Algorithms (OCR A-Level Computer Science): Flashcards

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Algorithm Efficiency using Big O Notation
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What does Big O notation describe?

Algorithm efficiency: upper bound of growth rate, worst-case performance

Time complexity definition

How execution time increases with input size

Space complexity definition

How memory usage increases with input size

O(1)O(1) complexity characteristic

Performance unaffected by input size

Algorithm example with O(1)O(1)

Accessing an array element

O(log⁡n)O(\log n) complexity growth

Performance grows logarithmically with input size

Algorithm example with O(log⁡n)O(\log n)

Binary search

O(n)O(n) complexity growth

Performance grows linearly with input size

Algorithm example with O(n2)O(n^2)

Bubble sort

O(2n)O(2^n) complexity growth

Performance doubles with each additional input element

Big O of nested loop over nn

O(n2)O(n^2)

Big O simplification rule

Drop lower-order terms and constants

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Algorithms

Algorithms for the Main Data Structures

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Algorithms

Algorithms for the Main Data Structures

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Algorithms

Algorithms for the Main Data Structures

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Algorithms

Algorithms for the Main Data Structures

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