code> and the right parenthesis <strong>must</strong> be added to the right of <code>&#39;+&#39;</code>.</p>

<p>Return <code>expression</code><em> after adding a pair of parentheses such that </em><code>expression</code><em> evaluates to the <strong>smallest</strong> possible value.</em> If there are multiple answers that yield the same result, return any of them.</p>

<p>The input has been generated such that the original value of <code>expression</code>, and the value of <code>expression</code> after adding any pair of parentheses that meets the requirements fits within a signed 32-bit integer.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> expression = &quot;247+38&quot;
<strong>Output:</strong> &quot;2(47+38)&quot;
<strong>Explanation:</strong> The <code>expression</code> evaluates to 2 * (47 + 38) = 2 * 85 = 170.
Note that &quot;2(4)7+38&quot; is invalid because the right parenthesis must be to the right of the <code>&#39;+&#39;</code>.
It can be shown that 170 is the smallest possible value.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> expression = &quot;12+34&quot;
<strong>Output:</strong> &quot;1(2+3)4&quot;
<strong>Explanation:</strong> The expression evaluates to 1 * (2 + 3) * 4 = 1 * 5 * 4 = 20.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> expression = &quot;999+999&quot;
<strong>Output:</strong> &quot;(999+999)&quot;
<strong>Explanation:</strong> The <code>expression</code> evaluates to 999 + 999 = 1998.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>3 &lt;= expression.length &lt;= 10</code></li>
	<li><code>expression</code> consists of digits from <code>&#39;1&#39;</code> to <code>&#39;9&#39;</code> and <code>&#39;+&#39;</code>.</li>
	<li><code>expression</code> starts and ends with digits.</li>
	<li><code>expression</code> contains exactly one <code>&#39;+&#39;</code>.</li>
	<li>The original value of <code>expression</code>, and the value of <code>expression</code> after adding any pair of parentheses that meets the requirements fits within a signed 32-bit integer.</li>
</ul>

class Solution {
public:
    string minimizeResult(string expression) {
        vector<int> left;
        vector<int> right;
        bool is_left = true;
        for (auto c : expression) {
            if (c == '+') {
                is_left = false;
            } else {
                if (is_left) {
                    left.push_back(c - '0');
                } else {
                    right.push_back(c - '0');
                }
            }
        }
        auto to_num = [](vector<int>& di, int start, int end) {
            if (start == end) return 1;
            int res = 0;
            for (int i = start; i < end; ++i) {
                res = res * 10 + di[i];
            }
            return res;

        };

        string res;
        int min_v = INT_MAX;
        for (int i = 0; i < left.size(); ++i) {
            for (int j = 1; j <= right.size(); ++j) {
                auto t = to_num(left, 0, i) * (to_num(left, i, left.size()) + to_num(right, 0, j)) * to_num(right, j, right.size());
                if (min_v > t) {
                    min_v = t;
                    res = expression.substr(0, i) + '(' + expression.substr(i, left.size() + 1 + j - i)
                        + ')' + expression.substr(left.size() + 1 + j);
                }
            }
        }
        return res;
    }
};
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