DATA STRUCTURES AND ALGORITHMS IN
CPLUSPLUS EXAM PREP QUESTIONS AND
ANSWERS FULL SOLUTION PREMIUM
LEARNING RESOURCE
●● Divide and Conquer
Answer: works by recursively breaking down a problem into two or
more sub problems until the problems become simple enough to be
solved directly. An example would be mergesort.
●● Recursive Algorithms
Answer: solve a problem by solving smaller internal instances of a
problem -- work towards a base case.
●● Dynamic Programming
Answer: Break down a problem into smaller and smaller subproblems.
At their lowest levels, the subproblems are solved and their answers
stored in memory. These saved answers are used again with other larger
(sub)problems which may call for a recomputation of the same
information for their own answer. Reusing the stored answers allows for
optimization by combining the answers of previously solved
subproblems.
●● Selection Sort
,Answer: 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
Answer: 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
Answer: 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.
●● Quick Sort
Answer: 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.
●● 3-Way Quick Sort
Answer: Non-stable, in place sort with an order of growth between N
and NlogN. Needs lgN of extra space. Is probabilistic and dependent on
the distribution of input keys.
●● Mergesort
Answer: 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
Answer: 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.
●● Counting Sort (Key Indexed sort)
Answer: An integer sorting algorithm which counts the number of
objects that have a distinct key value, and then used arithmetic on those
countes to determine the positions of each key value in the output array.
It cannot handle large keys efficiently, and is often used as a subroutine
for other sorting algorithms such as radix sort.
Has a time complexity of N.
●● Unordered Linked List
Answer: 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
Answer: 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.
CPLUSPLUS EXAM PREP QUESTIONS AND
ANSWERS FULL SOLUTION PREMIUM
LEARNING RESOURCE
●● Divide and Conquer
Answer: works by recursively breaking down a problem into two or
more sub problems until the problems become simple enough to be
solved directly. An example would be mergesort.
●● Recursive Algorithms
Answer: solve a problem by solving smaller internal instances of a
problem -- work towards a base case.
●● Dynamic Programming
Answer: Break down a problem into smaller and smaller subproblems.
At their lowest levels, the subproblems are solved and their answers
stored in memory. These saved answers are used again with other larger
(sub)problems which may call for a recomputation of the same
information for their own answer. Reusing the stored answers allows for
optimization by combining the answers of previously solved
subproblems.
●● Selection Sort
,Answer: 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
Answer: 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
Answer: 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.
●● Quick Sort
Answer: 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.
●● 3-Way Quick Sort
Answer: Non-stable, in place sort with an order of growth between N
and NlogN. Needs lgN of extra space. Is probabilistic and dependent on
the distribution of input keys.
●● Mergesort
Answer: 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
Answer: 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.
●● Counting Sort (Key Indexed sort)
Answer: An integer sorting algorithm which counts the number of
objects that have a distinct key value, and then used arithmetic on those
countes to determine the positions of each key value in the output array.
It cannot handle large keys efficiently, and is often used as a subroutine
for other sorting algorithms such as radix sort.
Has a time complexity of N.
●● Unordered Linked List
Answer: 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
Answer: 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.
