lecture22
... Everything inside the cloud has the correct shortest path Proof is by induction on the # of nodes in the cloud: – initial cloud is just the source with shortest path 0 – inductive step: once we prove the shortest path to G is correct, we add it to the cloud ...
... Everything inside the cloud has the correct shortest path Proof is by induction on the # of nodes in the cloud: – initial cloud is just the source with shortest path 0 – inductive step: once we prove the shortest path to G is correct, we add it to the cloud ...
Building Trees
... Now we learn how to build them Initially trees may be unbalanced Worst case, they may be so-called leftspine (or right-spine) trees, i.e. no different from linear lists, but more costly to process ...
... Now we learn how to build them Initially trees may be unbalanced Worst case, they may be so-called leftspine (or right-spine) trees, i.e. no different from linear lists, but more costly to process ...
Ch 10 - Personal.kent.edu
... (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. ...
Data Structures and Algorithms IT2003
... Continue till the node is found or the entire tree is traversed. Time required to find a node depends on how many levels down it is situated, i.e. O(log N). ...
... Continue till the node is found or the entire tree is traversed. Time required to find a node depends on how many levels down it is situated, i.e. O(log N). ...
The Quadtree and Related Hierarchical Data Structures
... larger areas from consideration. Another query might be to determine whether two roads intersect within a given area. We could check them point by point, but a more efficient method of analysis would be to represent them by a hierarchical sequence of enclosing rectangles and to discover whether in f ...
... larger areas from consideration. Another query might be to determine whether two roads intersect within a given area. We could check them point by point, but a more efficient method of analysis would be to represent them by a hierarchical sequence of enclosing rectangles and to discover whether in f ...
Lecture 15 Student Notes
... rightmost element of the tree created so far. For example, if we have a tree for which the subarray [2, 4, 5] has been inserted, and the next element is 3, then insertion has the following result: ...
... rightmost element of the tree created so far. For example, if we have a tree for which the subarray [2, 4, 5] has been inserted, and the next element is 3, then insertion has the following result: ...
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.