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computer notes - Data Structures - 30
computer notes - Data Structures - 30ecomputernotes The document discusses different techniques for improving the efficiency of union-find algorithms, including union-by-size, path compression, and union-by-height. Union-by-size works by making the root of the smaller tree the child of the larger tree during a union operation, keeping tree heights small. Path compression further optimizes find operations by updating the parent pointers along the search path. Together these optimizations allow union-find algorithms to run in almost linear time for practical purposes.
computer notes - Data Structures - 39
computer notes - Data Structures - 39ecomputernotes The document discusses divide and conquer algorithms for sorting, specifically mergesort and quicksort. It explains that mergesort works by recursively splitting a list in half, sorting the halves, and then merging the sorted halves together. Quicksort works by picking a pivot value and partitioning the list into elements less than and greater than the pivot, before recursively sorting the sublists. Both algorithms run in O(n log n) time.
computer notes - Data Structures - 11
computer notes - Data Structures - 11ecomputernotes The document discusses different types of tree data structures, focusing on binary trees. It defines a binary tree recursively as a finite set of elements that is either empty or partitioned into three disjoint subsets containing a single root element and left and right subtrees. The document outlines common binary tree terminology like nodes, parents, descendants, and levels. It also describes complete binary trees where all levels are fully filled except the lowest, which has nodes filled from left to right.
computer notes - Data Structures - 20
computer notes - Data Structures - 20ecomputernotes The document discusses AVL trees and balanced binary search trees. It provides the following key points:
1) An AVL tree is a self-balancing binary search tree where the height of the two child subtrees of every node differ by at most one.
2) A balanced binary search tree is one where the height of the left and right subtrees of each node differ by no more than one.
3) Inserting new nodes can cause the tree to become unbalanced if the insertion breaks the height balance property. Rotations may be needed to rebalance the tree.
computer notes - Data Structures - 15
computer notes - Data Structures - 15ecomputernotes The document discusses level-order traversal of binary trees. Level-order traversal visits all nodes at each level from left to right before moving to the next level. This can be implemented by using a queue, where the left and right children of each dequeued node are enqueued. The code provided traverses a binary tree using this level-order technique.
computer notes - Data Structures - 28
computer notes - Data Structures - 28ecomputernotes The document discusses equivalence relations and the union-find algorithm. It defines what makes a binary relation an equivalence relation by having the properties of reflexivity, symmetry, and transitivity. It gives examples like electrical connectivity being an equivalence relation. The union-find algorithm can be used to dynamically determine if elements are in the same equivalence class based on the given relations, by performing find and union operations in time proportional to m+n for m finds and n-1 unions.
computer notes - Data Structures - 19
computer notes - Data Structures - 19ecomputernotes The document discusses various aspects of balanced binary search trees, including:
1) Const keyword can be used to mark parameters and return values as constant to prevent unintended modification.
2) AVL trees are binary search trees where the heights of left and right subtrees differ by at most 1.
3) For a binary search tree to be balanced, the heights of left and right subtrees should be close to equal to avoid a skewed or degenerate tree structure.
computer notes - Data Structures - 31
computer notes - Data Structures - 31ecomputernotes Union-find data structures can be used to efficiently generate random mazes. A maze can be represented as a grid of cells where each cell is initially isolated by walls. Removing walls corresponds to union operations, joining the cells' sets. A maze is generated by randomly performing unions until the entrance and exit cells are in the same set, connected by a path through the maze.
computer notes - Data Structures - 4
computer notes - Data Structures - 4ecomputernotes The document discusses different types of linked lists, including singly linked lists, doubly linked lists, and circularly linked lists. It provides code examples for implementing linked lists in C++ and compares the time complexity of different linked list operations. It also describes how a circularly linked list can be used to solve the Josephus problem of eliminating people seated in a circle.
computer notes - Data Structures - 13
computer notes - Data Structures - 13ecomputernotes The document discusses binary search trees and different ways to traverse them. It explains that traversing a binary search tree can be done in preorder, inorder, or postorder fashion by recursively visiting the left child, then the node, then the right child in different orders. Searching for a value in a balanced binary search tree takes O(log n) time, while searching an unsorted linked list takes O(n) time.
computer notes - Data Structures - 16
computer notes - Data Structures - 16ecomputernotes The document discusses deleting nodes from a binary search tree (BST). There are three cases to consider when deleting a node: 1) if the node is a leaf, it can be deleted immediately, 2) if the node has one child, its parent pointer is redirected to the child node, 3) if the node has two children, it is replaced with its inorder successor. The algorithm and C++ code for deleting nodes from a BST is presented.
computer notes - Data Structures - 22
computer notes - Data Structures - 22ecomputernotes The document discusses deletion in AVL trees and outlines 5 cases to consider when deleting nodes from an AVL tree. It also discusses expression trees and parse trees, providing examples of an expression tree for a mathematical expression and a parse tree for an SQL query. Other uses of binary trees mentioned include their use in compilers for expression trees, parse trees, and abstract syntax trees.
computer notes - Data Structures - 35
computer notes - Data Structures - 35ecomputernotes The document discusses various data structures including skip lists, AVL trees, and hashing. It explains that skip lists allow for logarithmic-time operations and are simple to implement. Hashing provides constant-time operations by mapping keys to array indices via a hash function, but collisions must be handled. Common hash functions discussed include summing character codes or converting to a number in a prime base.
computer notes - Data Structures - 36
computer notes - Data Structures - 36ecomputernotes The document discusses different methods for handling collisions in hash tables, which occur when two keys hash to the same slot. It describes linear probing, where the next empty slot is used to store the colliding key; quadratic probing which uses a quadratic function to determine subsequent slots; and chaining, where each slot contains a linked list of colliding keys. It notes the advantages and disadvantages of each approach.
computer notes - Data Structures - 14
computer notes - Data Structures - 14ecomputernotes The document discusses recursion and different traversal methods for binary trees. It explains how the call stack is used during recursive function calls and shows examples of preorder and inorder recursive tree traversals. It then describes how to perform non-recursive inorder traversal using an explicit stack. Finally, it introduces level-order traversal, which visits all nodes at each level from left to right before proceeding to the next level.
computer notes - Data Structures - 10
computer notes - Data Structures - 10ecomputernotes The document describes a simulation of customer transactions at a bank with 4 tellers. It discusses how customers arrive at certain times, are assigned to the shortest teller queue if a teller is available, or must wait in line if all tellers are busy. The simulation proceeds by maintaining a priority queue of upcoming arrival and departure events and processing customers from the queue. Statistics like total wait time are tracked to calculate the average time customers spend at the bank. Code for implementing the simulation with data structures like queues and priority queues is also presented.
computer notes - Data Structures - 5
computer notes - Data Structures - 5ecomputernotes The document discusses implementing a stack data structure using both an array and linked list. A stack is a last-in, first-out data structure where elements can only be inserted or removed from one end, called the top. The key stack operations of push, pop, top, isEmpty and isFull are described. Implementing a stack with an array allows for constant time operations but has size limitations, while a linked list avoids size limits but has slower insertion and removal.
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computer notes - Data Structures - 28
computer notes - Data Structures - 28ecomputernotes The document discusses equivalence relations and the union-find algorithm. It defines what makes a binary relation an equivalence relation by having the properties of reflexivity, symmetry, and transitivity. It gives examples like electrical connectivity being an equivalence relation. The union-find algorithm can be used to dynamically determine if elements are in the same equivalence class based on the given relations, by performing find and union operations in time proportional to m+n for m finds and n-1 unions.
computer notes - Data Structures - 19
computer notes - Data Structures - 19ecomputernotes The document discusses various aspects of balanced binary search trees, including:
1) Const keyword can be used to mark parameters and return values as constant to prevent unintended modification.
2) AVL trees are binary search trees where the heights of left and right subtrees differ by at most 1.
3) For a binary search tree to be balanced, the heights of left and right subtrees should be close to equal to avoid a skewed or degenerate tree structure.
computer notes - Data Structures - 31
computer notes - Data Structures - 31ecomputernotes Union-find data structures can be used to efficiently generate random mazes. A maze can be represented as a grid of cells where each cell is initially isolated by walls. Removing walls corresponds to union operations, joining the cells' sets. A maze is generated by randomly performing unions until the entrance and exit cells are in the same set, connected by a path through the maze.
computer notes - Data Structures - 4
computer notes - Data Structures - 4ecomputernotes The document discusses different types of linked lists, including singly linked lists, doubly linked lists, and circularly linked lists. It provides code examples for implementing linked lists in C++ and compares the time complexity of different linked list operations. It also describes how a circularly linked list can be used to solve the Josephus problem of eliminating people seated in a circle.
computer notes - Data Structures - 13
computer notes - Data Structures - 13ecomputernotes The document discusses binary search trees and different ways to traverse them. It explains that traversing a binary search tree can be done in preorder, inorder, or postorder fashion by recursively visiting the left child, then the node, then the right child in different orders. Searching for a value in a balanced binary search tree takes O(log n) time, while searching an unsorted linked list takes O(n) time.
computer notes - Data Structures - 16
computer notes - Data Structures - 16ecomputernotes The document discusses deleting nodes from a binary search tree (BST). There are three cases to consider when deleting a node: 1) if the node is a leaf, it can be deleted immediately, 2) if the node has one child, its parent pointer is redirected to the child node, 3) if the node has two children, it is replaced with its inorder successor. The algorithm and C++ code for deleting nodes from a BST is presented.
computer notes - Data Structures - 22
computer notes - Data Structures - 22ecomputernotes The document discusses deletion in AVL trees and outlines 5 cases to consider when deleting nodes from an AVL tree. It also discusses expression trees and parse trees, providing examples of an expression tree for a mathematical expression and a parse tree for an SQL query. Other uses of binary trees mentioned include their use in compilers for expression trees, parse trees, and abstract syntax trees.
computer notes - Data Structures - 35
computer notes - Data Structures - 35ecomputernotes The document discusses various data structures including skip lists, AVL trees, and hashing. It explains that skip lists allow for logarithmic-time operations and are simple to implement. Hashing provides constant-time operations by mapping keys to array indices via a hash function, but collisions must be handled. Common hash functions discussed include summing character codes or converting to a number in a prime base.
computer notes - Data Structures - 36
computer notes - Data Structures - 36ecomputernotes The document discusses different methods for handling collisions in hash tables, which occur when two keys hash to the same slot. It describes linear probing, where the next empty slot is used to store the colliding key; quadratic probing which uses a quadratic function to determine subsequent slots; and chaining, where each slot contains a linked list of colliding keys. It notes the advantages and disadvantages of each approach.
computer notes - Data Structures - 14
computer notes - Data Structures - 14ecomputernotes The document discusses recursion and different traversal methods for binary trees. It explains how the call stack is used during recursive function calls and shows examples of preorder and inorder recursive tree traversals. It then describes how to perform non-recursive inorder traversal using an explicit stack. Finally, it introduces level-order traversal, which visits all nodes at each level from left to right before proceeding to the next level.
computer notes - Data Structures - 10
computer notes - Data Structures - 10ecomputernotes The document describes a simulation of customer transactions at a bank with 4 tellers. It discusses how customers arrive at certain times, are assigned to the shortest teller queue if a teller is available, or must wait in line if all tellers are busy. The simulation proceeds by maintaining a priority queue of upcoming arrival and departure events and processing customers from the queue. Statistics like total wait time are tracked to calculate the average time customers spend at the bank. Code for implementing the simulation with data structures like queues and priority queues is also presented.
computer notes - Data Structures - 5
computer notes - Data Structures - 5ecomputernotes The document discusses implementing a stack data structure using both an array and linked list. A stack is a last-in, first-out data structure where elements can only be inserted or removed from one end, called the top. The key stack operations of push, pop, top, isEmpty and isFull are described. Implementing a stack with an array allows for constant time operations but has size limitations, while a linked list avoids size limits but has slower insertion and removal.