optimal binary search trees

Optimal binary search trees are data structures designed for efficient searching of elements. They are created by arranging the elements in a binary tree, where each node represents an element. The search key of the node determines its position in the tree, with smaller keys on the left and larger keys on the right. The term "optimal" refers to the tree structure that minimizes the expected cost of searching, which includes the number of comparisons needed to find an element. This optimal structure is achieved by assigning probabilities to each element, indicating their likelihood of being searched for. In an optimal binary search tree, the elements with higher probabilities are placed closer to the root, reducing the average search time. This arrangement allows for efficient searching, with a time complexity of O(log n) on average.

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