Algorithm Complexity
0.0(0)
Studied by 0 people
View linked note
Call Kai
Learn
Practice Test
Spaced Repetition
Match
Flashcards
Knowt PlayCard Sorting
1/32
There's no tags or description
Looks like no tags are added yet.
Last updated 2:40 PM on 3/9/25
Name | Mastery | Learn | Test | Matching | Spaced | Call with Kai |
|---|
No analytics yet
Send a link to your students to track their progress
33 Terms
1
New cards
Algorithm Complexity
Measures the efficiency of an algorithm in terms of time and memory usage.
2
New cards
Time Complexity
The number of steps executed by an algorithm.
3
New cards
Memory Complexity
The amount of memory used during the execution of an algorithm.
4
New cards
Factors Affecting Algorithm Running Time
Input size and type, efficiency of the compiler, speed of the executing machine, and complexity of the algorithm itself.
5
New cards
Constant Complexity (O(1))
Execution time does not depend on the input size; example includes arithmetic operations.
6
New cards
Linear Complexity (O(n))
Execution time grows proportionally with the input size; example includes printing an array.
7
New cards
Logarithmic Complexity (O(log n))
Execution time grows slowly as input size increases; example includes binary search.
8
New cards
Linear Logarithmic Complexity (O(n log n))
Increases more than linear but less than quadratic; example includes Merge Sort.
9
New cards
Quadratic Complexity (O(n²))
Execution time grows rapidly with input size; example includes nested loops like Bubble Sort.
10
New cards
Cubic Complexity (O(n³))
More expensive than quadratic; often used for small problems such as matrix multiplication.
11
New cards
Exponential Complexity (O(2ⁿ))
Grows exponentially, which is infeasible for large input sizes; example includes Towers of Hanoi.
12
New cards
Factorial Complexity (O(n!))
Grows the fastest; often represents worst-case complexity such as permutations.
13
New cards
Big-O Notation
Describes the upper bound (worst-case scenario) of an algorithm’s complexity.
14
New cards
Dominant Term
The largest term in a function that determines the algorithm’s complexity.
15
New cards
Ignoring Coefficients
Coefficients are ignored as constants don’t affect complexity ranking.
16
New cards
Ranking of Complexities
Order of common complexities: O(1), O(log n), O(n), O(n log n), O(n²), O(n³), O(2ⁿ), O(n!).
17
New cards
Example of O(1) Complexity
Arithmetic operations, assignments, and comparisons.
18
New cards
Example of O(n) Complexity
Printing an array of size n.
19
New cards
Example of O(log n) Complexity
Binary search.
20
New cards
Example of O(n log n) Complexity
Merge Sort and Quick Sort.
21
New cards
Example of O(n²) Complexity
Nested loops like Bubble Sort.
22
New cards
Example of O(n³) Complexity
Matrix multiplication.
23
New cards
Example of O(2ⁿ) Complexity
Towers of Hanoi.
24
New cards
Example of O(n!) Complexity
Permutations.
25
New cards
Worst-Case Scenario
The scenario in which an algorithm takes the longest time to complete.
26
New cards
Efficiency Measurement
How the execution time of algorithms increases with input size.
27
New cards
Growth Rate
The rate at which the execution time increases relative to the input size.
28
New cards
Basic Complexity Categories
Different types of algorithm efficiencies categorized by their growth rates.
29
New cards
Algorithm Efficiency
The effectiveness of an algorithm in minimizing time and resource usage.
30
New cards
Input Size Impact
Larger inputs generally lead to longer execution times.
31
New cards
Compiler Efficiency Impact
A more efficient compiler can improve the performance of an algorithm.
32
New cards
Machine Speed Impact
The speed of the machine executing the algorithm can affect overall execution time.
33
New cards
Algorithm Complexity Analysis
The process of determining the time and memory required by an algorithm.
