Unique Binary Search Trees

numTrees.py

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+# Given n, how many structurally unique BST's (binary search trees) that store values 1...n?
+
+# For 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
+
+class Solution:
+    # @return an integer
+    def numTrees(self, n):
+        num = [0]*(n+1)
+        if n == 0:
+            return 1
+        if n == 1:
+            return 1
+        num[0] = 1
+        num[1] = 1
+        for i in range(2,n+1):
+            for j in range(0,i):
+                num[i] += num[j] * num[i-j-1]
+        return num[-1]
+