ch10ppt - Learn District 196
... • Example: a dictionary is a map that maps words to definitions ...
... • Example: a dictionary is a map that maps words to definitions ...
Binary Search Trees A Generic Tree Binary Trees
... Binary Search Trees are fast if they’re shallow: – e.g.: perfectly complete – e.g.: perfectly complete except the “fringe” (leafs) ...
... Binary Search Trees are fast if they’re shallow: – e.g.: perfectly complete – e.g.: perfectly complete except the “fringe” (leafs) ...
Binary trees
... There are 24 permutations (=different orderings) of these numbers (4 x 3 x 2 x 1 = 24). Each insert order (permutation) gives rise to a particular tree, but sometimes the same tree occurs for 2 different permutations. For example, inserting 3124 and 3241 and 3214 all make the same tree. In parenthes ...
... There are 24 permutations (=different orderings) of these numbers (4 x 3 x 2 x 1 = 24). Each insert order (permutation) gives rise to a particular tree, but sometimes the same tree occurs for 2 different permutations. For example, inserting 3124 and 3241 and 3214 all make the same tree. In parenthes ...
Chapter08
... WHILE (deck not empty) Pop the deckStack Check for Aces While (There are playStacks to check) If(can place card) Push card onto playStack Else push card onto usedStack Does implementation matter at this point? ...
... WHILE (deck not empty) Pop the deckStack Check for Aces While (There are playStacks to check) If(can place card) Push card onto playStack Else push card onto usedStack Does implementation matter at this point? ...
ppt
... Complete tree has depth = logMN Each internal node in a complete tree has M - 1 keys runtime: ...
... Complete tree has depth = logMN Each internal node in a complete tree has M - 1 keys runtime: ...
Singly-linked List
... If data is entered in sorted order, the tree becomes a list. This degeneration loses the O(log2 n) behaviour. How can we get around this? ...
... If data is entered in sorted order, the tree becomes a list. This degeneration loses the O(log2 n) behaviour. How can we get around this? ...
Traversal of a Binary Tree
... node. It has to be traversed from the root to reach to a particular node. As compared to sequential representation, the memory needed per node is more. This is due to two link fields (left child and right child for binary trees) in the node. The programming languages not supporting dynamic memory ma ...
... node. It has to be traversed from the root to reach to a particular node. As compared to sequential representation, the memory needed per node is more. This is due to two link fields (left child and right child for binary trees) in the node. The programming languages not supporting dynamic memory ma ...
Succinct tree representations
... Supports finding left child or right child of a node (in constant time). For each extra operation (eg. parent, subtree size) we have to pay, roughly, an additional n lg n bits. ...
... Supports finding left child or right child of a node (in constant time). For each extra operation (eg. parent, subtree size) we have to pay, roughly, an additional n lg n bits. ...
Trees
... A labeled binary tree containing the labels 1 to n with root 1, branches leading to nodes labeled 2 and 3, branches from these leading to 4, 5 and 6, 7, respectively, and so on. A binary tree with n nodes and level k is complete iff its nodes correspond to the nodes numbered from 1 to n in the full ...
... A labeled binary tree containing the labels 1 to n with root 1, branches leading to nodes labeled 2 and 3, branches from these leading to 4, 5 and 6, 7, respectively, and so on. A binary tree with n nodes and level k is complete iff its nodes correspond to the nodes numbered from 1 to n in the full ...
Part-1
... A labeled binary tree containing the labels 1 to n with root 1, branches leading to nodes labeled 2 and 3, branches from these leading to 4, 5 and 6, 7, respectively, and so on. A binary tree with n nodes and level k is complete iff its nodes correspond to the nodes numbered from 1 to n in the full ...
... A labeled binary tree containing the labels 1 to n with root 1, branches leading to nodes labeled 2 and 3, branches from these leading to 4, 5 and 6, 7, respectively, and so on. A binary tree with n nodes and level k is complete iff its nodes correspond to the nodes numbered from 1 to n in the full ...
BINARY SEARCH TREE PERFORMANCE
... Binary search trees, such as those above, in which the nodes are in order so that all links are to right children (or all are to left children), are called skewed trees. Average Running Time The average running time of the binary search tree operations is difficult to establish because it is not cle ...
... Binary search trees, such as those above, in which the nodes are in order so that all links are to right children (or all are to left children), are called skewed trees. Average Running Time The average running time of the binary search tree operations is difficult to establish because it is not cle ...
Trees - GearBox
... Search Tree: tree structure (usually node-based) that facilitates “binary search” of the nodes ...
... Search Tree: tree structure (usually node-based) that facilitates “binary search” of the nodes ...
Lecture 8 Data Structures (DAT037)
... A tree is a hierarchical data structure Each node can have several children but only has one parent The root has no parents; there is only one root ...
... A tree is a hierarchical data structure Each node can have several children but only has one parent The root has no parents; there is only one root ...
Searching: Binary Tress
... Some Tree Definition, p656 • Complete trees (might different form other books) – Each level is completely filled except the bottom level – The leftmost positions are filled at the bottom level – Array storage is perfect for them ...
... Some Tree Definition, p656 • Complete trees (might different form other books) – Each level is completely filled except the bottom level – The leftmost positions are filled at the bottom level – Array storage is perfect for them ...
Searching: Binary Tress
... Some Tree Definition, p656 • Complete trees (might different form other books) – Each level is completely filled except the bottom level – The leftmost positions are filled at the bottom level – Array storage is perfect for them ...
... Some Tree Definition, p656 • Complete trees (might different form other books) – Each level is completely filled except the bottom level – The leftmost positions are filled at the bottom level – Array storage is perfect for them ...
Search/Insert Properties of BSTs
... The next node visited depends on the outcome of the comparison of k with the key of the current node If we reach a nonmatching leaf, the key is not found and we return a null position Example: search(4,root) ...
... The next node visited depends on the outcome of the comparison of k with the key of the current node If we reach a nonmatching leaf, the key is not found and we return a null position Example: search(4,root) ...
1 Persistent Data Structures
... • full persistence: queries and changes to all past versions (creates “multiple worlds” situtation) Goal: general technique that can be applied to any data structure. Application: planar point location. • planar subdivision – n segments meeting only at ends – defines set of polygons – query: “wh ...
... • full persistence: queries and changes to all past versions (creates “multiple worlds” situtation) Goal: general technique that can be applied to any data structure. Application: planar point location. • planar subdivision – n segments meeting only at ends – defines set of polygons – query: “wh ...
Data structures & ANALYSIS OF ALGORITHMS
... • Deque (double-ended queue) is another form of a queue in which insertions and deletions are made at both the front and rear ends of the queue. There are two variations of a deque, namely, input restricted deque and output restricted deque. • The input restricted deque allows insertion at one end ( ...
... • Deque (double-ended queue) is another form of a queue in which insertions and deletions are made at both the front and rear ends of the queue. There are two variations of a deque, namely, input restricted deque and output restricted deque. • The input restricted deque allows insertion at one end ( ...
Divide and Conquer - CS Course Webpages
... • If you need to compute xn, could do it with n multiplications • But, it is faster to compute xn/2 * xn/2 • Need to account for the cases where n is odd: x*xn/2*xn/2 • More generally, notice that x can be things other than numbers (e.g. a matrix) and * does not have to be standard multiplication ...
... • If you need to compute xn, could do it with n multiplications • But, it is faster to compute xn/2 * xn/2 • Need to account for the cases where n is odd: x*xn/2*xn/2 • More generally, notice that x can be things other than numbers (e.g. a matrix) and * does not have to be standard multiplication ...
cs2110-15-trees
... – There are recursive methods inside the lower-level classes that are closely related (same name!) to the ADT-level operation ...
... – There are recursive methods inside the lower-level classes that are closely related (same name!) to the ADT-level operation ...
binary search tree
... – Binary search algorithm assumes that the items in the list being searched are sorted – The algorithm begins at the middle of the list in a binary search – If the item for which we are searching is less than the item in the middle, we know that the item won’t be in the second half of the list – Onc ...
... – Binary search algorithm assumes that the items in the list being searched are sorted – The algorithm begins at the middle of the list in a binary search – If the item for which we are searching is less than the item in the middle, we know that the item won’t be in the second half of the list – Onc ...
Binary tree
In computer science, a binary tree is a tree data structure in which each node has at most two children, which are referred to as the left child and the right child. A recursive definition using just set theory notions is that a (non-empty) binary tree is a triple (L, S, R), where L and R are binary trees or the empty set and S is a singleton set. Some authors allow the binary tree to be the empty set as well.From a graph theory perspective, binary (and K-ary) trees as defined here are actually arborescences. A binary tree may thus be also called a bifurcating arborescence—a term which actually appears in some very old programming books, before the modern computer science terminology prevailed. It is also possible to interpret a binary tree as an undirected, rather than a directed graph, in which case a binary tree is an ordered, rooted tree. Some authors use rooted binary tree instead of binary tree to emphasize the fact that the tree is rooted, but as defined above, a binary tree is always rooted. A binary tree is a special case of an ordered K-ary tree, where k is 2.In computing, binary trees are seldom used solely for their structure. Much more typical is to define a labeling function on the nodes, which associates some value to each node. Binary trees labelled this way are used to implement binary search trees and binary heaps, and are used for efficient searching and sorting. The designation of non-root nodes as left or right child even when there is only one child present matters in some of these applications, in particular it is significant in binary search trees. In mathematics, what is termed binary tree can vary significantly from author to author. Some use the definition commonly used in computer science, but others define it as every non-leaf having exactly two children and don't necessarily order (as left/right) the children either.