If an Θ(n2) algorithm and an Θ(n) algorithm exist for the same task, then for large enough n, the Θ(n2) algorithm does more work and takes longer to execute, regardless of the constant factors for peripheral work.

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Quizplus · Accepted Answer

The notation Θ(n2) implies that the algorithm has a quadratic time complexity, while Θ(n) implies a linear time complexity. As n grows larger, the time required by the quadratic algorithm to execute will increase at a faster rate than the time required for the linear algorithm. Therefore, regardless of the constant factors, the quadratic algorithm will eventually take longer to execute than the linear algorithm.

If an Θ(N2) Algorithm and an Θ(N) Algorithm Exist for the Same