Time vs Space Complexity | Java Fresher Interview

Time complexity and space complexity measure two different resources. Time complexity is about how the number of operations grows as the input size grows. Space complexity is about how the extra memory the algorithm uses grows with the input. By convention, when I talk about space I usually mean auxiliary space, meaning the structures I allocate beyond the input itself, not the input array. The interesting part is that the two are usually a tradeoff. A great example is Two Sum. The brute-force double loop is O of n squared time but O of one space, because it allocates nothing extra. The hash-map version flips that: it's O of n time but O of n space, because I'm storing values I've seen to get faster lookups. So I spent memory to buy speed, which is a very common pattern. The detail freshers most often miss is that recursion costs space too. Even if a recursive function allocates nothing, every pending call sits on the call stack until it returns, so a recursion that goes n levels deep uses O of n stack space. That's why a recursive sum over an array is O of n in both time and space, while the iterative loop is O of n time but O of one space. So when an interviewer asks about complexity, I always state both numbers, and I'm explicit about whether the space is from data structures I allocate or from the recursion depth.