How many distinct binary search trees can be formed using 5 distinct keys?
Options
- A. 14
- B. 42
- C. 120
- D. More than one of the above
- E. None of the above
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Quiz Practice:
Correct Answer (Detailed Explanation is Below)
B. 42
Detailed Explanation
The number of distinct BSTs formed from N distinct keys is the Catalan number CN. For five keys, C5 = 42. The recurrence can also be written as CN = Σ CiCN-1-i, where each possible key is considered as the root and the remaining keys are divided between the left and right subtrees. This recurrence explains why the number grows rapidly.