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12 Abstract Data Types
12 Abstract Data Types

Amortization, Lazy Evaluation, and Persistence: Lists
Amortization, Lazy Evaluation, and Persistence: Lists

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... The HPBNET procedure is a high-performance procedure that can learn different types of Bayesian networks—naï ve, tree-augmented naï ve (TAN), Bayesian network-augmented naï ve (BAN), parent-child Bayesian network (PC), or Markov blanket (MB)—from an input data set. PROC HPBNET runs in either single- ...
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... 1. Write a program that can handle duplicate nodes in a binary search tree as follows: include a field in the structure of each node that will contain a count of the number of occurrences of a particular value. Increment the count by one when inserting a value that is already in the tree. Decrement ...
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... b) Suppose the following list of numbers is inserted in order into an empty binary search tree: 45, 32, 90, 34, 68, 72, 15, 24, 30, 66, 11, 50, 10. Construct the binary search tree. (8M+8M) ...
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... The cost of an insertion is clearly proportional to the length of the search paths for v and w, which are O(log n) in expectation. To perform a deletion, we apply the Split operation on treaps to make three trees. The tree T1 contains t1 , . . . , ti−1 , the tree T2 contains ti , . . . , ti+l−1 and ...
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... complete binary tree (a full tree with any additional leaves as far left as possible) with the items being arranges by heap-order property, i.e., each node is ≤ either of its children. An example of a min heap “viewed” as a complete binary tree would be: ...
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... The AVL tree and red-black tree are two of the many types of balanced binary search trees that guarantee a worst case search / insert / delete time of O(log n). An AVL tree is a binary search tree in which the heights of the left and right subtrees of every node differ by at most 1. Recursive defini ...
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Quadtree



A quadtree is a tree data structure in which each internal node has exactly four children. Quadtrees are most often used to partition a two-dimensional space by recursively subdividing it into four quadrants or regions. The regions may be square or rectangular, or may have arbitrary shapes. This data structure was named a quadtree by Raphael Finkel and J.L. Bentley in 1974. A similar partitioning is also known as a Q-tree. All forms of quadtrees share some common features: They decompose space into adaptable cells Each cell (or bucket) has a maximum capacity. When maximum capacity is reached, the bucket splits The tree directory follows the spatial decomposition of the quadtree.
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