Each class names how the running time reacts when you double the input.
O(1)constant: the cost stays the same no matter the size. Reading one array slot by its index never gets slower.
O(n)linear: cost grows in step with size. Scanning n items takes twice as long when n doubles.
O(log n)logarithmic: doubling the input adds just one more step. Binary search on sorted data behaves this way.
O(n^2)quadratic: cost grows with the square. Comparing every pair quadruples when the list doubles.
The gaps between these decide real performance. At a million items, O(log n) is about twenty steps while O(n^2) is a trillion. That difference is why picking the right class matters more than any small code tweak.
Rewriting in plainer words…
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Does O(1) mean an operation is fast?It means the cost doesn't grow with n, not that it's cheap. A large constant can make an O(1) step slower than a short O(n) scan.
Each of these classes describes how the running time reacts when you double the input.
O(1) is constant, so reading one array slot by its index costs the same whether the array is small or huge.
O(n) is linear, meaning cost grows in step with size, so scanning n items takes twice as long when n doubles.
O(log n) is logarithmic, where doubling the input adds just one more step, and binary search on sorted data works that way.
O(n^2) is quadratic, so comparing every pair takes four times as long when the list doubles.
At a million items, O(log n) is about twenty steps and O(n^2) is a trillion, so picking the right class matters more than any small code tweak.
Weak answers to avoid
Names the classes, never says what growsSaying O(log n) is logarithmic just repeats the name. Say what happens to the work when n doubles and tie each class to one real operation.
Treats Big-O as a time in secondsBig-O describes how cost grows with input size. Claiming O(1) is always fast misses that the notation hides the constant, which can be large.
Says binary search is O(log n) with no reasonIt sounds memorized. Say each step throws away half the remaining data, so doubling the input adds only one step.
Leaves out the scale of the gapsWithout numbers, O(n^2) sounds only a bit worse. Give one comparison, like twenty steps for O(log n) versus a trillion for O(n^2) at a million items.
Interview lens
Likely follow-ups, what you can say, and the weak answers to avoid.
