It looks like the content was cut off, but I'll summarize and provide additional context for each of the complexities mentioned in your document:
Summary of Complexity Classes
-
O(1) - Constant Time
- The number of operations is constant regardless of input size.
- Example: Accessing an element in an array by index.
-
O(log n) - Logarithmic Time
- The number of operations grows logarithmically with the input size.
- Example: Binary search on a sorted list.
-
O(n) - Linear Time
- The number of operations is directly proportional to the input size.
- Example: Iterating through an array once.
-
O(n log n) - Linearithmic Time
- Slightly worse than linear time but much better than quadratic time.
- Example: Merge sort, quicksort (average case).
-
O(n^2) - Quadratic Time
- The number of operations grows quadratically with the input size.
- Example: Bubble sort, nested loops.
-
O(2^n) - Exponential Time
- The number of operations doubles with each additional element in the
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