Closest Subsequence Sum
<p>You are given an integer array <code>nums</code> and an integer <code>goal</code>.</p>

<p>You want to choose a subsequence of <code>nums</code> such that the sum of its elements is the closest possible to <code>goal</code>. That is, if the sum of the subsequence&#39;s elements is <code>sum</code>, then you want to <strong>minimize the absolute difference</strong> <code>abs(sum - goal)</code>.</p>

<p>Return <em>the <strong>minimum</strong> possible value of</em> <code>abs(sum - goal)</code>.</p>

<p>Note that a subsequence of an array is an array formed by removing some elements <strong>(possibly all or none)</strong> of the original array.</p>

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

<pre>
<strong>Input:</strong> nums = [5,-7,3,5], goal = 6
<strong>Output:</strong> 0
<strong>Explanation:</strong> Choose the whole array as a subsequence, with a sum of 6.
This is equal to the goal, so the absolute difference is 0.
</pre>

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

<pre>
<strong>Input:</strong> nums = [7,-9,15,-2], goal = -5
<strong>Output:</strong> 1
<strong>Explanation:</strong> Choose the subsequence [7,-9,-2], with a sum of -4.
The absolute difference is abs(-4 - (-5)) = abs(1) = 1, which is the minimum.
</pre>

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

<pre>
<strong>Input:</strong> nums = [1,2,3], goal = -7
<strong>Output:</strong> 7
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 40</code></li>
	<li><code>-10<sup>7</sup> &lt;= nums[i] &lt;= 10<sup>7</sup></code></li>
	<li><code>-10<sup>9</sup> &lt;= goal &lt;= 10<sup>9</sup></code></li>
</ul>
Bit Manipulation; Array; Two Pointers; Dynamic Programming; Bitmask; Sorting
func minAbsDifference(nums []int, goal int) int {
	n := len(nums)
	lsum := make([]int, 0)
	rsum := make([]int, 0)

	dfs(nums[:n/2], &lsum, 0, 0)
	dfs(nums[n/2:], &rsum, 0, 0)

	sort.Ints(rsum)
	res := math.MaxInt32

	for _, x := range lsum {
		t := goal - x
		l, r := 0, len(rsum)
		for l < r {
			m := int(uint(l+r) >> 1)
			if rsum[m] < t {
				l = m + 1
			} else {
				r = m
			}
		}
		if l < len(rsum) {
			res = min(res, abs(t-rsum[l]))
		}
		if l > 0 {
			res = min(res, abs(t-rsum[l-1]))
		}
	}

	return res
}

func dfs(nums []int, sum *[]int, i, cur int) {
	if i == len(nums) {
		*sum = append(*sum, cur)
		return
	}

	dfs(nums, sum, i+1, cur)
	dfs(nums, sum, i+1, cur+nums[i])
}

func abs(x int) int {
	if x < 0 {
		return -x
	}
	return x
}