WGU C949 DATA STRUCTURES AND ALGORITHMS OA
EXAM TEST BANK QUESTIONS AND WELL ELABORATED
ANSWERS TOP GRADED
bucket - each array element in a hash table
ie A 100 elements hash table has 100 buckets
modulo hash function - computes a bucket index from the items key.
It will map (num_keys / num_buckets) keys to each bucket.
ie... keys range 0 to 49 will have 5 keys per bucket.
= 5
hash table searching - Hash tables support fast search, insert, and remove.
Requires on average O(1)
Linear search requires O(N)
modulo operator % - common has function uses this. which computes the integer
remainder when dividing two numbers.
Ex: For a 20 element hash table, a hash function of key % 20 will map keys to bucket
indices 0 to 19.
Max-Heap - A binary tree that maintains the simple property that a node's key is greater
than or equal to the node's childrens' keys. (Actually, a max-heap may be any tree, but
is commonly a binary tree).
Array - A data structure that stores an ordered list of items, with each item is directly
accessible by a positional index.
Linked List - A data structure that stores ordered list of items in nodes, where each node
stores data and has a pointer to the next node.
Bianary Search Tree - A data structure in which each node stores data and has up to
two children, known as a left child and a right child.
Hash Table - A data structure that stores unordered items by mapping (or hashing)
each item to a location in an array (or vector).
Hashing - mapping each item to a location in an array (in a hash table).
Chaining - handles hash table collisions by using a list for each bucket, where each list
may store multiple items that map to the same bucket.
, Hash key - value used to map an index
*a max-heap's root always has the maximum key in the entire tree.
Heap storage - Heaps are typically stored using arrays. Given a tree representation of a
heap, the heap's array form is produced by traversing the tree's levels from left to right
and top to bottom. The root node is always the entry at index 0 in the array, the root's
left child is the entry at index 1, the root's right child is the entry at index 2, and so on.
Max-heap insert - An insert into a max-heap starts by inserting the node in the tree's last
level, and then swapping the node with its parent until no max-heap property violation
occurs.
The upward movement of a node in a max-heap is sometime called percolating.
Complexity O(logN)
Max-heap remove - Always a removal of the root, and is done by replacing the root with
the last level's last node, and swapping that node with its greatest child until no max-
heap property violation occurs.
Complexity O(logN)
Percolating - The upward movement of a node in a max-heap
Min-Heap - Similar to a max-heap, but a node's key is less than or equal to its children's
keys.
Heap - Parent and child indices - Because heaps are not implemented with node
structures and parent/child pointers, traversing from a node to parent or child nodes
requires referring to nodes by index. The table below shows parent and child index
formulas for a heap.
ie
1) parent index for node at index 12? 5
*** ((12-1) // 2) = 5 or 12 //2 -1 = 5
2) child indices for a node at index 6? 13 & 14
*** 2 * 6 + 1 = 13 and 2 * 6 + 2 = 14
**Double# and add 1, double# and add 2
Node index Parent Index Child Indices
0 N/A 1, 2
1 0 3, 4
2 0 5, 6
3 1 7, 8
4 1 9, 10
EXAM TEST BANK QUESTIONS AND WELL ELABORATED
ANSWERS TOP GRADED
bucket - each array element in a hash table
ie A 100 elements hash table has 100 buckets
modulo hash function - computes a bucket index from the items key.
It will map (num_keys / num_buckets) keys to each bucket.
ie... keys range 0 to 49 will have 5 keys per bucket.
= 5
hash table searching - Hash tables support fast search, insert, and remove.
Requires on average O(1)
Linear search requires O(N)
modulo operator % - common has function uses this. which computes the integer
remainder when dividing two numbers.
Ex: For a 20 element hash table, a hash function of key % 20 will map keys to bucket
indices 0 to 19.
Max-Heap - A binary tree that maintains the simple property that a node's key is greater
than or equal to the node's childrens' keys. (Actually, a max-heap may be any tree, but
is commonly a binary tree).
Array - A data structure that stores an ordered list of items, with each item is directly
accessible by a positional index.
Linked List - A data structure that stores ordered list of items in nodes, where each node
stores data and has a pointer to the next node.
Bianary Search Tree - A data structure in which each node stores data and has up to
two children, known as a left child and a right child.
Hash Table - A data structure that stores unordered items by mapping (or hashing)
each item to a location in an array (or vector).
Hashing - mapping each item to a location in an array (in a hash table).
Chaining - handles hash table collisions by using a list for each bucket, where each list
may store multiple items that map to the same bucket.
, Hash key - value used to map an index
*a max-heap's root always has the maximum key in the entire tree.
Heap storage - Heaps are typically stored using arrays. Given a tree representation of a
heap, the heap's array form is produced by traversing the tree's levels from left to right
and top to bottom. The root node is always the entry at index 0 in the array, the root's
left child is the entry at index 1, the root's right child is the entry at index 2, and so on.
Max-heap insert - An insert into a max-heap starts by inserting the node in the tree's last
level, and then swapping the node with its parent until no max-heap property violation
occurs.
The upward movement of a node in a max-heap is sometime called percolating.
Complexity O(logN)
Max-heap remove - Always a removal of the root, and is done by replacing the root with
the last level's last node, and swapping that node with its greatest child until no max-
heap property violation occurs.
Complexity O(logN)
Percolating - The upward movement of a node in a max-heap
Min-Heap - Similar to a max-heap, but a node's key is less than or equal to its children's
keys.
Heap - Parent and child indices - Because heaps are not implemented with node
structures and parent/child pointers, traversing from a node to parent or child nodes
requires referring to nodes by index. The table below shows parent and child index
formulas for a heap.
ie
1) parent index for node at index 12? 5
*** ((12-1) // 2) = 5 or 12 //2 -1 = 5
2) child indices for a node at index 6? 13 & 14
*** 2 * 6 + 1 = 13 and 2 * 6 + 2 = 14
**Double# and add 1, double# and add 2
Node index Parent Index Child Indices
0 N/A 1, 2
1 0 3, 4
2 0 5, 6
3 1 7, 8
4 1 9, 10
