Sync LeetCode submission Runtime - 3 ms (95.31%), Memory - 17.8 MB (41.41%)

Author: jimit105

1819-construct-the-lexicographically-largest-valid-sequence/README.md

@@ -0,0 +1,36 @@
+<p>Given an integer <code>n</code>, find a sequence that satisfies all of the following:</p>
+
+<ul>
+	<li>The integer <code>1</code> occurs once in the sequence.</li>
+	<li>Each integer between <code>2</code> and <code>n</code> occurs twice in the sequence.</li>
+	<li>For every integer <code>i</code> between <code>2</code> and <code>n</code>, the <strong>distance</strong> between the two occurrences of <code>i</code> is exactly <code>i</code>.</li>
+</ul>
+
+<p>The <strong>distance</strong> between two numbers on the sequence, <code>a[i]</code> and <code>a[j]</code>, is the absolute difference of their indices, <code>|j - i|</code>.</p>
+
+<p>Return <em>the <strong>lexicographically largest</strong> sequence</em><em>. It is guaranteed that under the given constraints, there is always a solution. </em></p>
+
+<p>A sequence <code>a</code> is lexicographically larger than a sequence <code>b</code> (of the same length) if in the first position where <code>a</code> and <code>b</code> differ, sequence <code>a</code> has a number greater than the corresponding number in <code>b</code>. For example, <code>[0,1,9,0]</code> is lexicographically larger than <code>[0,1,5,6]</code> because the first position they differ is at the third number, and <code>9</code> is greater than <code>5</code>.</p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+
+<pre>
+<strong>Input:</strong> n = 3
+<strong>Output:</strong> [3,1,2,3,2]
+<strong>Explanation:</strong> [2,3,2,1,3] is also a valid sequence, but [3,1,2,3,2] is the lexicographically largest valid sequence.
+</pre>
+
+<p><strong class="example">Example 2:</strong></p>
+
+<pre>
+<strong>Input:</strong> n = 5
+<strong>Output:</strong> [5,3,1,4,3,5,2,4,2]
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>1 &lt;= n &lt;= 20</code></li>
+</ul>

1819-construct-the-lexicographically-largest-valid-sequence/solution.py

@@ -0,0 +1,48 @@
+# Approach: Backtracking
+
+# Time: O(n!)
+# Space: O(n)
+
+class Solution:
+    def constructDistancedSequence(self, n: int) -> List[int]:
+        result_sequence = [0] * (n * 2 - 1)
+        is_number_used = [False] * (n + 1)
+
+        self.find_lexicographically_largest_sequence(0, result_sequence, is_number_used, n)
+
+        return result_sequence
+
+    def find_lexicographically_largest_sequence(self, current_idx, result_sequence, is_number_used, n):
+        if current_idx == len(result_sequence):
+            return True
+
+        if result_sequence[current_idx] != 0:
+            return self.find_lexicographically_largest_sequence(current_idx + 1, result_sequence, is_number_used, n)
+
+        for number_to_place in range(n, 0, -1):
+            if is_number_used[number_to_place]:
+                continue
+
+            is_number_used[number_to_place] = True
+            result_sequence[current_idx] = number_to_place
+
+            # If placing number 1, move to the next index directly
+            if number_to_place == 1:
+                if self.find_lexicographically_largest_sequence(current_idx + 1, result_sequence, is_number_used, n):
+                    return True
+
+            # Place larger numbers at two positions if valid
+            elif (current_idx + number_to_place < len(result_sequence) and result_sequence[current_idx + number_to_place] == 0):
+                result_sequence[current_idx + number_to_place] = number_to_place
+
+                if self.find_lexicographically_largest_sequence(current_idx + 1, result_sequence, is_number_used, n):
+                    return True
+
+                # undo placement for backtracking
+                result_sequence[current_idx + number_to_place] = 0
+
+            # Undo current placement and mark number as unused
+            result_sequence[current_idx] = 0
+            is_number_used[number_to_place] = False
+
+        return False