fib

1. Self-Assessment Questions 1
1. The rules for performing
arithmetic using Arabic numerals
were originally known as
_____________.
2. The efficiency of algorithms
depends upon ____________,
________ and __________
consumption.
3. An algorithm is considered as
the cornerstone of ____________.
4. To analyze an algorithm is to
determine the amount of
________ necessary to execute it.
5. __________ algorithms are
used to combine to sets of
elements to form a single set
according to some criteria.
6. ___________ is the expression
of an algorithm in a programming
language with all the language
specific codes.
7. An algorithm that invokes itself
within the process is called
_______.
8. ______ is the method of
expressing the upper bound of an
algorithm's running time.
9. _____________ is defined as
the number of memory cells which
an algorithm needs.
10. A ____________ algorithm
converts the solution to a simpler
sub problem to arrive at the
correct solution.
11. A ______________ algorithm
simply tries all possibilities until a
satisfactory solution is found.
12. ___________ algorithms are
based on a depth-first recursive
search.
13. A ______ is a set of data
elements grouped together under
one name.
14. _________ data structure has
all the elements of same data type
in it.
15. For ____________ data
structure, the memory is allocated
at the compile time itself.
Self-Assessment Questions
1. Algorism 2. Speed, size,
resources
3. Good programming
4. Resources 5. Merging
6. Programs 7. Direct recursive
8. Big – O 9. Space complexity
10. Simple recursive
11. Brute force 12.
Backtracking
13. Data structure 14.
Homogeneous
15. Static
Self-Assessment Questions
2
1.The ________ of an algorithm
can be determined by calculating
its performance.
2.___________ of an algorithm is
the amount of time required by an
algorithm to execute.
3.If an algorithm takes least
amount of time to execute a
specific set of inputs then it is
called __________ time
complexity.
4.The method of calculating
primitive operations produces a
computational model called
_______________.
5._________ describes how to
count the maximum number of
primitive operations an algorithm
executes.
6.Recursive procedure should
define a ________ which is small
enough to solve without using
recursion.
7.__________ technique is used to
perform an amortized analysis
method based on a financial
model.
8.If you can setup such a scheme
called amortization scheme then
each operation in the series has
an_______.
9._____________ technique is
used to perform an amortized
analysis method based on an
energy model.
10.The running time of the
algorithm prefixAverages1 is
_______.
11.The running time of the
algorithm prefixAverages2 is
_______.
12.In prefixAverages2 algorithm
________ is the time taken for
initiating the variable s.
Self-Assessment Questions
1.Efficiency 2.Time
complexity
3.Best case
4.Random assess machine
5.Counting primitive operations
6.Base case 7.Accounting
method
8.Amortised running time O(a)
9.Potential function method
10.O(n2) 11.O(n)
12.O(1)
Self-Assessment Questions 3
1. ___________ is more accurate
than Big Oh notation and Omega
notation.
2. ____________ asymptotic
notation is a simple notational
convenience.
3. ___________ depicts the
running time between the upper
bound and lower bound.
4. Tower of Hanoi is a ________
puzzle.
5. The time required to perform a
step should always bound above
by a ________________.
6. ____________ is of no
importance between two
operations for the algorithm’s
basic operation.
Self-Assessment Questions
1. Theta notation 2.
Conditional
3. Theta notation 4.
Mathematical
5. Constant 6. Choice
Self-Assessment Questions
4
1. _________ is defined as the
process that refers itself to simplify
a problem.
2. _____________ need very few
lines of code as it performs the
same process again and again on
different data.
3. In the towers of Hanoi problem,
if the numbers of disks is n, the
number of steps will be
___________.
4. ___________________ of
algorithm means analyzing the
behavior of the algorithm with a
specific set of inputs.
5. We can measure efficiency of
algorithms using
________________ and
_______________ methods.
6. The __________ analysis of the
algorithm makes it easy to study
7. _________________ is defined
as a technique which uses images
to convey the information about
algorithms.
8. ___________ visualization is the
type of visualization which uses
still images to illustrate the
algorithm.
9. ___________ visualization is the
type of visualization which uses
animations to illustrate the
algorithm. This is also known as
algorithm animation.
Self-Assessment Questions
1. Recursion 2. Recursive
algorithms
3. 2n-1 4. Empirical analysis
5. Counters, system clocking
6. Pictorial 7. Algorithm
visualization
8. Static algorithm
9. Dynamic algorithm
Self-Assessment Questions
5
1. A value that satisfies the
constraint is called a ___________.
2. ____________ is a function that
is associated with an optimization
problem determining how good a
solution is.
3. The running time needed to
determine whether a possible
value of a feasible solution is O(n)
and the time required to compute
the objective function is also O(n)
is ________.
4. Selection sort is one of the
simplest and ________ sorting
techniques.
5. Bubble sort has __________,
best and average case run-time of
O(n2).
6. ______________________ is
the simplest sorting algorithm.
7. ________________ is also
known as linear search.
8. We program sequential search
in an array by _________an index
variable until it reaches the last
index.
9. In this pseudocode
implementation, we execute the
__________ only after all list items
are examined with none matching.
10. Exhaustive search
implementation is more important
than _________.
11. Exhaustive search algorithm
gives the ______________ for
every candidate that is a solution
to the given instance P.
12. Exhaustive search is typically
used when the problem size is
___________.
Self Assessment Questions
1. Feasible solution
2. Objective function 3.
O(n2n).
4. Performance oriented 5.
Worst
6. Bubble sort 7. Sequential
search
8. Stepping up 9. Last line
10. Speed 11. Output
12. Limited
Self-Assessment Questions
6
1. Mergesort is a perfect example
of a successful application of the
_________ and ____________
methodology.
2. ____________ is a comparison-
based sorting.
3. What are the three steps
involved in mergesort?
4. If the array has two or more
cells, the algorithm calls the
________ method.
5. Unlike the merge sort, which
breaks up its input elements
according to their position in the
array, quick sort breaks them
according to their ____________.
6. After the partition, if the pivot is
inserted at the boundary between
the ___________ sub-arrays, it will
be in its final sorted position.
7. Binary search is an algorithm for
identifying the position of an
element in a ____________ array.
8. Say if the following statement is
true or false. To find a value in
unsorted array, we need to scan
through only half the elements of
an array.
9. Say if the following statement is
true or false. The benefit of binary
search is that its complexity
depends on the array size
logarithmically.
10. ________________________
methodology can solve most of
the problems regarding binary
trees.
11. The three typical traversals:

2. _____________, _____________,
and _____________ are the most
important Divide and Conquer
algorithms of binary trees.
12. Two kinds of traversal are
_____________ and
_____________.
13. At the expense of a slight
increase in the number of
additions, the strassen’s matrix
multiplication algorithm will
_____________ the total number
of multiplications performed.
14. The normal method of matrix
multiplication of two n X n
matrices takes ___________
operators.
15. By the strassen’s matrix
multiplication algorithm, two 2 X 2
matrices takes 2 only 7
multiplicators and _______
adders.
Self-Assessment Questions
1. Divide, Conquer 2.
Mergesort
3. Divide, recur, conquer
4. Partition 5. Value
6. Left and right 7. Sorted
8. False 9. True
10. Divide and Conquer
11. Pre-order, in-order, post-order
12. Breadth-first traversal, depth-
first traversal 13.
Decrease
14. O( ) 15. 18
Self Assessment Questions
7
1. Decrease and conquer can be
implemented by a
________________ or
____________ approach.
2. Decrease and conquer is also
known as ______________
approach.
3. Decrease and conquer is a
method by which we find a
solution to a given problem based
upon the __________ of a number
of problems.
4. There are ________ major
categories in insertion sort.
5. In insertion sort, the best-case
input is an array that is already
__________.
6. To carry out an insertion sort,
begin at the ______ most element
of the array
7. DFS uses the __________
technique.
8. It is easier to use a ________ to
trace the working of a depth first
search.
9. Depth-first search starts
exploring vertices of a graph at a
_______ vertex.
10. The data structure which is
used to track the working of
Breadth-first search is a
___________.
11. Breadth-first search is an
algorithm which travels in such a
way that all vertices are finished
along every ___________.
12. The data structure which is
used to track the working of
Breadth-first search is a
______________.
13. Topological ordering of a
_________ is a linear ordering of
its nodes.
14. In topological sorting the jobs
are denoted by _________.
15. Being a DAG is also a necessary
condition for
______________sorting to be
possible.
16. Theoretically, the traveling
salesman problem can always be
solved by specifying all
_____________ Hamiltonian
circuits.
17. The cities are represented by
____________ and the roads
between them are shown as
edges.
18. Each of the cities is connected
to another city by a road a
complete
_____________________ is
obtained.
Self Assessment Questions
1. Top down or Bottom-up
2. Incremental 3. Solution
4. Two 5. Sorted
6. Left 7.
Backtracking
8. Time and space 9.
Backtracks
10. Graph 11.
Uninformed
12. Goal 13. Directed
acyclic graph 14. Vertices
15. Topological 16.
Combinatorial
17. Subset 18. Decrease-by-
one
Self Assessment Questions 8
1. _______, ________ & ________
are three instances of transform
and conquer technique.
2. The worst case efficiency of
brute force algorithm is _______.
3. The searching requires _______
comparisons to in the worst case,
when the array is sorted first.
4. Gaussian elimination is an
algorithm for solving systems of
__________ equations.
5. In Gaussian elimination we
make the ________ coefficient
matrix zero.
6. Gaussian elimination can be
used to find the _________of a
matrix.
7. An AVL tree is a _________ tree.
8. The _________________ is the
mirror image of the RL-rotation.
9. The two nodes of 2-3 tree are
___________ and ____________.
10. _________ heap construction
algorithm is less efficient than its
counterpart.
11. A heap can be defined as
________ with keys assigned to its
nodes.
12. The time efficiency of heapsort
is ________ in both worst and
average cases.
13. Greatest common divisor can
be computed easily by ________.
14. The problem of counting a
graph’s paths can be solved with
an algorithm for an appropriate
power of its __________.
15. What is the formula obtained
to find the lcm in the problem
reduction approach to find the
lcm?
Self Assessment Questions
1. Instance simplification, problem
reduction , representation change
2. ө(n2) 3. [log2 n] +1
4. Linear 5. Lower triangular
6. Rank 7. Binary search
8. LR-rotation 9. 2-node, 3-
node
10. Top-down 11. Binary
trees
12. O(n log n) 13. Euclid’s
algorithm
14. Adjacent matrix
15.
Self Assessment Questions 9
1. Input enhancement is based on
___________________ the
instance.
2. The information which is used to
place the elements at proper
positions is accumulated sum of
frequencies which is called as
__________.
3. Sorting is an example of input
enhancement that achieves
___________.
4. Input enhancement is to
_____________ the input pattern.
5. In Horspool’s algorithm, the
characters from the pattern are
matched __________________.
6. The two heuristics in Boyre-
Moore algorithm are
_______________ and
________________.
7. Each slot of a hash table is often
called a _____________.
8. Collision occurs when a hash
function maps two or more keys to
the
____________________________
.
9. When the interval between
probes is computed by another
hash function it is
______________________.
10. As the
______________________
increases the height of the tree
decreases thus speeding access.
11. Access time increases slowly as
the number of records
__________.
12. The insertions in a B-Tree start
from a ________.
Self Assessment Questions
1. Preprocessing 2.
Distribution
3. Time efficiency 4.
Preprocess
5. Right to left
6. Good suffix and bad character
shift
7. Bucket 8. Same hash value
9. Double hashing
10. Branching factor 11.
Increases
12. Leaf node
Self Assessment Questions 10
1. The ____________ and
_____________ are the two
approaches to dynamic
programming.
2. __________ is a technique to
store answers to sub-problems in a
table.
3. The _________________
algorithm is similar to the dynamic
approach.
4. The formula to calculate the nth
Fibonacci series is
_______________.
5. The asymptotic running time
when we first run to calculate the
nth Fibonacci number is _______.
6. To compute the nth Fibonacci
number we followed the
__________ dynamic approach.
7. What formula can we use to find
the value of the binomial
coefficient?
8. The gamma function z! (z
1) allows the binomial coefficient
to be generalized to non-integer
arguments like
_________________.
9. Binomial coefficients are a study
of _____________.
10. Both Warshall’s and Floyd’s
algorithms have the run time as
________.
11. The Warshall’s algorithm is
used to solve _______________
problems.
12. The Floyd’s algorithm is used
to solve ________________
problems.
Self Assessment Questions
1. Top-down, bottom-up
2. Memoization 3. Divide and
conquer
4.
5. O(n) 6. Bottom-up
7.
8. Complex n and k 9.

3. Combinatorics
10. θ(n3) 11. Transitive
closure
12. Shortest path
Self Assessment Questions 11
1. Principle of __________ is
defined as a basic dynamic
programming principle which
helps us to view problems as a
sequence of sub problems.
2. ______________, a
mathematician, invented the
Principle of Optimality.
3. All optimization problems tend
to minimizing cost, time and
maximizing ________.
4. ________________are node
based data structures used in
many system programming
applications for managing dynamic
sets.
5. The Insertion, deletion and
search operations of a binary
search tree has an average case
complexity of _________.
6. The time taken to perform
operations on a binary search tree
is directly proportional to the
_______ of the tree.
7. The __________ expresses the
problem using its sub-instances.
8. ________________ is an NP-
hard optimization problem.
9. The Knapsack problem
minimizes the total _________
and maximizes the total value.
10. The goal of using
______________ is to solve only
the sub problems which are
necessary.
11. Memory functions use a
dynamic programming technique
called _____ in order to reduce
the inefficiency of recursion that
might occur.
12. Memory functions method
solves the problem using
_________approach.
Self Assessment Questions
1. Optimality 2. Richard Ernest
Bellman 3. Profits 4.
Binary search trees 5. O(log n)
6. Height
7. Recurrence relation
8. Bounded Knapsack problem
9. Weight 10. Memory
functions
11. Memoization 12. Top
down
Self Assessment Questions 12
1. The choices made in a greedy
algorithm cannot depend on
_________ choices.
2. The __________________ is
greedy in the sense that at each
iteration it approximates the
residual possible by a single
function.
3. A greedy strategy usually
progresses in a ___________
fashion.
4. The
_______________________ is
obtained by selecting the adjacent
vertices of already selected
vertices.
5. Each _________________
generated by prim’s algorithm is a
part of some other minimum
spanning tree.
6. The greedy strategy in prim’s
algorithm is greedy since the tree
is added with an edge that
contributes the __________
amount possible to the tree's
weight.
7. In Kruskal’s algorithm if the
graph is not connected, then the
algorithm yields a
__________________.
8. The Union-Find data structure is
helpful for managing
_____________ which is vital for
Kruskal’s algorithm.
9. Correctness of Kruskal’s
algorithm can be proved by saying
that the constructed spanning tree
is of _______________.
10. Dijkstra’s algorithm solves the
single-source ____________
problem for a tree.
11. The algorithm finds the path
with lowest cost between the
________ vertex and every other
vertex.
12. The time complexity of
Dijkstra’s algorithm can be
improved for _____________
graphs.
13. Huffman codes are digital
_________________ codes.
14. The Huffman Encoding scheme
falls in the category of
____________.
15. Static Huffman coding is done
with the help of ___________
tables.
Self Assessment Questions
1. Future 2. Pure greedy
algorithm
3. Top-down
4. Minimum spanning tree
5. Sub-tree 6. Minimum
7. Minimum spanning forest
8. Equivalence classes
9. Minimal weight 10. Shortest
path
11. Originating 12. Sparse
13. Data compression
14. Variable length encoding
15. Statistical symbol frequency
Self Assessment Question 13
1. _____________________
means calculating the minimum
amount of work required to solve
the problem.
2. Trivial lower bound is obtained
by the count of the input data that
the algorithm reads and the
output it produces.
3. _______________________
method defines the lower bound
of an algorithm based on the
amount of the comparisons the
algorithm makes.
4. Comparison is the basic
operation of
_____________algorithm.
5. For sorting algorithms the
average case efficiencies are
better than their worst case
efficiencies.
6. We use a ________________
decision tree to represent an
algorithm for searching a sorted
array with three way comparisons.
7. Problems that are solved within
polynomial time are called
_________.
8. ____________ problem finds
the chromatic number of the given
graph.
9. An algorithm in which every
operation is exclusively defined is
called ______________ algorithm.
Self Assessment Questions
1. Lower – bound 2. True
3. Information – theoretic
4. Sorting 5. True
6. Ternary 7. Tractable
8. Graph coloring 9.
Deterministic
Self Assessment Questions 14
1. We can implement Backtracking
by constructing the
_______________.
2. Backtracking, in the _______
case may have to generate all
possible candidates in a problem
state that is growing exponentially.
3. The n-Queens problem, the
_____________ circuit and the
Subset Sum problem are some
examples of problems that can be
solved by Backtracking.
4.
___________________________
organizes details of all candidate
solutions, and discards large
subsets of fruitless candidate
solutions.
5. A ________ is a solution that
satisfies all the constraints of a
problem.
6. In Branch and Bound algorithm,
the ratio of the number of
solutions verified largely
_______________ as the size of
the problem increases.
7. ________________ algorithms
can be used to solve NP-Hard
problems that have small
instances.
8. Minimum Spanning tree
provides us a good basis for
constructing a _________
approximation tour.
9. We select the items in
__________ order of their weights
in order to use the knapsack
capacity efficiently.
Self Assessment Questions
1. State-space tree 2. Worst
3. Hamiltonian4. Branch and
Bound
5. Decreases 6. Optimal
7. Exhaustive search 8. Shortest
9. Decreasing