Time complexity measures how many operations an algorithm performs. Space complexity measures how much extra memory it needs while running. Both are measured against input size, but they answer different questions about cost.
Consider summing an array. You touch each element once, so time is O(n). You only keep one running total, so extra space is O(1). The two numbers move independently of each other.
They often trade against each other. A lookup table can make code faster while using more memory. Knowing both matters because a program can be quick yet crash by exhausting RAM, or use little memory yet run far too slowly.
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Interview lens
How interviewers actually use this question
Likely follow-ups
Does space complexity count the input itself, or only the extra memory your algorithm adds?Separate auxiliary space from total space, say which one you are quoting, and note whether the output counts.
When would you pick a slower algorithm because it uses less memory?Point to a hard memory limit, such as data larger than RAM or many requests running at once, and say what slowdown you accept.
Can an algorithm use more space than time?In the usual model no. Writing each memory cell takes at least one step, so time is at least the space actually used.
What you can say
Time complexity counts how many operations an algorithm does, and space complexity counts how much extra memory it needs while it runs.
Both are measured against input size, but they answer different questions about what the algorithm costs.
Take summing an array. I touch each element once, so time is O(n), but I only keep one running total, so extra space is O(1).
So the two numbers move independently, and I work each one out on its own.
They often trade against each other. A lookup table can make code faster, but it uses more memory.
You need both, because a program can be fast and still crash by running out of RAM, or use little memory and be far too slow.
Weak answers to avoid
Counts the input as the algorithm's spaceSpace complexity usually means the extra memory the algorithm adds. Summing an array of n items is O(1) extra space, so say the word extra.
Assumes faster code always uses more memoryThe two are independent. Summing an array is O(n) time and O(1) space. Say they often trade off, then give one case where they do.
Forgets the call stack when judging spaceA recursive solution uses a stack frame per level, so it can need O(n) space without allocating a single array. Check recursion depth.
Gives two definitions and stopsAdd a worked example with both Big-O values and say why both matter. A fast program can still crash by exhausting RAM.
Interview lens
Likely follow-ups, what you can say, and the weak answers to avoid.
