Maximum Strength of a Group
<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code> representing the score of students in an exam. The teacher would like to form one <strong>non-empty</strong> group of students with maximal <strong>strength</strong>, where the strength of a group of students of indices <code>i<sub>0</sub></code>, <code>i<sub>1</sub></code>, <code>i<sub>2</sub></code>, ... , <code>i<sub>k</sub></code> is defined as <code>nums[i<sub>0</sub>] * nums[i<sub>1</sub>] * nums[i<sub>2</sub>] * ... * nums[i<sub>k</sub>​]</code>.</p>

<p>Return <em>the maximum strength of a group the teacher can create</em>.</p>

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

<pre>
<strong>Input:</strong> nums = [3,-1,-5,2,5,-9]
<strong>Output:</strong> 1350
<strong>Explanation:</strong> One way to form a group of maximal strength is to group the students at indices [0,2,3,4,5]. Their strength is 3 * (-5) * 2 * 5 * (-9) = 1350, which we can show is optimal.
</pre>

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

<pre>
<strong>Input:</strong> nums = [-4,-5,-4]
<strong>Output:</strong> 20
<strong>Explanation:</strong> Group the students at indices [0, 1] . Then, we&rsquo;ll have a resulting strength of 20. We cannot achieve greater strength.
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 13</code></li>
	<li><code>-9 &lt;= nums[i] &lt;= 9</code></li>
</ul>
Greedy; Bit Manipulation; Array; Dynamic Programming; Backtracking; Enumeration; Sorting
function maxStrength(nums: number[]): number {
    let ans = -Infinity;
    const n = nums.length;
    for (let i = 1; i < 1 << n; ++i) {
        let t = 1;
        for (let j = 0; j < n; ++j) {
            if ((i >> j) & 1) {
                t *= nums[j];
            }
        }
        ans = Math.max(ans, t);
    }
    return ans;
}
