ALGORITHMS & DATA STRUCTURES
EXAM QUESTIONS WITH 100%
CORRECT ANSWERS L LATEST
VERSION 2025/2026.
Recursive Algorithms - ANS solve a problem by solving smaller internal instances of a
problem -- work towards a base case.
Selection Sort - ANS Non-stable, in place sort. Has an N-squared order of growth, needs only
one spot of extra space. Works by searching the entire array for the smallest item, then
exchanging it with the first item in the array. Repeats this process down the entire array until it
is sorted.
Insertion Sort - ANS Stable, in place sort with an order of growth which is between N and N-
squared, needs only one spot of extra space and is dependent on the order of the items. Works
by scanning over the list, then inserting the current item to the front of the list where it would
fit sequentially. All the items to the left of the list will be sorted, but may not be in their final
place as the larger items are continuously pushed back to make room for smaller items if
necessary.
ShellSort - ANS Non-stable, in place sort with an order of growth which is undetermined,
though usually given at being N-to-the 6/5. Needs only one spot of extra space. Works as an
extension of insertion sort. It gains speed by allowing exchanges of entries which are far apart,
producing partially sorted arrays which are eventually sorted quickly at the end with an
insertion sort. The idea is to rearrange the array so that every h-th entry yields a sorted
sequence. The array is h-sorted.
1 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED.
, Quick Sort - ANS Non-stable, in place sort with an order of growth of NlogN. Needs lgN of
extra space. It has a probabilistic guarantee. Works by making use of a divide and conquer
method. The array is divided into two parts, and then the parts are sorted independently. An
arbitrary value is chosen as the partition. Afterwards, all items which are larger than this value
go to the right of it, and all items which are less than this value go to the left of it.
We arbitrarily choose a[lo] as a partitioning item. Then we scan from the left end of the array
one by one until we find an entry that is greater than a[lo]. At the same time, we are scanning
from a[lo] to the right to find an entry that is less than or equal to a[lo]. Once we find these two
values, we swap them.
Mergesort - ANS Stable sort which is not in place. It has an order of growth of NlogN and
requires N amount of extra space. Works by dividing an array in half continuously into smaller
and smaller arrays. At the lowest level, these arrays are sorted and then merged together after
sorting in the reverse order they were divided apart in.
Heap Sort - ANS Non-stable, in place sort which has an order of growth of NlogN. Requires
only one spot of extra space. Works like an improved version of selection sort. It divides its input
into a sorted and unsorted region, and iteratively shrinks the unsorted region by extracting the
smallest element and moving it into the sorted region. It will make use of a heap structure
instead of a linear time search to find the minimum.
Unordered Linked List - ANS Data structure with non-efficently supported operations. Is
unordered. Has a worst case cost of search and insertion at N, an average case cost of insertion
at N, and an average case cost of searching at N/2.
Binary Search - ANS An ordered array of data which has efficiently supported operations. The
worst and average case of a search using this structure is lgN. The Worst case of an insertion is
N, and the average case of an insertion is N/2.
Directed Graph - ANS Given a path connecting vertices A and B you can only travel in 1
direction
Path - ANS The edge, or link between two vertices
2 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED.
EXAM QUESTIONS WITH 100%
CORRECT ANSWERS L LATEST
VERSION 2025/2026.
Recursive Algorithms - ANS solve a problem by solving smaller internal instances of a
problem -- work towards a base case.
Selection Sort - ANS Non-stable, in place sort. Has an N-squared order of growth, needs only
one spot of extra space. Works by searching the entire array for the smallest item, then
exchanging it with the first item in the array. Repeats this process down the entire array until it
is sorted.
Insertion Sort - ANS Stable, in place sort with an order of growth which is between N and N-
squared, needs only one spot of extra space and is dependent on the order of the items. Works
by scanning over the list, then inserting the current item to the front of the list where it would
fit sequentially. All the items to the left of the list will be sorted, but may not be in their final
place as the larger items are continuously pushed back to make room for smaller items if
necessary.
ShellSort - ANS Non-stable, in place sort with an order of growth which is undetermined,
though usually given at being N-to-the 6/5. Needs only one spot of extra space. Works as an
extension of insertion sort. It gains speed by allowing exchanges of entries which are far apart,
producing partially sorted arrays which are eventually sorted quickly at the end with an
insertion sort. The idea is to rearrange the array so that every h-th entry yields a sorted
sequence. The array is h-sorted.
1 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED.
, Quick Sort - ANS Non-stable, in place sort with an order of growth of NlogN. Needs lgN of
extra space. It has a probabilistic guarantee. Works by making use of a divide and conquer
method. The array is divided into two parts, and then the parts are sorted independently. An
arbitrary value is chosen as the partition. Afterwards, all items which are larger than this value
go to the right of it, and all items which are less than this value go to the left of it.
We arbitrarily choose a[lo] as a partitioning item. Then we scan from the left end of the array
one by one until we find an entry that is greater than a[lo]. At the same time, we are scanning
from a[lo] to the right to find an entry that is less than or equal to a[lo]. Once we find these two
values, we swap them.
Mergesort - ANS Stable sort which is not in place. It has an order of growth of NlogN and
requires N amount of extra space. Works by dividing an array in half continuously into smaller
and smaller arrays. At the lowest level, these arrays are sorted and then merged together after
sorting in the reverse order they were divided apart in.
Heap Sort - ANS Non-stable, in place sort which has an order of growth of NlogN. Requires
only one spot of extra space. Works like an improved version of selection sort. It divides its input
into a sorted and unsorted region, and iteratively shrinks the unsorted region by extracting the
smallest element and moving it into the sorted region. It will make use of a heap structure
instead of a linear time search to find the minimum.
Unordered Linked List - ANS Data structure with non-efficently supported operations. Is
unordered. Has a worst case cost of search and insertion at N, an average case cost of insertion
at N, and an average case cost of searching at N/2.
Binary Search - ANS An ordered array of data which has efficiently supported operations. The
worst and average case of a search using this structure is lgN. The Worst case of an insertion is
N, and the average case of an insertion is N/2.
Directed Graph - ANS Given a path connecting vertices A and B you can only travel in 1
direction
Path - ANS The edge, or link between two vertices
2 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED.
