10 Questions
What type of Big O notation is characterized by algorithms that must examine every element in a collection?
O(n) - Linear time complexity
Which type of algorithm involves doubling the number of operations with each iteration?
O(2^n) - Exponential time complexity
In which type of Big O notation do algorithms divide the problem size in half with each iteration?
O(log n) - Logarithmic time complexity
Which type of Big O notation is characterized by algorithms that take the same amount of time regardless of the input size?
O(1) - Constant time complexity
Which type of algorithm involve permutations or combinations of all elements in a collection?
O(n!) - Factorial time complexity
Which Big O notation represents an algorithm that has a time complexity that increases quadratically as the input size grows?
O(n^2)
In which Big O notation does the time complexity grow exponentially, making it particularly inefficient for large input sizes?
O(2^n)
Which type of Big O notation is used to describe algorithms that have a time complexity proportional to the factorial of the input size?
O(n!)
An algorithm with which Big O notation will take the same amount of time regardless of the input size?
O(1)
Which Big O notation represents algorithms where the number of operations increases linearly with the input size?
O(n^2)
Study Notes
Big O Notation Types
- O(1) represents constant time complexity, where the algorithm takes the same amount of time regardless of the input size.
- O(log n) represents logarithmic time complexity, often seen in algorithms that divide the problem size in half with each iteration, such as binary search.
- O(n) represents linear time complexity, often seen in algorithms that must examine every element in a collection, such as linear search.
- O(n log n) represents linear logarithmic time complexity.
- O(n^2) represents quadratic time complexity, often seen in algorithms that involve nested loops, such as bubble sort.
- O(n^3) represents cubic time complexity.
- O(2^n) represents exponential time complexity, often seen in algorithms that double the number of operations with each iteration, such as the naive recursive calculation of Fibonacci numbers.
- O(n!) represents factorial time complexity, often seen in algorithms that involve permutations or combinations of all elements in a collection, such as the traveling salesman problem.
Learn about the various types of Big O notation, such as constant time complexity (O(1)), logarithmic time complexity (O(log n)), linear time complexity (O(n)), and more. Each type of Big O notation signifies a different growth rate in algorithm time complexity, with O(1) being the fastest and O(n!) being the slowest.
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