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Determine the cost and structure of an optimal binary search tree for a set of n = 7 keys with the following probabilities: That is, provide the main and root tables.
Expert Answer
We have to solve this by using OPTIMAL-BST(p, q, 7). As per this algorithm it returns two
matrices, e and root. Matrix e is abput expected search costs and root allows us to construct optimal binary search tree.
The e matrix e is as follows:
Root matrix is :
Then the optimal binary search tree is as follows:
| 5 is the root | d3 is the left child of 4 |
| 2 is the left child of 5 | d4 is the right child of 4 |
| of 1 is the left child of 2 | 7 is the right child of 5 |
| d0 is the left child of 1 | 6 is the left child of 7 |
| d1 is the right child of 1 | d5 is the left child of 6 |
| 3 is the right child of 2 | d6 is the right child of 6 |
| d2 is the left child of 3 | d7 is the right child of 7 |
| 4 is the right child of 3 |
Finally calculate the expected search cost.
