Worst Case Constant Time Priority Queue
... 3 The Split Tagged Tree Since leaves represents elements of M we will talk We now introduce a new data structure called Split about the leaves and the corresponding element inTagged Tree, which is a slightly modified strati- terchangeably. Internal nodes are represented by the structure fied tree, a ...
... 3 The Split Tagged Tree Since leaves represents elements of M we will talk We now introduce a new data structure called Split about the leaves and the corresponding element inTagged Tree, which is a slightly modified strati- terchangeably. Internal nodes are represented by the structure fied tree, a ...
Chapter 12 Trees - Margaret M. Fleck
... finite. We will also assume that each set of siblings is ordered from left to right, because this is common in computer science applications. A leaf node is a node that has no children. A node that does have children is known as an internal node. The root is an internal node, except in the special c ...
... finite. We will also assume that each set of siblings is ordered from left to right, because this is common in computer science applications. A leaf node is a node that has no children. A node that does have children is known as an internal node. The root is an internal node, except in the special c ...
Succinct Data Structures
... Theorem (Golynski): Given a bit vector of length n and an “index” (extra data) of size r bits, let t be the number of bits probed to perform rank (or select) then: r=Ω(n (lg t)/t). Proof idea: Argue to reconstructing the entire string with too few rank queries (similarly for select) Corollary (Golyn ...
... Theorem (Golynski): Given a bit vector of length n and an “index” (extra data) of size r bits, let t be the number of bits probed to perform rank (or select) then: r=Ω(n (lg t)/t). Proof idea: Argue to reconstructing the entire string with too few rank queries (similarly for select) Corollary (Golyn ...
Data Structures Question Bank Short Answers Section 1
... 2. Adjacency matrix representation is preferred for dense or sparse graphs? Explain. 3. Adjacency list representation is preferred for dense or sparse graphs? Explain. 4. What is a minimum spanning tree, in reference to a weighted graph? 5. Why are shortest path problems important? Name an applicati ...
... 2. Adjacency matrix representation is preferred for dense or sparse graphs? Explain. 3. Adjacency list representation is preferred for dense or sparse graphs? Explain. 4. What is a minimum spanning tree, in reference to a weighted graph? 5. Why are shortest path problems important? Name an applicati ...
Powerpoint
... For all nodes in the tree: ▪ All nodes in a left subtree have labels less than the label of the subtree's root ▪ All nodes in a right subtree have labels greater than or equal to the label of the subtree's root ...
... For all nodes in the tree: ▪ All nodes in a left subtree have labels less than the label of the subtree's root ▪ All nodes in a right subtree have labels greater than or equal to the label of the subtree's root ...
II. Dictionaries
... One thing that's important to note about all of the data structures that have been discussed so far is that none of them are well suited to searching their contents. For example, say we have a collection of players in our game. We want to find the player named "Bob" in that collection, because we ha ...
... One thing that's important to note about all of the data structures that have been discussed so far is that none of them are well suited to searching their contents. For example, say we have a collection of players in our game. We want to find the player named "Bob" in that collection, because we ha ...
Advanced Data Structures Spring Semester 2017 Exercise Set 7
... range reporting. The rough idea is as follows: 1. In addition to the vertical rays, extend a horizontal line from each point until the endpoints hit another ray as shown in the left of Fig. 1. (It could be a line segment, a ray or a line.) 2. For a query point p, find out all the regions which are l ...
... range reporting. The rough idea is as follows: 1. In addition to the vertical rays, extend a horizontal line from each point until the endpoints hit another ray as shown in the left of Fig. 1. (It could be a line segment, a ray or a line.) 2. For a query point p, find out all the regions which are l ...
Lecture 16 Student Notes
... [l, n], for each i. With the augmentation, this is equivalent to looking for the $i whose stored value is < l, because this indicates that the previous $i is outside of the interval [l, n]. We can solve this problem with an RMQ query from L15. Find the minimum in O(1) time. Suppose the minimum is fo ...
... [l, n], for each i. With the augmentation, this is equivalent to looking for the $i whose stored value is < l, because this indicates that the previous $i is outside of the interval [l, n]. We can solve this problem with an RMQ query from L15. Find the minimum in O(1) time. Suppose the minimum is fo ...
Binary search tree
In computer science, binary search trees (BST), sometimes called ordered or sorted binary trees, are a particular type of containers: data structures that store ""items"" (such as numbers, names and etc.) in memory. They allow fast lookup, addition and removal of items, and can be used to implement either dynamic sets of items, or lookup tables that allow finding an item by its key (e.g., finding the phone number of a person by name).Binary search trees keep their keys in sorted order, so that lookup and other operations can use the principle of binary search: when looking for a key in a tree (or a place to insert a new key), they traverse the tree from root to leaf, making comparisons to keys stored in the nodes of the tree and deciding, based on the comparison, to continue searching in the left or right subtrees. On average, this means that each comparison allows the operations to skip about half of the tree, so that each lookup, insertion or deletion takes time proportional to the logarithm of the number of items stored in the tree. This is much better than the linear time required to find items by key in an (unsorted) array, but slower than the corresponding operations on hash tables.They are a special case of the more general B-tree with order equal to two.