Algorithms Final Exam
Suppose each operation takes 1 microsecond and the problem size n=1,000,000. A running time of 3n computes the result in _____.
3 seconds
Scalability refers to what quantity?
Input data size
A CPU can access memory cell 100 with the same speed as accessing memory cell 1,000,000.
True
Assigns x with y.
x <- y
If f(n)=2n+6n^2+4n then f(n) is _____.
O(n^2)
n^2+2n is OMEGA(n^2)
True
n^2+2n is THETA(n^2)
True
An experimental study could test all possible inputs for an algorithm that concatenates two strings.
False: [A string's length has no limit, so all possible pairs of strings cannot be generated. Thus all possible inputs cannot be tested by an experimental study.]
If f(n) = 2n + log n + 8 then f(n) is ____.
Linear
The _____ case analysis is commonly used as the standard for choosing a well-performing algorithm.
worst
If an algorithm has a logarithmic running time, the algorithm is asymptotically better than a THETA(n) algorithm.
True
Suppose an unordered list of employees is converted to a hierarchical management diagram. The hierarchical management diagram is a data structure.
True
The fractional knapsack problem can be solved in worst case O(n log n) time.
True
The greedy algorithm guarantees an optimal solution to the fractional knapsack problem.
True
Identifying an algorithm's _____ case is usually the most difficult.
average
The following four items are available: Item 1: 10 grams, $10 benefit Item 2: 20 grams, $40 benefit Item 3: 4 grams, $5 benefit Item 4: 12 grams, $6 benefit How will the greedy algorithm fill a 40 gram knapsack?
20 grams of item 2 4 grams of item 3 10 grams of item 1 6 grams of item 4
Which running time expression is in closed form?
T(n) = 7 + 2n/3
The following four items are available: Item 1: 10 grams, $10 benefit Item 2: 20 grams, $40 benefit Item 3: 4 grams, $5 benefit Item 4: 12 grams, $6 benefit Assuming a knapsack with positive capacity, when would the greedy algorithm not choose any of item 2?
The greedy algorithm always chooses item 2
Counting the number of primitive operations provides a good estimate of an algorithm's running time.
True
Refer to the animation above. 2) Using the fractional knapsack approach, how many green apples can fill the 22 ounce grocery bag?
2.75
An algorithm that takes theta(log n) time is faster than an algorithm that takes (Theta)(n) time.
False
An experimental study requires implementing and running the algorithm.
True
The following four items are available: Item 1: 10 grams, $10 benefit Item 2: 20 grams, $40 benefit Item 3: 4 grams, $5 benefit Item 4: 12 grams, $6 benefit Sorting items from highest value to lowest yields _____.
(item 2, item 3, item 1, item 4)
Refer to the animation above. 1) Assume a 0-1 knapsack problem where yellow apples are sold out. The greedy method chooses _____ to fill the 22 ounce grocery bag.
2 green apples and 3 red apples
Loop that starts with i=0 and goes up to i=n.
for i <- 0 to n do
The following four items are available: Item 1: 10 grams, $10 benefit Item 2: 20 grams, $40 benefit Item 3: 4 grams, $5 benefit Item 4: 12 grams, $6 benefit The value of _____ is $2 / gram.
item 2
What functions stay below 2,000,000 when n <= 50,000
n and n log n only
If an algorithm's best case does 15n+31 primitive operations, the algorithm's worst case may do _____ primitive operations.
n^2+100
Assume a 0-1 knapsack problem with a greedy method that makes choices that maximize the (cost / weight) ratio. Two apples exist: Red apples each cost $2 and weigh 5 ounces Green apples each cost $3 and weigh 6 ounces If maximizing just the cost for each choice, rather than the (cost / weight) ratio, the greedy method is _____.
not optimal for the 10 ounce bag
Assume a 0-1 knapsack problem with a greedy method that makes choices that maximize the (cost / weight) ratio. Two apples exist: Red apples each cost $2 and weigh 5 ounces Green apples each cost $3 and weigh 6 ounces The greedy method chooses _____ for a 10 ounce bag.
one green apple
A base case in a recursive algorithm is _____.
required
An algorithm is commonly scientifically characterized by _____.
running time
Assume a 0-1 knapsack problem with a greedy method that makes choices that maximize the (cost / weight) ratio. Two apples exist: Red apples each cost $2 and weigh 5 ounces Green apples each cost $3 and weigh 6 ounces The (cost / weight) ratio is _____ for a red apple and _____ for a green apple.
0.4, 0.5
Assume a 0-1 knapsack problem with a greedy method that makes choices that maximize the (cost / weight) ratio. Two apples exist: Red apples each cost $2 and weigh 5 ounces Green apples each cost $3 and weigh 6 ounces The greedy method makes the optimal choice for the 10 ounce bag.
False
If a CPU takes 2 microseconds to return from a method then the same CPU should also take 2 microseconds to index into an array.
False
An experimental study does 1,000,000 runs of an algorithm. Each is done in less than 5 milliseconds, implying that the algorithm is very fast for practical use.
False [The high number of runs and low runtime of each isn't enough to conclude that the algorithm is fast for practical use. Perhaps an input that wasn't used makes the algorithm take 900 milliseconds. Or maybe the computer running the tests is much faster than the average computer.]
A linearithmic's big-Oh notation is _____.
O(n log n)
Encloses parameters in a method declaration.
Parentheses: ()
An algorithm that calls itself two times in the non-base case can have a recurrence function that has two instances of T(n).
True
If f(n) is O(log n) then saying _____ is also mathematically correct.
f(n) subset O(log n)
An algorithm must _____.
finish in a finite amount of time