created solution for problem62'

Author: dampdigits

problem62/Solution.py

@@ -0,0 +1,30 @@
+class Solution:
+    def numTilings(self, n: int) -> int:
+        MOD = 10**9 + 7
+        # Memoization
+        evenCache = [0] * (n+1)
+        oddCache = [0] * (n+1)
+
+        # Place a domino
+        def domino(N):
+            if N == 0: return 1
+            if evenCache[N]: return evenCache[N]
+
+            ways = domino(N-1) % MOD
+            if N-1 > 0:
+                ways += (domino(N-2) % MOD) + ((2 * tromino(N-2)) % MOD)
+            
+            evenCache[N] = ways % MOD
+            return evenCache[N]
+
+        # Place a tromino (previously a tromino was placed)
+        def tromino(N):
+            if N == 0: return 0
+            if oddCache[N]: return oddCache[N]
+
+            ways = (tromino(N-1) % MOD) + (domino(N-1) % MOD)
+            
+            oddCache[N] = ways % MOD
+            return oddCache[N]
+
+        return domino(n) % MOD