Create construct-the-lexicographically-largest-valid-sequence.py

Author: kamyu104

Python/construct-the-lexicographically-largest-valid-sequence.py

@@ -0,0 +1,27 @@
+# Time:  O(n!)
+# Space: O(n)
+
+class Solution(object):
+    def constructDistancedSequence(self, n):
+        """
+        :type n: int
+        :rtype: List[int]
+        """
+        def backtracking(n, i, s, lookup):
+            if i == len(s):
+                return True
+            if s[i]:
+                return backtracking(n, i+1, s, lookup)
+            for x in reversed(xrange(1, n+1)):
+                j = i if x == 1 else i+x
+                if lookup[x] or j >= len(s) or s[j]:
+                    continue
+                s[i], s[j], lookup[x] = x, x, True
+                if backtracking(n, i+1, s, lookup):
+                    return True
+                s[i], s[j], lookup[x] = 0, 0, False
+            return False
+
+        s, lookup = [0]*(2*n-1), [False]*(n+1)
+        backtracking(n, 0, s, lookup)
+        return s