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What's time complexity in CS?

Mar 4, 2024

What's time complexity in CS?

Time complexity in computer science is a measure of the amount of time an algorithm takes to run as a function of the length of the input.

It is commonly expressed using Big O notation, which provides an upper bound on the time requirements and is useful for comparing the efficiency of different algorithms.

For example, an algorithm with a time complexity of

O(n)

is linear, which means the time it takes to complete increases linearly with the input size.

Here are some common time complexities you might encounter:

Common Time Complexities

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O(1)

: Constant time - the algorithm takes the same amount of time regardless of the input size

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O(\log n)

: Logarithmic time - the time increases logarithmically as the input size increases

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O(n)

: Linear time - the time increases linearly with the input size

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O(n \log n)

: Linearithmic time - common in efficient sorting algorithms like mergesort and heapsort

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O(n^2)

: Quadratic time - often seen in algorithms with nested loops over the input data

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O(2^n)

: Exponential time - the time doubles with each additional element in the input

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O(n!)

: Factorial time - the time grows factorially with the input size, common in brute-force solutions to the traveling salesman problem

Understanding time complexity is crucial for designing efficient algorithms and can significantly impact the performance of software, especially with large datasets.