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Illustration Big O Notation (Landau Symbol) - Growth Rates

O Notation (Landau Symbol) - Growth Behavior
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Runtime \(t\) of an algorithm as a function of the number of input data. Entered are different possible runtime behaviors using the Big O notation. As can be seen, with increasing number of input data an algorithm with runtime in the order \(\mathcal{O}(n! )\) is the slowest, slightly faster algorithms have the runtime of the order \(\mathcal{O}(2^n)\), even faster are the algorithms of the order \(\mathcal{O}(n^2)\) or \(\mathcal{O}(n)\), even better \(\mathcal{O}(\log(n))\). The fastest algorithm with a large number of input data has a constant runtime rate \(\mathcal{O}(1)\).