Create number-of-ways-to-build-house-of-cards.py

Author: kamyu104

Python/number-of-ways-to-build-house-of-cards.py

@@ -0,0 +1,33 @@
+# Time:  O(n^2)
+# Space: O(n)
+
+# dp
+class Solution(object):
+    def houseOfCards(self, n):
+        """
+        :type n: int
+        :rtype: int
+        """
+        dp = [0]*(n+1)  # dp[i]: number of ways with i cards and at most t triangles in the first row
+        dp[0] = 1
+        for t in xrange(1, (n+1)//3+1):
+            for i in reversed(xrange(3*t-1, n+1)):
+                dp[i] += dp[i-(3*t-1)]
+        return dp[n]
+
+
+# Time:  O(n^3)
+# Space: O(n^2)
+# dp
+class Solution_TLE(object):
+    def houseOfCards(self, n):
+        """
+        :type n: int
+        :rtype: int
+        """
+        dp = [[0]*(n+1) for _ in xrange((n+1)//3+1)]  # dp[t][i]: number of ways with i cards and t triangles in the first row
+        dp[0][0] = 1
+        for t in xrange(1, (n+1)//3+1):
+            for i in xrange(3*t-1, n+1):
+                dp[t][i] = sum(dp[j][i-(3*t-1)] for j in xrange(t))
+        return sum(dp[t][n] for t in xrange((n+1)//3+1))