Algorithmic Complexity and Running Time Measurements Quiz

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Questions and Answers

For which algorithm does the running time have a linear relationship with $n$?

Third algorithm

None of the algorithms

First algorithm (correct)

Second algorithm

If the running time of each algorithm is 1 second on the original processor, what is being calculated?

Maximum $n$ for given times (correct)

New productivity ratios

The fastest overall algorithm

None of the above

What happens to the running time of each algorithm when a processor ten times faster is used?

It becomes unpredictable

It is reduced by a factor of ten (correct)

It remains the same

It is increased by a factor of ten

Which algorithm has the fastest running time for large values of $n$?

Algorithm with complexity $O(n)$ and actual running time $0.1n$ seconds Signup and view all the answers

For which algorithm does the actual running time increase most rapidly as $n$ grows?

Algorithm with complexity $O(2^n)$ and actual running time $0.0001* 2^n$ seconds Signup and view all the answers

If the number of data items to be processed doubles, which algorithm will have the biggest increase in running time?

Algorithm with complexity $O(2^n)$ and actual running time $0.0001* 2^n$ seconds Signup and view all the answers

What is the growth rate of the function $T(n) = 10$?

Constant Signup and view all the answers

What is the growth rate of the function $T(n) = n^2 - 1000 + 2$?

Quadratic Signup and view all the answers

What is the growth rate of the function $T(n) = 3 imes 8^n - 10$?

Exponential Signup and view all the answers

For which algorithm does the actual running time increase most rapidly as $n$ grows?

Algorithm C with complexity $O(2^n)$ Signup and view all the answers

If the running time of each algorithm is 1 second on the original processor, what is being calculated?

The maximum value of $n$ for which the problem can be solved in 1 second Signup and view all the answers

What is the growth rate of the function $T(n) = 3 imes 8^n - 10$?

$O(8^n)$ Signup and view all the answers

Qual es le crescita del function $T(n) = extstylerac{1}{2}n^2 + 3n + 1$?

Quadratic Signup and view all the answers

Qual representa le notation O(g(n)) pro le function $T(n) = 5n + 2$?

O(n) Signup and view all the answers

Qual es le notation O(g(n)) pro le function $T(n) = extstylerac{1}{3}n^3 + 4n^2 + 2n$?

O(n^3) Signup and view all the answers

What is the growth rate of the function $T(n)=3 ext{log}_{10}n^2+3.56n^2$?

Quadratic Signup and view all the answers

Which notation represents the growth rate of the function $T(n)=3 ext{log}_{10}n^2+3.56n^2$?

$O(n^2)$ Signup and view all the answers

What can be said about the growth rate of the function $T(n)=3 ext{log}_{10}n^2+3.56n^2$?

It grows quadratically due to the dominant term $3.56n^2$ Signup and view all the answers

Arrange the following expressions by growth rate from slowest to fastest: 4 n2 , n ! , n log2 n, log2 n, 3n , log3 n , n2 /3 , 3n, 1000

log2 n, log3 n, n log2 n, 4 n2, n2 /3, 3n, 1000, n !, 3n Signup and view all the answers

Which expression has the slowest growth rate?

log2 n Signup and view all the answers

Which expression has the fastest growth rate?

3n Signup and view all the answers

What is the algorithmic growth rate for program skeleton 'a'?

O(n) Signup and view all the answers

What is the algorithmic growth rate for program skeleton 'b'?

O(n^2) Signup and view all the answers

What is the algorithmic growth rate for the given program skeleton?

O(1) Signup and view all the answers

If the value of n doubles, which algorithm will have the biggest increase in running time?

O(3n) Signup and view all the answers

Which notation represents the growth rate of the function T(n) = 3log2n + 3.56n^2?

O(n^2) Signup and view all the answers

What is the algorithmic growth rate for the given program skeleton?

O(log n) Signup and view all the answers

If the loop condition was changed to 'i=i-1', what would be the algorithmic growth rate?

O(log n) Signup and view all the answers

If the loop condition was changed to 'i=i*2', what would be the algorithmic growth rate?

O(log n) Signup and view all the answers

What is the algorithmic growth rate for the given program skeleton?

O(n) Signup and view all the answers

If the loop condition was changed to 'i=i*2', what would be the algorithmic growth rate?

O(log n) Signup and view all the answers

What happens to the running time of each algorithm when a processor ten times faster is used?

Running time decreases by a factor of 10 Signup and view all the answers

If the loop condition was changed to 'i=i*2', what would be the algorithmic growth rate?

O(log n) Signup and view all the answers

For which algorithm does the actual running time increase most rapidly as n grows?

O(n!) Signup and view all the answers

What is the algorithmic growth rate if the loop condition was changed to 'i=i*2'?

O(log n) Signup and view all the answers

If the value of n doubles, which algorithm will have the biggest increase in running time?

O(3n) Signup and view all the answers

For which algorithm does the running time have a linear relationship with n?

Algorithm A: T(n) = 2n + 3 Signup and view all the answers

What is the algorithmic growth rate for the given program skeleton?

O(n squareroot of n ) Signup and view all the answers

What happens to the running time of each algorithm when a processor ten times faster is used?

The running time decreases by a factor of 10 Signup and view all the answers

What is the algorithmic growth rate for the given program skeleton?

O(log n) Signup and view all the answers

Which notation represents the growth rate of the function T(n)=3log2n+3.56n^2?

O(n^2) Signup and view all the answers

What is the algorithmic growth rate for the given program skeleton?

O(nlog n) Signup and view all the answers

If the loop condition was changed to 'l=l*2', what would be the algorithmic growth rate?

O(2^n) Signup and view all the answers

What does the notation a[ins+1..right+1] represent?

A subarray of elements starting from the index ins+1 Signup and view all the answers

What elements does a[ins+1..right+1] array include?

Elements starting from the index ins+1 Signup and view all the answers

If a is an array [10, 20, 30, 40, 50] and ins is 2, what does a[ins..right] represent?

The subarray [30, 40, 50] Signup and view all the answers

What does a[ins+1..right+1] represent in the given context?

The range of elements selected to be moved to the right Signup and view all the answers

What is the first step of inserting 35 at ins:2 of the array [10,20,30,40,50]?

30, 40, 50 Signup and view all the answers

What happens after a[ins+1..right+1] is moved to the right?

30 moves to the right to occupy 40's position Signup and view all the answers

What is the goal of array deletions?

Remove a specific value from an array or subarray Signup and view all the answers

How is the array's integrity maintained during deletions?

By shifting the remaining elements Signup and view all the answers

For which type of arrays does a linear search work?

Both unsorted and sorted arrays Signup and view all the answers

What is assumed when indicating array deletion?

All elements to the left of the deletion point, including itself, are removed Signup and view all the answers

What is the goal of array deletions?

Remove a specific value from an array or subarray Signup and view all the answers

When indicating array deletion, what happens to the elements to the right of the deletion point?

They are shifted to the left to fill the empty space Signup and view all the answers

What is done when an element is deleted from an array?

The elements to the right of it are copied and their indexes are changed Signup and view all the answers

What does the notation a[del+1..right] indicate in the context of array deletion?

The subarray for elements to the right of the site of deletion Signup and view all the answers

What happens to the elements in the subarray a[del..right-1] after an element is deleted from the array?

The index of the subarray is decreased by one Signup and view all the answers

What is one of the abilities provided by reflection?

Inspect classes and objects Signup and view all the answers

What part of classes does reflection inspect?

Fields Signup and view all the answers

Why is reflection useful?

Inspect, invoke, and instantiate without prior knowledge of class names/types during runtime Signup and view all the answers

How do you dynamically load a class in Java?

Class.forName("ClassName") Signup and view all the answers

What is the method to declare a new instance of a class in Java?

Class.newInstance(); Signup and view all the answers

How do you call the constructor onto the object for instantiation in Java?

object.getConstructor(double.class, double.class) Signup and view all the answers

How do you add a method onto the instantiated object using Dynamic Invocation?

By using the getMethod() method on the object Signup and view all the answers

How do you invoke a method in Dynamic Invocation?

By using the invoke() method on the Method object Signup and view all the answers

What parameter does the invoke() method take in Dynamic Invocation?

The object you're calling and the method's parameters Signup and view all the answers

Study Notes

Algorithm Running Times and Growth Rates

Linear relationship in running time with $n$ typically refers to algorithms with an $O(n)$ complexity.
If running time is 1 second on an original processor, it indicates the baseline time for the algorithm's execution.
With a processor ten times faster, the running time of algorithms will reduce to 0.1 seconds (1 second / 10).
The fastest running time for large values of $n$ is often characterized by $O(1)$ and $O(\log n)$ complexities, while algorithms with $O(n)$ come next.
The actual running time increases most rapidly for exponential algorithms, such as those with $O(2^n)$ or $O(n!)$ complexities.
Doubling the number of data items significantly increases running time for algorithms like $O(n^2)$, compared to $O(\log n)$.
The growth rate of $T(n) = 10$ is constant, denoted as $O(1)$.
The growth rate of $T(n) = n^2 - 1000 + 2$ simplifies to $O(n^2)$ due to the dominant term.
For $T(n) = 3 \times 8^n - 10$, the growth rate is $O(8^n)$, indicative of exponential growth.
The algorithm with the most rapid increase in actual running time as $n$ grows is often exponential or factorial in nature like $O(n!)$.
If $T(n) = \frac{1}{2}n^2 + 3n + 1$, its growth rate is $O(n^2)$.
The notation $O(g(n))$ for $T(n) = 5n + 2$ is $O(n)$.
For $T(n) = \frac{1}{3}n^3 + 4n^2 + 2n$, the growth rate is $O(n^3)$.
The growth rate for $T(n) = 3 \log_{10} n^2 + 3.56n^2$ is dominated by the $n^2$ term, hence $O(n^2)$.
Notation $O(n^2)$ represents the growth rate for $T(n) = 3 \log_{10} n^2 + 3.56n^2$.

Expression Growth Rates

Arrange growth rates from slowest to fastest: $log_{2} n$, $log_{3} n$, $3n$, $4n^2$, $n \log_{2} n$, $n^2/3$, $n!$, $1000$.
The slowest growth rate expression is $log_{2} n$.
The fastest growth rate expression is $n!$.

Algorithmic Growth Rates and Changes in Conditions

The algorithmic growth rate for program skeletons depends on their operations: loops and conditional statements.
For a loop condition of 'i=i-1', if the loop runs a fixed number of times, it could be $O(1)$.
If 'i=i*2', it shifts the growth to logarithmic, typically $O(\log n)$.
Doubling $n$ increases running time notably in quadratic $O(n^2)$ or above, while linear $O(n)$ increases less dramatically.

Array Operations

Notation $a[ins+1..right+1]$ represents a subarray starting just after index ins to right+1.
For an array $a = [10, 20, 30, 40, 50]$ with ins at 2, $a[ins..right]$ includes elements from index 2 to the last index.
Inserting elements (e.g., 35 at ins:2) requires shifting elements to the right to maintain order.
Array deletions maintain integrity by following operations that keep the elements contiguous.
After deletion, elements to the right of the deletion point are shifted left to fill the gap.
The notation $a[del+1..right]$ in deletions indicates elements that follow the deleted element.

Reflection in Java

Reflection allows inspection and manipulation of class properties at runtime in Java.
It inspects class metadata such as methods, fields, and constructors.
Reflection is useful for frameworks that require dynamic behavior or for debugging.
Classes are dynamically loaded using methods like Class.forName().
A new instance of a class is declared with ClassName obj = new ClassName();.
The constructor is called during instantiation when the object is created.
A method is added to an object through Dynamic Invocation using Method.invoke().
The invoke() method takes the target object and parameters for method execution.

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Quiz: "Algorithmic Complexity and Running Time Measurements" Test your understanding of algorithmic complexity and running time measurements with this quiz. Complete the table with the largest values of n for which the problem can be solved within a specified time limit using different algorithms with complexities O(n), O(n^2), and O(2^n).

Algorithmic Complexity and Running Time Measurements Quiz

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Questions and Answers

For which algorithm does the running time have a linear relationship with $n$?

If the running time of each algorithm is 1 second on the original processor, what is being calculated?

What happens to the running time of each algorithm when a processor ten times faster is used?

Which algorithm has the fastest running time for large values of $n$?

For which algorithm does the actual running time increase most rapidly as $n$ grows?

If the number of data items to be processed doubles, which algorithm will have the biggest increase in running time?

What is the growth rate of the function $T(n) = 10$?

What is the growth rate of the function $T(n) = n^2 - 1000 + 2$?

What is the growth rate of the function $T(n) = 3 imes 8^n - 10$?

For which algorithm does the actual running time increase most rapidly as $n$ grows?

If the running time of each algorithm is 1 second on the original processor, what is being calculated?

What is the growth rate of the function $T(n) = 3 imes 8^n - 10$?

Qual es le crescita del function $T(n) = extstylerac{1}{2}n^2 + 3n + 1$?

Qual representa le notation O(g(n)) pro le function $T(n) = 5n + 2$?

Qual es le notation O(g(n)) pro le function $T(n) = extstylerac{1}{3}n^3 + 4n^2 + 2n$?

What is the growth rate of the function $T(n)=3 ext{log}_{10}n^2+3.56n^2$?

Which notation represents the growth rate of the function $T(n)=3 ext{log}_{10}n^2+3.56n^2$?

What can be said about the growth rate of the function $T(n)=3 ext{log}_{10}n^2+3.56n^2$?

Arrange the following expressions by growth rate from slowest to fastest: 4 n2 , n ! , n log2 n, log2 n, 3n , log3 n , n2 /3 , 3n, 1000

Which expression has the slowest growth rate?

Which expression has the fastest growth rate?

What is the algorithmic growth rate for program skeleton 'a'?

What is the algorithmic growth rate for program skeleton 'b'?

What is the algorithmic growth rate for the given program skeleton?

If the value of n doubles, which algorithm will have the biggest increase in running time?

Which notation represents the growth rate of the function T(n) = 3log2n + 3.56n^2?

What is the algorithmic growth rate for the given program skeleton?

If the loop condition was changed to 'i=i-1', what would be the algorithmic growth rate?

If the loop condition was changed to 'i=i*2', what would be the algorithmic growth rate?

What is the algorithmic growth rate for the given program skeleton?

If the loop condition was changed to 'i=i*2', what would be the algorithmic growth rate?

What happens to the running time of each algorithm when a processor ten times faster is used?

If the loop condition was changed to 'i=i*2', what would be the algorithmic growth rate?

For which algorithm does the actual running time increase most rapidly as n grows?

What is the algorithmic growth rate if the loop condition was changed to 'i=i*2'?

If the value of n doubles, which algorithm will have the biggest increase in running time?

For which algorithm does the running time have a linear relationship with n?

What is the algorithmic growth rate for the given program skeleton?

What happens to the running time of each algorithm when a processor ten times faster is used?

What is the algorithmic growth rate for the given program skeleton?

Which notation represents the growth rate of the function T(n)=3log2n+3.56n^2?

What is the algorithmic growth rate for the given program skeleton?

If the loop condition was changed to 'l=l*2', what would be the algorithmic growth rate?

What does the notation a[ins+1..right+1] represent?

What elements does a[ins+1..right+1] array include?

If a is an array [10, 20, 30, 40, 50] and ins is 2, what does a[ins..right] represent?

What does a[ins+1..right+1] represent in the given context?

What is the first step of inserting 35 at ins:2 of the array [10,20,30,40,50]?

What happens after a[ins+1..right+1] is moved to the right?

What is the goal of array deletions?

How is the array's integrity maintained during deletions?

For which type of arrays does a linear search work?

What is assumed when indicating array deletion?

What is the goal of array deletions?

When indicating array deletion, what happens to the elements to the right of the deletion point?

What is done when an element is deleted from an array?

What does the notation a[del+1..right] indicate in the context of array deletion?

What happens to the elements in the subarray a[del..right-1] after an element is deleted from the array?

What is one of the abilities provided by reflection?

What part of classes does reflection inspect?

Why is reflection useful?

How do you dynamically load a class in Java?

What is the method to declare a new instance of a class in Java?

How do you call the constructor onto the object for instantiation in Java?

How do you add a method onto the instantiated object using Dynamic Invocation?

How do you invoke a method in Dynamic Invocation?

What parameter does the invoke() method take in Dynamic Invocation?

Study Notes

Algorithm Running Times and Growth Rates

Expression Growth Rates

Algorithmic Growth Rates and Changes in Conditions

Array Operations

Reflection in Java

Studying That Suits You

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