feat: add solution 1755. Closest Subsequence Sum

Author: tzuyi0817

solutions/1755. Closest Subsequence Sum/README.md

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+# [1755. Closest Subsequence Sum](https://leetcode.com/problems/closest-subsequence-sum)
+
+## Description
+
+<div class="elfjS" data-track-load="description_content"><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'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>
+</div>
+
+<p>&nbsp;</p>
+
+## Solutions
+
+**Solution: `Depth-First Search + Binary Search`**
+
+- Time complexity: <em>O(n\*2<sup>n/2</sup>)</em>
+- Space complexity: <em>O(2<sup>n/2</sup>)</em>
+
+<p>&nbsp;</p>
+
+### **JavaScript**
+
+```js
+/**
+ * @param {number[]} nums
+ * @param {number} goal
+ * @return {number}
+ */
+const minAbsDifference = function (nums, goal) {
+  const n = nums.length;
+  const half = Math.floor(n / 2);
+  const lNums = nums.slice(0, half);
+  const rNums = nums.slice(half, n);
+  let lSums = new Set();
+  let rSums = new Set();
+  let result = Number.MAX_SAFE_INTEGER;
+
+  const getSums = (values, index, sum, sums) => {
+    if (index >= values.length) {
+      sums.add(sum);
+      return;
+    }
+    const value = values[index];
+
+    getSums(values, index + 1, sum, sums);
+    getSums(values, index + 1, sum + value, sums);
+  };
+
+  getSums(lNums, 0, 0, lSums);
+  getSums(rNums, 0, 0, rSums);
+  lSums = [...lSums];
+  rSums = [...rSums].sort((a, b) => a - b);
+
+  const findFirstGreaterEqual = (sums, target) => {
+    let left = 0;
+    let right = sums.length - 1;
+
+    while (left <= right) {
+      const mid = Math.floor((left + right) / 2);
+
+      sums[mid] >= target ? (right = mid - 1) : (left = mid + 1);
+    }
+
+    return left;
+  };
+
+  for (const sum of lSums) {
+    const index = findFirstGreaterEqual(rSums, goal - sum);
+
+    if (index < rSums.length) {
+      result = Math.min(Math.abs(goal - sum - rSums[index]), result);
+    }
+
+    if (index > 0) {
+      result = Math.min(Math.abs(goal - sum - rSums[index - 1]), result);
+    }
+  }
+
+  return result;
+};
+```

solutions/1755. Closest Subsequence Sum/solution.js

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+/**
+ * @param {number[]} nums
+ * @param {number} goal
+ * @return {number}
+ */
+const minAbsDifference = function (nums, goal) {
+  const n = nums.length;
+  const half = Math.floor(n / 2);
+  const lNums = nums.slice(0, half);
+  const rNums = nums.slice(half, n);
+  let lSums = new Set();
+  let rSums = new Set();
+  let result = Number.MAX_SAFE_INTEGER;
+
+  const getSums = (values, index, sum, sums) => {
+    if (index >= values.length) {
+      sums.add(sum);
+      return;
+    }
+    const value = values[index];
+
+    getSums(values, index + 1, sum, sums);
+    getSums(values, index + 1, sum + value, sums);
+  };
+
+  getSums(lNums, 0, 0, lSums);
+  getSums(rNums, 0, 0, rSums);
+  lSums = [...lSums];
+  rSums = [...rSums].sort((a, b) => a - b);
+
+  const findFirstGreaterEqual = (sums, target) => {
+    let left = 0;
+    let right = sums.length - 1;
+
+    while (left <= right) {
+      const mid = Math.floor((left + right) / 2);
+
+      sums[mid] >= target ? (right = mid - 1) : (left = mid + 1);
+    }
+
+    return left;
+  };
+
+  for (const sum of lSums) {
+    const index = findFirstGreaterEqual(rSums, goal - sum);
+
+    if (index < rSums.length) {
+      result = Math.min(Math.abs(goal - sum - rSums[index]), result);
+    }
+
+    if (index > 0) {
+      result = Math.min(Math.abs(goal - sum - rSums[index - 1]), result);
+    }
+  }
+
+  return result;
+};