Create number-of-distinct-roll-sequences.py

Author: kamyu104

Python/number-of-distinct-roll-sequences.py

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+# Time:  O(6^3 * n)
+# Space: O(6^2)
+
+import collections
+
+
+# dp
+class Solution(object):
+    def distinctSequences(self, n):
+        """
+        :type n: int
+        :rtype: int
+        """
+        def gcd(a, b):
+            while b:
+                a, b = b, a%b
+            return a
+
+        if n == 1:
+            return 6
+        MOD = 10**9 + 7
+        dp = [[0]*6 for _ in xrange(6)]
+        for i in xrange(6):
+            for j in xrange(6):
+                if i != j and gcd(i+1, j+1) == 1:
+                    dp[i][j] = 1
+        for _ in xrange(n-2):
+            new_dp = [[0]*6 for _ in xrange(6)]
+            for i in xrange(6):
+                for j in xrange(6):
+                    if not dp[i][j]:
+                        continue
+                    for k in xrange(6):
+                        if not dp[j][k]:
+                            continue
+                        if k != i:
+                            new_dp[i][j] = (new_dp[i][j]+dp[j][k]) % MOD
+            dp = new_dp
+        return sum(dp[i][j] for i in xrange(6) for j in xrange(6)) % MOD