**Time Complexity:** The time complexity of a computational problem *P* is the minimum time needed by an algorithm to solve it:

**Asymptotic Notation:** When we want to bound the running time of an algorithm while ignoring multiplicative constants, we use the following notation.

See Chapter 25.

**An Upper Bound Is an Algorithm:** An upper bound for *P* is obtained by constructing an algorithm *A* that outputs the correct answer, namely *A*(*I*) = *P*(*I*), within the bounded time, i.e., *Time*(*A*, *I*) ≤ *T*_{upper} (|*I*|), on every input instance ...

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