Big-O Complexity and Anagrams Quiz

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Questions and Answers

What is the primary goal of the Anagram Detection Problem (ADP)?

To find the shortest path in a graph

To convert strings to uppercase letters

To determine if two strings are anagrams (correct)

To count the frequency of each character in a string

Which of the following is a correct example of an anagram?

night = bright

apple = grape

listen = silent (correct)

stop = starts

In the first solution algorithm for ADP, what does replacing a character with 'None' accomplish?

It checks off that the character has been accounted for (correct)

It counts the total number of characters

It marks a character for removal from the string

It sorts the characters in the string

What is primarily assumed about the two strings when deciding if they are anagrams?

They must be of equal length Signup and view all the answers

What is meant by the big-O complexity in algorithms?

It describes the worst-case or upper bound performance. Signup and view all the answers

What is the primary focus of the first lecture in the DS 8001 course?

Introduction to Algorithms Signup and view all the answers

In the function 'myFunc1(n)', what happens when the base condition 'n == 0' is met?

It returns a value from the function foo. Signup and view all the answers

What is the time complexity of the function 'myFunc2(n)' as described?

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

Which of the following best describes the behavior of the function 'foo(m, n)'?

It is a recursive function that calls itself multiple times. Signup and view all the answers

Which of the following statements about the function 'myFunc1(n)' is true?

'myFunc1' requires a non-negative integer 'n'. Signup and view all the answers

Which of the following complexities might indicate an efficient algorithm?

O(log n) Signup and view all the answers

If 'foo(1, 1)' is called, what will be the most likely result based on the description?

It returns three. Signup and view all the answers

From the information, what could be a potential issue when 'n' increases significantly in 'myFunc1(n)'?

It may run out of stack space due to too many recursive calls. Signup and view all the answers

What is the purpose of the function ADP1?

To determine if two strings are anagrams. Signup and view all the answers

What data structure is used to manipulate the second string in the ADP1 function?

List Signup and view all the answers

What condition indicates that the function ADP1 has failed to find an anagram?

When still_ok is set to false. Signup and view all the answers

What is the initial value of the variable still_ok in the ADP1 function?

True Signup and view all the answers

In the context of the ADP1 function, what happens after a character from s1 is successfully found in s2_list?

The character in s2_list is replaced with None. Signup and view all the answers

What does the pos1 variable track in the ADP1 function?

The current position in string s1. Signup and view all the answers

Which of the following correctly describes the worst-case time complexity of the ADP1 algorithm?

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

What is the main logical flow of the ADP1 function when checking for anagrams?

It finds each character of one string in the other and marks it. Signup and view all the answers

Study Notes

Big-O Complexity Calculation

myFunc1(n): has a complexity of O(2^n). This is because the function calls itself twice for each iteration, making the number of calls grow exponentially.
myFunc2(n): has a complexity of O(1). The function performs a constant amount of work, regardless of the input size.

Anagrams

An anagram is a word or phrase formed by rearranging the letters of a different word or phrase, using all the original letters exactly once.
Examples: "arc = car", "python = typhon", and "eleven plus two = twelve plus one"
The Anagram Detection Problem (ADP) is to determine if two given strings are anagrams. The strings are assumed to be of equal length (n) and composed of lowercase alphabetical characters.

Anagram Detection Problem Algorithm 1 (ADP1)

ADP1 checks if each character in the first string appears in the second string. If every character can be "checked off" then the strings are anagrams.
"Checking off" involves replacing the character in the second string with the Python value "None".
ADP1's big-O complexity is O(n^2). This is because the outer loop iterates n times, and the inner loop iterates n times in the worst case.
Input size is the length of the strings (n).
Elementary operations include: comparing characters, replacing characters with "None", and incrementing loop counters.

Anagram Detection Problem Algorithm 2 (ADP2)

ADP2's main logic is to sort both strings alphabetically and then compare them. If the sorted strings are identical, then the original strings were anagrams.
It's assumed that the sorted strings will be compared in O(n) time.
The big-O complexity of ADP2 is determined by the sorting algorithm used.
If a sorting algorithm with O(n log n) complexity is used (like merge sort or quick sort), then the overall complexity of ADP2 is also O(n log n).

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Description

Test your understanding of Big-O complexity calculations and the Anagram Detection Problem. This quiz covers function complexities like O(2^n) and O(1), as well as methods to determine if two strings are anagrams. Challenge your knowledge with practical examples and algorithms.