Exam questions
Mark Allen Weiss
School of Computer Science
Florida International University
University Park
Miami FL
Abstract
This rep ort contains a collection of multiple choice questions organized by b o ok chapter that can b e used
1
a
for examinations Answers are provided at the end This rep ort was typeset in L T X Original source is
E
available
Chapter
What is the approximate value of log
a
b
e none of the ab ove
If log n equals what is the value of log n
a
b
c
d
e none of the ab ove
When p erforming a pro of by induction which is the case that is trivially true
a the basis
b the inductive hypothesis
c the lemma
d the theorem
e none of the ab ove
1
Many of these questions app ear in di erent form in the Instructor s Resource Manual for Algorithms Data
Structures and Problem Solving with C published by Addison Wesley
The following routine violates which rule s of recursion
function Recurse N Integer return Integer is
begin
if N then
return
else
return N Recurse N Recurse N
end if
end Recurse
a No base case
b Fails to make progress
c Performs redundant work
d Two of the ab ove
e All of a b and c
Which of the following is the most likely result of failing to make progress towards a base
case in a recursive call
a compiler enters into an in nite lo op
b error at compilation time
c exception is raised at run time
d recursive routine enters an in nite lo op when it runs
e recursive routine terminates with bad value but no other error
Answers B A A D C
Chapter
Which of the following functions grows fastest
a n log n
n
b
c log n
2
d n
20
e n
Which of the following functions grows fastest
a n log n
b n log n
c n log n
d n
e There is a tie among two or more functions for fastest growth rate
The next three questions apply to the fol lowing code fragment
for i in N loop
for j in i loop
for k in i j loop
Sum Sum
end loop
end loop
end loop
for p in N N loop
for q in p loop
Sum Sum
end loop
end loop
How many times is statement executed
a O N
2
b O N
3
c O N
4
d O N
e none of the ab ove
How many times is statement executed
a O N
2
b O N
3
c O N
4
d O N
e none of the ab ove
What is the running time of the fragment
4
a O N
5
b O N
6
c O N
7
d O N
e none of the ab ove
Supp ose T n O F n and T n O F n Which of the following are true
1 2
a T n T n O F n
1 2
b T n T n O F n
1 2
c T n T n O
1 2
d T n O T n
1 2
e none of the ab ove
Programs A and B are analyzed and found to have worst case running times no greater than
2
n log n and n resp ectively Which of the following statements do es the analysis imply
a Program A will run faster on average for su ciently large n
b Program B will run faster on average for small n
c Program A is probably simpler to co de than program B
d There exists some input for which program B takes longer than program A
e none of the ab ove
An algorithm takes seconds for an input size of If the algorithm is quadratic approx
imately how long do es it take to solve a problem of size
a seconds
b seconds
c seconds
d seconds
e none of the ab ove
An algorithm takes seconds for an input of size If the algorithm is quadratic how
large a problem can b e solved in two minutes
a
b
c
d
e none of the ab ove
An algorithm takes seconds to solve a problem of size and ten minutes to solve a problem
of size What is the likely running time of the algorithm
a constant
b linear
c quadratic
d cubic
e none of the ab ove
Which of a to d is false ab out the binary search
a the input array must b e sorted
b successful searches take logarithmic time on average
c unsuccessful searches take logarithmic time on average
d the worst case for any search is logarithmic
e all of the ab ove are true
Which of the following can b e done in O log n arithmetic op erations
a Raising a number to the nth p ower
b Computing the greatest common divisor of some integer and n
c Adding two n digit numbers
d Two of the ab ove
e All of a b and c
A recursive algorithm works by solving two half sized problems recursively with an additional
linear time overhead The total running time is most accurately given by
a O log n
b O n
c O n log n
2
d O n
e none of the ab ove
The solution to T n T b n c with T is most accurately given by
a O log n
b O n
c O n log n
2
d O n
e none of the ab ove
Approximately how many random numbers are using in the p ermutation generation algorithm
in Exercise c
a
b log n
c n
d n log n
e none of the ab ove
What is the running time of the following routine
Check if N is prime
function Is Prime N Integer return Boolean is
I Integer
begin
if N or else N then
return TRUE
end if
if N MOD then
return FALSE
end if
while i i N loop
if N MOD i then
return FALSE
else
I I
end if
end loop
return TRUE
end Is Prime
a constant time
b O log N
c O N
p
d O N
e none of the ab ove
Answers B B C D A A E C A C E D C A C D
Chapter
Which of the following op erations is not e ciently supp orted by a singly linked list
a accessing the element in the current p osition
b insertion after the current p osition
c insertion b efore the current p osition
d moving to the p osition immediately following the current p osition
e all of the ab ove are e ciently supp orted
Which statement placed in the list package implementation inserts an item X after p osition
Current
a Current new Node X Current
b Current new Node X Current Next
c Current Next new Node X Current
d Current Next new Node X Current Next
e none of the ab ove
The header no de of a linked list
a simpli es deletion
b simpli es insertion
c uses only constant extra space
d two of the ab ove
e all three of a b and c
If a header no de is used which of the following indicates a list L with one item
a L Header Next null
b L Header Next null
c L Header Next null and then L Header Next Next null
d L Header Next null and then L Header Next Next null
e none of the ab ove
Insertion of a no de into a doubly linked list requires how many changes to various Next and
Prev p ointers
a no changes
b Next Prev
c Next Prev
d Next Prev
e none of the ab ove
What op eration is supp orted in constant time by the doubly linked list but not by the singly
linked list
a Advance
b Backup
c First
d Retrieve
e all of the ab ove are always constant time
The UNIX editor vi allows searching in b oth directions with wraparound if necessary If the
sequence of lines is stored as a linked list which of the following is most reasonable
a singly linked list
b doubly linked list
c circular singly linked list
d circular doubly linked list
e none of the ab ove
What happ ens when wraparound is implemented for a queue
a If Front advances past the last array p osition it is reset to the rst array p osition
b If Rear advances past the last array p osition it is reset to the rst array p osition
c Both a and b
d Neither a nor b
Using the text implementation if Front and Rear have identical values what is the size of
the queue
a
b
c
d the answer cannot b e determined
e none of the ab ove
For the linked list implementation of the stack where are the pushes and p ops p erformed
a Push in front of the rst element p op the rst element
b Push after the last element p op the last element
c Push after the last element p op the rst element
d Push in front of the rst element p op the last element
e Push after the rst element p op the rst element
For the linked list implementation of the queue where are the enqueue and dequeues p er
formed
a Enqueue in front of the rst element dequeue the rst element
b Enqueue after the last element dequeue the last element
c Enqueue after the last element dequeue the rst element
d Enqueue in front of the rst element dequeue the last element
e Enqueue after the rst element dequeue the rst element
For the linked list implementation if the stack is not empty which of the following statements
in a main pro cedure can b e used to access the top element in the stack S
a S Element
b S TopOfStack
c S TopOfStack Element
d TopOfStack Element
e none of the ab ove
Answers C D E D C B D C B A C E
Chapter
Which of the following traversals requires more than linear time in the worst case
a inorder
b level order
c p ostorder
d preorder
e all of these traversals are linear time
In which of the following traversals is the no de pro cessed b efore the recursive calls to the
children complete
a inorder
b level order
c p ostorder
d preorder
e none of the ab ove
What is the maximum number of no des in a binary tree with L leaves
a L
L
b
L+1
c
d there is no maximum
e none of the ab ove
Which of the following is true ab out the height of a no de
a The height of a no de is one less than the height of its parent
b The height of an empty tree is
c The height of a leaf is
d The height of a tree can b e larger than its depth
e all of the ab ove are false
The rst child next sibling implementation
a allows easy access to the parent
b is appropriate for binary trees
c uses C p ointers p er no de where C is the number of children
d all of the ab ove
e none of a b and c
Which traversal computes the total size of each directory in the UNIX le system
a inorder
b level order
c p ostorder
d preorder
e two or more of the ab ove traversals could b e used
Let C X b e the number of leaves in a binary tree ro oted at T Assume that IsLeaf T returns
if T is a leaf Which of the following observations leads to a recursive implementation
a C T C T Left C T Right
b C T C T Left C T Right
c C T C T Left C T Right IsLeaf T
d C T C T Left C T Right IsLeaf T
e none of the ab ove
Which traversal do es not use a stack
a inorder
b level order
c p ostorder
d preorder
e all of these traversals uses a stack
How many n no de binary trees with items n have identical p ostorder and inorder
traversals
a
b
c n
d n
e none of the ab ove
The next three questions relate to the binary tree with root A The root has left child B and
right child C B has left child D and right child E There are no other nodes in the tree
Which of the following traversals yields ABCDE
a inorder
b level order
c p ostorder
d preorder
e two of the ab ove
Which of the following is an inorder traversal of the tree
a ABCDE
b ABDEC
c DBEAC
d DEBAC
e none of the ab ove
The height of the tree is
a
b
c
d
e none of the ab ove
Approximately what is the maximum height of a binary search tree of n no des
a log n
b log n
c log n
d log n
e none of the ab ove
The following items are inserted into a binary search tree Which item
is placed at a ro ot
a
b
c
d
e none of the ab ove
The following items are inserted into a binary search tree Which no de is
the deep est
a
b
c
d
e none of the ab ove
Which of the following statements is true ab out deleting the ro ot of a binary search tree
a the ro ot p ointer always changes
b the ro ot p ointer changes if it do es not have two children
c if the ro ot has two children its item is replaced by the largest element in the right
subtree
d all of the ab ove
e none of a b and c
For an insertion of a single item into an n item AVL tree the maximum number of rotations
double rotations count as one rotation is
a
b
c approximately log n
d approximately log n
e none of the ab ove
The following items are inserted into an AVL tree How many rotations are
p erformed
a no rotations
b single rotation only
c double rotation only
d single rotation and double rotation
e none of the ab ove
Items and are inserted into an AVL tree What happ ens when is inserted
a no rotation is needed
b a single rotation b etween some no de and its left child is p erformed
c a single rotation b etween some no de and its right child is p erformed
d a double rotation with a no de its left child and a third no de is p erformed
e a double rotation with a no de its right child and a third no de is p erformed
Which of the following data structures has the strongest height guarantee
a AVL tree
b B tree of order
c B tree of order
e tree
Supp ose a disk blo ck stores bytes and the basic key size is bytes Assuming that
p ointers cost bytes what is the correct choice of M for a B tree
a
b
c
d
e none of the ab ove
In addition to the data and left and right p ointers for any implementation what must b e
stored in each no de of a splay tree
a the no de s height
b the no de s level
c the no de s parent
d the no de s rank
e none of the ab ove
What is amortized cost of an op eration using rotate to ro ot
a O
b O log n
c O n
d O n log n
e none of the ab ove
An access of a splay tree of n no des results in a completely identical tree For how many
di erent no des would this b e p ossible
a
b
c
d n
e none of the ab ove
What is the worst case height of a splay tree
a log n
b log n
c log n
d n
e n
Which of the statements a to d ab out splay trees is false
a a single access op eration could examine every no de in the tree
b any n consecutive op erations from an initially empty splay tree must take at most
O n log n time
c inserting the items n into an initially empty splay tree takes O n total time
d the most recently accessed item is at the ro ot
e none of a to d is false
Which of the following splay tree rotations in e ect distinguishes it from rotate to ro ot
a zig only
b zig zag only
c zig zig only
d zig zig and zig zag only
e all of the ab ove
What item is at the ro ot after the following sequence of insertions into an empty splay tree
a
b
c
d
e none of the ab ove
How is deletion p erformed in a splay tree
a If the no de is found it is replaced with the smallest no de in its right subtree which itself
is recursively deleted
b It the no de is found it is replaced with the largest no de in its left subtree which itself
is recursively deleted
c A single splay is p erformed which places the deleted no de in a leaf that no de is then
easily removed
d A single splay is p erformed which places the deleted no de at the ro ot it is deleted and
the two subtrees are reattached by using a second splay
e none of the ab ove
In a splay tree how is the rank of a no de stored
a an extra array stores the information
b a linked list stores the information
c directly in each no de
d indirectly by storing the size in each no de
e the rank is not stored at all
Which of the following alternatives preserves the logarithmic amortized time b ound for the
splay tree
a do not splay on unsuccessful searches
b do not splay if an access path has fewer than log n no des
c replace the zig zig with two single b ottom up rotations
d splay on every other access
e none of the ab ove
Answers E D D C E C C B B B C C E C C B
A D C C A E C B D E C B D E B
Chapter
Which of the following data structures requires more than constant average time for inser
tions
b queue
c search tree
d stack
e all of the ab ove have constant time insertion algorithms
What is the range of values computed by the hash function H ash X X mo d
a to
b to
c to
d to
e none of the ab ove
Which of a to d is false The size of a hash table
a should b e a p ower of for quadratic probing
b should b e a prime number for linear probing
c should b e ab out n for quadratic probing
d should b e ab out n for separate chaining
e two or more of the ab ove are false
How are elements deleted in linear probing
a deletion is not allowed
b they are changed to zero
c they are marked deleted
d unchecked deallo cation
e none of the ab ove
Supp ose we are implementing quadratic probing with a hash function H ash X X mo d
If an element with key is inserted and the rst three lo cations attempted are already
o ccupied then the next cell that will b e tried is
a
b
c
d
e none of the ab ove
In a separate chaining hash table with load factor what is the average length of a
list
a
b
c
d there is not enough information
e there is enough information but none of the ab ove are correct
Which of the following costs are equal in a probing hash table
a insertion and successful search
b insertion and unsuccessful search
c successful search and unsuccessful search
d insertion successful search and unsuccessful search
e none of the ab ove
Which of the following statements ab out quadratic probing is true exp ensive do es not include
trivial op erations such as multiplication or division by p owers of computation of the hash
function is not included in the cost
a an exp ensive division must b e p erformed
b an exp ensive mo d op erator must b e p erformed
c an exp ensive multiplication must b e p erformed
d all of the ab ove
e none of a b and c
Linked lists are used in
a double hashing
b linear probing
c quadratic probing
d separate chaining
e all of the ab ove
Primary clustering o ccurs in
a linear probing
b quadratic probing
c separate chaining
d all of the ab ove
e none of a b and c
Rehashing can b e used in
a linear probing
b quadratic probing
c separate chaining
d all of the ab ove
e none of a b and c
Answers C A A C B A B E D A D
Chapter
Every no de in a min binary heap
a has two children
b is no larger than its children
c is no smaller than its children
d has a smaller left child than right child
e two or more of the ab ove
If an element in a binary heap is stored in p osition i and the ro ot is at p osition then where
is the parent stored
a bi c
b di e
c bi c
d i
e i
The running time of Build Heap is
a O n worst case and O n average case
b O n worst case and O log n average case
c O n worst case and O n log n average case
d O n log n worst case and O n average case
e O n log n worst case and O n log n average case
n elements are inserted one by one into an initially empty binary heap The total running
time is
a O n worst case and O n average case
b O n worst case and O log n average case
c O n worst case and O n log n average case
d O n log n worst case and O n average case
e O n log n worst case and O n log n average case
Which op eration is not supp orted in constant time by a double ended queue deque
a Insertion as the front or rear item
b Access of the front or rear item
c Deletion of the front or rear item
d Access and deletion of the minimum item
e all of the ab ove are supp orted
Which op eration is not e ciently supp orted by priority queues
a Delete Min
b Find
c Find Min
d Insert
e All of the ab ove are e ciently supp orted
Which data structure is used to check for balanced parentheses
a binary search tree
b hash table
d queue
e stack
Jobs sent to a printer are generally placed on a
a binary search tree
b hash table
c priority queue
d queue
e stack
Which data structure is generally used to implement a symbol table
a binary search tree
b hash table
c priority queue
d queue
e stack
Which data structure maintains the event set in an event driven discrete event simulation
a binary search tree
b hash table
c priority queue
d queue
e stack
Which of the following could b e used as an e cient priority queue
a binary search tree
b hash table
c linked list
d queue
e stack
Which of the following do es the binary heap implement
a binary search tree
b hash table
c priority queue
d queue
e stack
and are inserted into a data structure in that order An item is deleted using only
a basic data structure op eration If the deleted item is a the data structure cannot b e a
a hash table
b priority queue
c queue
d search tree
e stack
Which data structure is used by the compiler to implement recursion
a hash table
b priority queue
c queue
d search tree
e stack
Which of the following data structures uses a sentinel
a binary heap
b hash table
c queue
d stack
e none of the ab ove use sentinels
A no de with key has a left child with key Which of the following ob jects could this
no de b e found in
a binary search tree
b max heap
c min heap
d two of the ab ove
e none of a b and c
Percolate up and down are used for
a AVL trees
b B trees
c circular queue
d binary heaps
e none of the ab ove
Which of the following is true ab out the skew heap
a it is balanced
b each no de stores nothing b esides an item and two p ointers
c the right path contains at most a logarithmic number of no des
d two of the ab ove
e all of a b and c
Which of the four op erations b elow can b e used to implement the other three for the skew
heap
a Decrease Key
Min b Delete
c Insert
d Merge
e none of the ab ove
Which of the following is not a binary tree
a binary heap
b binomial queue
c skew heap
d splay tree
e all of the ab ove are binary trees
Answers B A A D D B E D B C A C C E A C
D B D B
Chapter
What is the basic algorithm used for external sorting
a nding the median
b merging
c selection
d all of the ab ove
e none of a b and c
Which of the following data structures do es not yield an e cient comparison based sort
a AVL tree
b hash table
c priority queue
d all can b e used for e cient sorting
e none can b e used for e cient sorting
Which of the following algorithms requires the most extra space on average when imple
mented as in the text
a heapsort
c mergesort
d quicksort
e shellsort
Which of the following is the strongest lower b ound for sorting when ordering information is
obtained only by adjacent comparisons
a O n log n
2
b O n
c n log n
2
d n
e none of the ab ove is a valid lower b ound for this problem
Which of the following algorithms runs in quadratic average time
a heapsort
b insertion sort
c mergesort
d quicksort
e shellsort
Which of the following algorithms runs in O n log n average time but quadratic worst case
time
a heapsort
b insertion sort
c mergesort
d quicksort
e shellsort
Which of the following algorithms implemented as in the text runs in O n time when
presented with an array of n identical elements
a heapsort
b insertion sort
c mergesort
d quicksort
e shellsort
Which of the following algorithms has the largest big Oh di erential b etween average case
and worst case p erformance
a heapsort
b insertion sort
c mergesort
d quicksort
e quickselect
How much extra space is used by heapsort
a O
b O log n
c O n
2
d O n
e none of the ab ove
Which sorting algorithm has the same average and worst case time b ounds in Big Oh as
heapsort
a insertion sort
b mergesort
c quicksort
d shellsort
e none of the ab ove
For quicksort what do I and J do when they see keys equal to the pivot
a I stops J stops
b I stops J go es
c I go es J stops
d I go es J go es
e I and J alternate b etween stopping and going
In median of three partitioning where is the pivot placed b efore partitioning b egins
a at the start of the array
b at the middle of the array
c at the end of the array
d in a temp orary variable
e none of the ab ove
Which of the following statements ab out sorting ve elements is the strongest statement that
is directly implied by the information theoretic lower b ound
a comparisons are su cient
b comparisons are necessary and su cient
c comparisons are necessary
d comparisons are su cient
e comparisons are necessary and su cient
Replacement selection is
a arranging the initial runs on the tap e in an optimal way
b constructing the runs so they have exp ected length M
c using K way merging instead of way merging
d using K tap es instead of K tap es
e none of the ab ove
Answers B B C D B D B E A B A E C B
Chapter
Which of the following trees can have height that is not logarithmic
a AVL tree
b binary heap
c B tree of order
d union nd tree with union by height
e all of the ab ove trees must have logarithmic depth
Which of the following prop erties is not required for an equivalence relation
a re exive
b symmetric
c transitive
d all of these prop erties are required
e none of these prop erties is required
Which of the following is an equivalence relationship
a a R b if there is a path from a to b in a directed graph G
b a R b if a and b are two p eople who know each other
c a R b if a and b end in the same two digits
d all of the ab ove
e none of a b c
Which of the following when p erformed by itself is su cient to ensure a b ound of O m log n
for m op erations
a path compression
b union by height
c union by size
d all of the ab ove
e none of a b and c
Path compression is
a p erformed during Unions to make Unions faster
b p erformed during Unions to make Finds faster
c p erformed during Finds to make Finds faster
d p erformed during Finds to make Unions faster
e p erformed during Finds to make b oth Finds and Unions faster
What is the value of log
a
b
c
d
e none of the ab ove
Answers E D C D C B
Chapter
Which of the following is a synonym for an edge
a arc
b no de
c path
d vertex
e none of the ab ove
Which of the following problems is not known to b e solvable in linear time
a top ological sort
b unweighted shortest path in general graphs
c weighted shortest path in acyclic graphs
d weighted shortest path in cyclic graphs
e all are solvable in linear time
Which of the following do es not use a queue
a negative weighted shortest path algorithm
b p ositive weighted shortest path algorithm
c top ological sort
d unweighted shortest path algorithm
e all of the ab ove use a queue
Which of the following algorithms solves the unweighted single source shortest path problem
a breadth rst search
b depth rst search
c Dijkstra s algorithm
d Kruskal s algorithm
e Prim s algorithm
Which of the following algorithms solves the p ositive weighted single source shortest path
problem
a breadth rst search
b depth rst search
c Dijkstra s algorithm
d Kruskal s algorithm
e Prim s algorithm
In a graph with v vertices and e edges which of the following maximum sizes is not correct
for an unweighted shortest path computation
a v for the number of adjacency lists
b e for the total size of all adjacency lists
c e for the size of the hash table that maps names to internal numbers
d v for the size of the queue
e all of the ab ove are correct
In a connected graph with no lo ops or multiple edges which of the following inequalities is
not correct v is the number of vertices e is the number of edges
2
a e v
b e v
2
c v e
d v e
e all of the ab ove are correct
If the shortest path algorithm is run and a vertex is not reachable from the starting p oint
what happ ens
a a distance of in nity is rep orted
b a distance of is rep orted
c a distance of zero is rep orted
d the algorithm enters an in nite lo op
e the algorithm s results are unde ned
For the weighted shortest path problem let d b e the cost of reaching the current vertex v
v
let w b e adjacent to v and assume the edge cost is c Supp ose that d was the cost of
v w w
reaching w prior to examining v Ties are broken in favor of the rst path seen Then under
what circumstances is w s distance lowered
a d d
w v
b d d
w v
c d d c
w v v w
d d d c
v w v w
e none of the ab ove
Which of the following statements is true
a A top ological ordering exists in every directed graph
b Every acyclic graph has at least one top ological ordering
c Every acyclic graph has exactly one top ological ordering
d Every acyclic graph has at most one top ological ordering
e none of the ab ove
The next four questions refer to the fol lowing directed graph V fV V V V V V V g
0 1 2 3 4 5 6
There are the fol lowing twelve edges with edge costs listed as the third item in the triplet E
f V V V V V V V V V V V V V V V V
0 2 1 0 1 3 3 0 3 2 3 5 3 6 4 1
V V V V V V V V g
4 3 4 6 5 2 6 5
The shortest weighted path from V to V has weight
4 5
a
b
c
d
e none of the ab ove
If the start vertex is V then using the standard weighted shortest path algorithm which is
4
the last vertex to b e declared known
a V
0
b V
1
c V
2
d V
4
e none of the ab ove
If the start vertex is V then using the acyclic weighted shortest path algorithm which is the
4
last vertex to b e declared known
a V
0
b V
1
c V
2
d the graph is not acyclic so the acyclic algorithm should not b e used
e none of the ab ove
If the ab ove graph were undirected then what would b e the cost of its minimum spanning
tree
a
b
c
d
e none of the ab ove
Which algorithm is used to compute minimum spanning trees
a breadth rst search
b depth rst search
c Dijkstra s
d Kruskal s
e none of the ab ove
Answers A D B A C C D A C B C B C B D
Chapter
Which of the following strategies do not directly invoke recursion
b divide and conquer
d two of the ab ove do not directly invoke recursion
e none of a b and c directly invoke recursion
random integers are generated randomly with a uniform distribution over the range
to inclusive Which of the following would indicate a p o or generator
a the average of the numbers is ab out
b each number app ears exactly once
c no four consecutive numbers are all even
d two of the ab ove
e all of a b and c
The seed of a linear congruential generator is
a always zero
b o ccasionally zero dep ending on other random events
c the initial value
d the multiplier
e the p erio d of the generator
Which of the following is a bad case for randomized quickselect
a any input with K
b reverse ordered input
c sorted input
d there are no bad inputs
e none of the ab ove
If the randomized primality testing algorithm with one iteration declares that P is prime
and C comp osite then which of the following is most accurate
a There is at most a p ercent chance that P has b een declared prime falsely and there
is at most a p ercent chance that C has b een declared comp osite falsely
b P is prime with p ercent certainty but there is at most a p ercent chance that C
has b een declared comp osite falsely
c There is at most a p ercent chance that P has b een declared prime falsely but C is
comp osite with at least p ercent certainty
d P is prime with p ercent certainty and C is comp osite with p ercent certainty
e All of the ab ove statements are factually incorrect
Answers C D C D C