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Questions and Answers
An algorithm's runtime is observed to remain roughly constant regardless of the input size. Which Big-O notation best describes this algorithm's time complexity?
An algorithm's runtime is observed to remain roughly constant regardless of the input size. Which Big-O notation best describes this algorithm's time complexity?
- O(1) (correct)
- O(n²)
- O(n)
- O(log n)
Which of the following scenarios would benefit most from an algorithm with O(log n) time complexity?
Which of the following scenarios would benefit most from an algorithm with O(log n) time complexity?
- Printing each element in an array.
- Searching for an element in a sorted array. (correct)
- Reversing the order of elements in a stack.
- Finding the largest number in an unsorted list.
Which of the following operations typically exhibits O(1) time complexity?
Which of the following operations typically exhibits O(1) time complexity?
- Searching for a specific value in a linked list.
- Inserting an element at the beginning of a dynamic array.
- Accessing an element in an array using its index. (correct)
- Deleting an element from a binary search tree.
Consider an algorithm that iterates through a list to find a specific element. In the worst-case scenario, it checks every element. What is the Big-O time complexity of this algorithm?
Consider an algorithm that iterates through a list to find a specific element. In the worst-case scenario, it checks every element. What is the Big-O time complexity of this algorithm?
Which sorting algorithm generally has a time complexity of O(n log n) in the average case?
Which sorting algorithm generally has a time complexity of O(n log n) in the average case?
An algorithm performs the same operation on each pair of elements in a list. What is the Big-O time complexity of this algorithm?
An algorithm performs the same operation on each pair of elements in a list. What is the Big-O time complexity of this algorithm?
Which data structure is most likely to use O(log n) time complexity for insertion and deletion operations, assuming it is properly maintained?
Which data structure is most likely to use O(log n) time complexity for insertion and deletion operations, assuming it is properly maintained?
What is the space complexity typically associated with a recursive algorithm, where h represents the maximum depth of the recursion tree?
What is the space complexity typically associated with a recursive algorithm, where h represents the maximum depth of the recursion tree?
Which data structure operation's time complexity is least affected by the size of the data it contains?
Which data structure operation's time complexity is least affected by the size of the data it contains?
Assuming a good hash function, what is the average-case time complexity for searching an element in a hash table?
Assuming a good hash function, what is the average-case time complexity for searching an element in a hash table?
Which of these searching methods has a logarithmic time complexity?
Which of these searching methods has a logarithmic time complexity?
Consider a scenario where you need to frequently search, insert, and delete elements. Which data structure would be most efficient if the data is unsorted and the size is dynamic?
Consider a scenario where you need to frequently search, insert, and delete elements. Which data structure would be most efficient if the data is unsorted and the size is dynamic?
What does Big-O notation primarily describe in the context of algorithms?
What does Big-O notation primarily describe in the context of algorithms?
If an algorithm has a quadratic time complexity, how does the runtime change if the input size doubles?
If an algorithm has a quadratic time complexity, how does the runtime change if the input size doubles?
Which of the following data structures is most suitable when the priority is fast retrieval by key and order isn't important?
Which of the following data structures is most suitable when the priority is fast retrieval by key and order isn't important?
Which operation demonstrates O(n) time complexity, where n represents the number of elements?
Which operation demonstrates O(n) time complexity, where n represents the number of elements?
What is a key difference between O(log n) and O(n) complexities in terms of scalability?
What is a key difference between O(log n) and O(n) complexities in terms of scalability?
In the context of Big-O notation, what does 'n' typically represent?
In the context of Big-O notation, what does 'n' typically represent?
Which of the following best describes the space complexity of an iterative algorithm that uses a few fixed-size variables, irrespective of the input size?
Which of the following best describes the space complexity of an iterative algorithm that uses a few fixed-size variables, irrespective of the input size?
Which search algorithm takes advantage of the ordered nature of data to achieve better performance than a linear search?
Which search algorithm takes advantage of the ordered nature of data to achieve better performance than a linear search?
Flashcards
Big-O Notation
Big-O Notation
Describes how runtime/space needs grow as input grows.
O(1) - Constant Time
O(1) - Constant Time
Runtime stays constant, regardless of input size.
O(log n) - Logarithmic Time
O(log n) - Logarithmic Time
Runtime grows logarithmically as input size increases.
O(n) - Linear Time
O(n) - Linear Time
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O(n log n) - Linearithmic Time
O(n log n) - Linearithmic Time
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O(n²) - Quadratic Time
O(n²) - Quadratic Time
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Array Access Time
Array Access Time
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Linked List Search Time
Linked List Search Time
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Balanced BST Operation Time
Balanced BST Operation Time
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Hash Table Operation Time
Hash Table Operation Time
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Linear Search Time
Linear Search Time
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Binary Search Time
Binary Search Time
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Study Notes
- Big-O notation describes how an algorithm's runtime or space needs increase as the input size increases.
Common Big-O Complexities
- O(1) Constant time reflects the runtime does not change with input size.
- Examples include accessing an array element by index and stack/queue push/pop operations.
- O(log n) Logarithmic time reflects the runtime grows logarithmically with input size.
- Examples include binary search and balanced tree search/insert/delete operations.
- O(n) Linear time reflects the runtime grows linearly with input size.
- Examples include linear search and traversing a list/array, and unbalanced tree search.
- O(n log n) Linearithmic time complexity.
- Examples include efficient sorting algorithms like merge sort and heap sort.
- O(n²) Quadratic time complexity.
- Examples include nested loops and bubble sort/insertion sort algorithms.
- O(n) operations eventually outgrow O(log n) as n increases, regardless of constants
- For nested data structures (like graphs), n often represents vertices and m represents edges
- The height of a complete binary tree with n nodes is approximately log n
- When analyzing recursive algorithms, the time complexity often depends on the recurrence relation
- For technical interviews or exams, focus on the dominant term (e.g., O(n² + n) simplifies to O(n²))
Big-O Reminders
- Array access is O(1).
- Linked list search/access is O(n).
- Balanced BST operations are O(log n).
- AVL/balanced tree operations are O(log n).
- Hash table operations average case is O(1).
- Linear search is O(n).
- Binary search is O(log n).
Space Complexity
- Recursive algorithms space complexity is often O(h) where h is the recursion tree height.
- Iterative algorithms space complexity is often O(1) if using fixed extra space, or O(n) if using dynamic data structures.
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