Programming for GCSE - Teaching London Computing
... • Where do lists and dictionaries come from? • Understand the problem • Introduce the following data structures ...
... • Where do lists and dictionaries come from? • Understand the problem • Introduce the following data structures ...
Encoding Nearest Larger Values
... Lemma 3. Consider the set of all possible chains with ci deleted nodes in a path compressed representation of a Cartesian tree, excluding chains having nodes representing array elements A[1] or A[n]. There are exactly ci +1 combinatorially distinct chains with respect to answering nearest larger va ...
... Lemma 3. Consider the set of all possible chains with ci deleted nodes in a path compressed representation of a Cartesian tree, excluding chains having nodes representing array elements A[1] or A[n]. There are exactly ci +1 combinatorially distinct chains with respect to answering nearest larger va ...
CS503: First Lecture, Fall 2008
... size, we will have to undo splits. • But first, the easy case: – If the leaf we remove from is more than half full, we simply remove it and we’re finished. ...
... size, we will have to undo splits. • But first, the easy case: – If the leaf we remove from is more than half full, we simply remove it and we’re finished. ...
Chapter 10: Efficient Collections (skip lists, trees)
... The skip list and the binary tree use these observations in very different ways. The first, the skip list, makes use of non-determinism. Non-determinism means using random chance, like flipping a coin. If you flip a coin once, you have no way to predict whether it will come up heads or tails. But if ...
... The skip list and the binary tree use these observations in very different ways. The first, the skip list, makes use of non-determinism. Non-determinism means using random chance, like flipping a coin. If you flip a coin once, you have no way to predict whether it will come up heads or tails. But if ...
Notes - CS.Duke
... Proof. We do a proof by induction on the tree depth d. Since a tree T with depth 0 has has 20 = 1 elements, the base case is trivial. For the inductive step, assume that the hypothesis holds for all trees with depth k − 1, i.e., any tree with depth k − 1 contains at least 2k−1 nodes. Observe that in ...
... Proof. We do a proof by induction on the tree depth d. Since a tree T with depth 0 has has 20 = 1 elements, the base case is trivial. For the inductive step, assume that the hypothesis holds for all trees with depth k − 1, i.e., any tree with depth k − 1 contains at least 2k−1 nodes. Observe that in ...
Tree
... but trees with higher branching factors are far more efficient when stored on slow external memory devices. For efficiency, all of an ordered key sequence in a B-tree is read into internal memory at once, and a fast binary search is used to find a key in this ordered sequence. This either gives the ...
... but trees with higher branching factors are far more efficient when stored on slow external memory devices. For efficiency, all of an ordered key sequence in a B-tree is read into internal memory at once, and a fast binary search is used to find a key in this ordered sequence. This either gives the ...
Binary Trees
... (a) T is a tree if the set of nodes is empty. (An empty tree is a tree.) (b) The set consists of a root, R, and exactly two distinct binary trees, the left subtree TL and the right subtreeTR. The nodes in T consist of node R and all the nodes in TL and TR. ...
... (a) T is a tree if the set of nodes is empty. (An empty tree is a tree.) (b) The set consists of a root, R, and exactly two distinct binary trees, the left subtree TL and the right subtreeTR. The nodes in T consist of node R and all the nodes in TL and TR. ...
Amortized Analysis - Carleton University
... is greater than or equal to x. Similarly, show how to find the largest element of S that is less than or equal to x. The running time of both algorithms should be proportional to the height of the tree. Remark 3 Storing the elements in the leaves has some advantages. For example, in so-called multi- ...
... is greater than or equal to x. Similarly, show how to find the largest element of S that is less than or equal to x. The running time of both algorithms should be proportional to the height of the tree. Remark 3 Storing the elements in the leaves has some advantages. For example, in so-called multi- ...
of data access
... Adding element is preceded by the search algorithm and there is a need to insert a new value if there is no result of the search process. Then we know the side of leaf to which a new element is to be added. This adding can be without collision or can cause overflowing of page (if there are already 2 ...
... Adding element is preceded by the search algorithm and there is a need to insert a new value if there is no result of the search process. Then we know the side of leaf to which a new element is to be added. This adding can be without collision or can cause overflowing of page (if there are already 2 ...
VIST: The Virtual Suffix Tree
... As it is shown above elements in the sequences represent nodes in the suffix tree. Since the nodes are involed in 2 different trees, there is 2 kinds of ancestor-descendent relationships among the nodes. i ) D-Ancestorship e.g. (S,P) is a D-ancestor of (L,PS) ii ) S-Ancestorship e.g. (v1,PSN) is a S ...
... As it is shown above elements in the sequences represent nodes in the suffix tree. Since the nodes are involed in 2 different trees, there is 2 kinds of ancestor-descendent relationships among the nodes. i ) D-Ancestorship e.g. (S,P) is a D-ancestor of (L,PS) ii ) S-Ancestorship e.g. (v1,PSN) is a S ...
Geometric Data Structures
... W. We can find such segments by performing a range query with W in the set of 2n endpoints of the segments in S, by using a 2D range tree T. 2D range tree can answer a range query in O(log2n + k) time; query time can be improved to O(logn + k) by fractional cascading. ...
... W. We can find such segments by performing a range query with W in the set of 2n endpoints of the segments in S, by using a 2D range tree T. 2D range tree can answer a range query in O(log2n + k) time; query time can be improved to O(logn + k) by fractional cascading. ...
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.