From lecture, we know that the number of BST (Binary search Tree) shapes with 3 nodes is 5. Suppose a student does not know this. The student draws all possible BSTs with 2 nodes. The student knows that there are 2 possible BST shapes with two nodes. Each of the two BSTs above have 3 null pointers. The root has 1 and the leaf has 2 null pointers. The student adds a 3rd node to each of the 3 null pointers to each of the 2 BST (above). The student concludes that there are 6 possible shapes of a BST with 3 nodes. Briefly and clearly explain why the student’s answer is wrong.

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07-06-2024
Mathematics

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From lecture, we know that the number of BST (Binary search Tree) shapes with 3 nodes is 5. Suppose a student does not know this. The student draws all possible BSTs with 2 nodes. The student knows that there are 2 possible BST shapes with two nodes. Each of the two BSTs above have 3 null pointers. The root has 1 and the leaf has 2 null pointers. The student adds a 3rd node to each of the 3 null pointers to each of the 2 BST (above). The student concludes that there are 6 possible shapes of a BST with 3 nodes. Briefly and clearly explain why the student’s answer is wrong.

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