combination product rule

Unique Binary Search Trees.py

@@ -0,0 +1,41 @@
+"""
+Given n, how many structurally unique BSTs (binary search trees) that store values 1...n?
+
+Have you met this question in a real interview? Yes
+Example
+Given n = 3, there are a total of 5 unique BST's.
+
+1           3    3       2      1
+ \         /    /       / \      \
+  3      2     1       1   3      2
+ /      /       \                  \
+2     1          2                  3
+"""
+__author__ = 'Daniel'
+
+
+class Solution:
+    def __init__(self):
+        self.cache = {}
+
+    def numTrees(self, n):
+        return self.dfs(n)
+
+    def dfs(self, n):
+        if n not in self.cache:
+            if n in (0, 1, 2):
+                self.cache[n] = max(1, n)
+            else:
+                s = 0
+                for i in xrange(1, n+1):
+                    l = self.dfs(i-1)
+                    r = self.dfs(n-i)
+                    s += l*r  # multiplication rather than plus
+
+                self.cache[n] = s
+
+        return self.cache[n]
+
+
+if __name__ == "__main__":
+    print Solution().numTrees(3)