Suppose that a loop executes n times. The loop contains a method call whose order is O(n^2), and some other statements that are O(1). From a complexity standpoint, the order of the loop is A. n B. n^2 C. n^3 D. {(n^2)}^n E. (n)^{n^2}
Question
Suppose that a loop executes n times. The loop contains a method call whose order is O(n^2), and some other statements that are O(1). From a complexity standpoint, the order of the loop is A. n B. n^2 C. n^3 D. {(n^2)}^n E. (n)^{n^2}
Solution
The order of the loop would be C. n^3.
Here's why:
The loop itself executes n times. Inside the loop, there is a method call that has a time complexity of O(n^2). Therefore, for each iteration of the loop, the method call takes n^2 operations.
Since the loop runs n times, and each iteration of the loop takes n^2 operations, the total number of operations is n * n^2 = n^3.
The other statements inside the loop that are O(1) do not change the overall time complexity, because they take a constant amount of time to execute regardless of the size of n. Therefore, they are overshadowed by the n^3 complexity of the method call inside the loop.
So, the overall time complexity of the loop is O(n^3).
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