Add solution #1718

Author: JoshCrozier

README.md

@@ -492,6 +492,7 @@
 1672|[Richest Customer Wealth](./1672-richest-customer-wealth.js)|Easy|
 1679|[Max Number of K-Sum Pairs](./1679-max-number-of-k-sum-pairs.js)|Medium|
 1716|[Calculate Money in Leetcode Bank](./1716-calculate-money-in-leetcode-bank.js)|Easy|
+1718|[Construct the Lexicographically Largest Valid Sequence](./1718-construct-the-lexicographically-largest-valid-sequence.js)|Medium|
 1726|[Tuple with Same Product](./1726-tuple-with-same-product.js)|Medium|
 1732|[Find the Highest Altitude](./1732-find-the-highest-altitude.js)|Easy|
 1748|[Sum of Unique Elements](./1748-sum-of-unique-elements.js)|Easy|

solutions/1718-construct-the-lexicographically-largest-valid-sequence.js

@@ -0,0 +1,64 @@
+/**
+ * 1718. Construct the Lexicographically Largest Valid Sequence
+ * https://leetcode.com/problems/construct-the-lexicographically-largest-valid-sequence/
+ * Difficulty: Medium
+ *
+ * Given an integer n, find a sequence that satisfies all of the following:
+ * - The integer 1 occurs once in the sequence.
+ * - Each integer between 2 and n occurs twice in the sequence.
+ * - For every integer i between 2 and n, the distance between the two occurrences of i is
+ *   exactly i.
+ *
+ * The distance between two numbers on the sequence, a[i] and a[j], is the absolute difference
+ * of their indices, |j - i|.
+ *
+ * Return the lexicographically largest sequence. It is guaranteed that under the given
+ * constraints, there is always a solution.
+ *
+ * A sequence a is lexicographically larger than a sequence b (of the same length) if in the first
+ * position where a and b differ, sequence a has a number greater than the corresponding number in
+ * b. For example, [0,1,9,0] is lexicographically larger than [0,1,5,6] because the first position
+ * they differ is at the third number, and 9 is greater than 5.
+ */
+
+/**
+ * @param {number} n
+ * @return {number[]}
+ */
+var constructDistancedSequence = function(n) {
+  const result = new Array(2 * n - 1).fill(0);
+  const group = new Array(n + 1).fill(false);
+
+  backtrack(0);
+
+  function backtrack(index) {
+    if (index === 2 * n - 1) {
+      return true;
+    } else if (result[index] !== 0) {
+      return backtrack(index + 1);
+    }
+    for (let num = n; num >= 1; num--) {
+      if (group[num]) {
+        continue;
+      }
+      group[num] = true;
+      result[index] = num;
+      if (num === 1 || (index + num < 2 * n - 1 && result[index + num] === 0)) {
+        if (num > 1) {
+          result[index + num] = num;
+        }
+        if (backtrack(index + 1)) {
+          return true;
+        }
+        if (num > 1) {
+          result[index + num] = 0;
+        }
+      }
+      result[index] = 0;
+      group[num] = false;
+    }
+    return false;
+  }
+
+  return result;
+};