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Author: Partho Biswas

README.md

@@ -900,6 +900,7 @@ BFS, DFS, Dijkstra, Floyd–Warshall, Bellman-Ford, Kruskal, Prim's, Minimum Spa
 |05| [Lowest_Common_Manager](algoexpert.io/questions/Lowest_Common_Manager.md) | [Python](algoexpert.io/python/Lowest_Common_Manager.py) |
 |06| [Number_Of_Possible_Binary_Tree_Topologies](algoexpert.io/questions/Number_Of_Binary_Tree_Topologies.md) | [Python](algoexpert.io/python/Number_Of_Possible_Binary_Tree_Topologies.py) |
 |07| [Interweaving_Strings](algoexpert.io/questions/Interweaving_Strings.md) | [Python](algoexpert.io/python/Interweaving_Strings.py) |
+|08| [Number_Of_Binary_Tree_Topologies](algoexpert.io/questions/Number_Of_Binary_Tree_Topologies.md) | [Python](algoexpert.io/python/Number_Of_Binary_Tree_Topologies.py) |
 
 </p>
 </details>

algoexpert.io/python/Number_Of_Binary_Tree_Topologies.py

@@ -0,0 +1,11 @@
+def numberOfBinaryTreeTopologies(n, cache={0: 1}):
+    if n in cache:
+		return cache[n]
+	numbersOfTree = 0
+	for leftTreeSize in range(n):
+		rightTreeSize = n - 1 - leftTreeSize
+		numOfLeftTree = numberOfBinaryTreeTopologies(leftTreeSize, cache)
+		numOfRigntTree = numberOfBinaryTreeTopologies(rightTreeSize, cache)
+		numbersOfTree += numOfRigntTree * numOfLeftTree
+	cache[n] = numbersOfTree
+	return numbersOfTree