VERSION 2 DATA STRUCTURES AND
ALGORITHMS I 2026 EXAM PREP STUDY GUIDE
COMPREHENSIVE SOLUTIONS
◉ Linked List. Answer: 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. Answer: 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. Answer: A data structure that stores unordered items
by mapping (or hashing) each item to a location in an array (or
vector).
◉ Hashing. Answer: mapping each item to a location in an array (in a
hash table).
◉ Chaining. Answer: 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. Answer: value used to map an index
◉ bucket. Answer: each array element in a hash table
ie A 100 elements hash table has 100 buckets
◉ modulo hash function. Answer: 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. Answer: Hash tables support fast search,
insert, and remove.
Requires on average O(1)
Linear search requires O(N)
◉ modulo operator %. Answer: 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. Answer: 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).
*a max-heap's root always has the maximum key in the entire tree.
◉ Heap storage. Answer: 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. Answer: 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. Answer: 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.
ALGORITHMS I 2026 EXAM PREP STUDY GUIDE
COMPREHENSIVE SOLUTIONS
◉ Linked List. Answer: 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. Answer: 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. Answer: A data structure that stores unordered items
by mapping (or hashing) each item to a location in an array (or
vector).
◉ Hashing. Answer: mapping each item to a location in an array (in a
hash table).
◉ Chaining. Answer: 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. Answer: value used to map an index
◉ bucket. Answer: each array element in a hash table
ie A 100 elements hash table has 100 buckets
◉ modulo hash function. Answer: 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. Answer: Hash tables support fast search,
insert, and remove.
Requires on average O(1)
Linear search requires O(N)
◉ modulo operator %. Answer: 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. Answer: 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).
*a max-heap's root always has the maximum key in the entire tree.
◉ Heap storage. Answer: 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. Answer: 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. Answer: 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.
