CS 2133: Data Structures
... if(xval)TreeDelete(root->left, x);
else if(x>root->val)TreeDelete(root->right, x);
else { // we have found it so lets delete it
// tree points at it right!?
// If No children we just delete it
if(root->left==NULL && root->right==NULL){
...
... if(x
- Online Guru Jee
... • To develop proficiency in the specification, representation, and implementation of Data Types and Data Structures. • To be able to carry out the Analysis of various Algorithms for mainly Time and Space Complexity. • To get a good understanding of applications of Data Structures. • To develop a bas ...
... • To develop proficiency in the specification, representation, and implementation of Data Types and Data Structures. • To be able to carry out the Analysis of various Algorithms for mainly Time and Space Complexity. • To get a good understanding of applications of Data Structures. • To develop a bas ...
Lists and Trees (continued)
... has more than one potential successor • Defines a partial order CS-2301 D-term 2009 ...
... has more than one potential successor • Defines a partial order CS-2301 D-term 2009 ...
Mid-term exam
... (a) Apply insertion sort to the array [4, 2, 3, 5, 1]. Give (at least) the intermediate result after every iteration of the for-loop. (b) Explain why the worst-case time complexity of insertion sort is in O(n2 ). Exercise 3. (8 points) This exercise is concerned with singly linked lists. (a) For a ...
... (a) Apply insertion sort to the array [4, 2, 3, 5, 1]. Give (at least) the intermediate result after every iteration of the for-loop. (b) Explain why the worst-case time complexity of insertion sort is in O(n2 ). Exercise 3. (8 points) This exercise is concerned with singly linked lists. (a) For a ...
Lecture 4
... Overhead depends on which nodes store data values (all nodes, or just the leaves), whether the leaves store child pointers, and whether the tree is a full binary tree. From the Full Binary Tree Theorem: Half of the pointers are null. Ex: Full tree, all nodes store data, with two pointers to children ...
... Overhead depends on which nodes store data values (all nodes, or just the leaves), whether the leaves store child pointers, and whether the tree is a full binary tree. From the Full Binary Tree Theorem: Half of the pointers are null. Ex: Full tree, all nodes store data, with two pointers to children ...
Name
... one, in addition to its left and right subtrees. Question 6. (12 points) Complete the definition of the following Java method so that, given a reference to some node in a binary search tree (implemented with the above node data structure) the method returns a reference to the node that precedes it i ...
... one, in addition to its left and right subtrees. Question 6. (12 points) Complete the definition of the following Java method so that, given a reference to some node in a binary search tree (implemented with the above node data structure) the method returns a reference to the node that precedes it i ...
1 Trees 1. What is a tree • The tree is a fundamental structure. The
... The depth of a node in a tree is the length of the path from the root to the node. Thus the depth of the root is always 0. The depth of any node is 1 more than the depth of its parents. The height of a node in a tree is the length of the path from the node to the deepest leaf. Nodes with the same pa ...
... The depth of a node in a tree is the length of the path from the root to the node. Thus the depth of the root is always 0. The depth of any node is 1 more than the depth of its parents. The height of a node in a tree is the length of the path from the node to the deepest leaf. Nodes with the same pa ...
Presentation on Implementing Binary Trees
... • Call this method recursively (effectively redefining this node as root), such that if the node pointed at is empty (base case) the new node is inserted, if not, check whether new node belongs left or right and then... ...
... • Call this method recursively (effectively redefining this node as root), such that if the node pointed at is empty (base case) the new node is inserted, if not, check whether new node belongs left or right and then... ...
Problem Set 3 - Princeton CS
... 1. Give the details of an efficient algorithm for “c-reduction” (complement-reduction) of a PQ-tree. Given a PQ-tree T and a subset S of the leaves of T, complement reduction produces the tree whose allowed leaf permutations are those allowed by T that in addition arrange all leaves not in S consecu ...
... 1. Give the details of an efficient algorithm for “c-reduction” (complement-reduction) of a PQ-tree. Given a PQ-tree T and a subset S of the leaves of T, complement reduction produces the tree whose allowed leaf permutations are those allowed by T that in addition arrange all leaves not in S consecu ...
1 Review: Data Structures 2 Heaps: A quick review
... is a binary tree which stores values at nodes with the following order relation. The value at a node is larger than the value of its left child and is at most the value of its right child. Exercise. Write a procedure to output the values of a binary search tree in sorted order. It should visit each ...
... is a binary tree which stores values at nodes with the following order relation. The value at a node is larger than the value of its left child and is at most the value of its right child. Exercise. Write a procedure to output the values of a binary search tree in sorted order. It should visit each ...
binary search tree
... • Dequeue, Deque, Deq, Delete, and Remove are used for the deletion operation. ...
... • Dequeue, Deque, Deq, Delete, and Remove are used for the deletion operation. ...
Solution - University of Toronto
... correctly, and that you explain and justify what you are doing. Marks may be deducted for incorrect/ambiguous use of notation and terminology, and for making incorrect, unjustified or vague claims in your solutions. 1. Let D be an ordered Dictionary with n items implemented with an AVL tree. Show ho ...
... correctly, and that you explain and justify what you are doing. Marks may be deducted for incorrect/ambiguous use of notation and terminology, and for making incorrect, unjustified or vague claims in your solutions. 1. Let D be an ordered Dictionary with n items implemented with an AVL tree. Show ho ...
Trees
... Definition and Tree Trivia Graph-theoretic definition of a Tree: A tree is a graph for which there exists a node, called root, such that: -- for any node x, there exists exactly one path from the root to x Recursive Definition of a Tree: A tree is either: a. empty, or b. it has a node called the ro ...
... Definition and Tree Trivia Graph-theoretic definition of a Tree: A tree is a graph for which there exists a node, called root, such that: -- for any node x, there exists exactly one path from the root to x Recursive Definition of a Tree: A tree is either: a. empty, or b. it has a node called the ro ...
Applications of Trees
... But the greedy approach may not always lead to an optimal solution overall for all problems The key is knowing which problems will work with this approach and which will not ...
... But the greedy approach may not always lead to an optimal solution overall for all problems The key is knowing which problems will work with this approach and which will not ...
Searching: Binary Tress
... – Use search operation to locate the insertion position or already existing item – Use a parent point pointing to the parent of the node currently being examined as descending the ...
... – Use search operation to locate the insertion position or already existing item – Use a parent point pointing to the parent of the node currently being examined as descending the ...
if - Read
... The code is broken into two cases If the right subtree of node x is nonempty, then the successor of x is just the left-most node in the right subtree, which found by calling Tree-Minimum(right) If the right subtree of x is empty and x has a successor y, then y is the lowest ancestor of x whose left ...
... The code is broken into two cases If the right subtree of node x is nonempty, then the successor of x is just the left-most node in the right subtree, which found by calling Tree-Minimum(right) If the right subtree of x is empty and x has a successor y, then y is the lowest ancestor of x whose left ...
Trees Informal Definition: Tree Formal Definition: Tree
... Let T be a (proper) binary tree with n nodes, and let h denote the height of T: 1. The number of external nodes in T is at least h+1 and at most 2h. 2. The number of internal nodes in T is at least h and at most 2h-1. 3. The total number of nodes in T is at least 2h+1 and at most 2h+1-1. 4. The heig ...
... Let T be a (proper) binary tree with n nodes, and let h denote the height of T: 1. The number of external nodes in T is at least h+1 and at most 2h. 2. The number of internal nodes in T is at least h and at most 2h-1. 3. The total number of nodes in T is at least 2h+1 and at most 2h+1-1. 4. The heig ...
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.