The answer
Memory is often cheaper and more abundant than CPU time. Storing pre-calculated data in memory (taking O(N) space) avoids forcing the CPU to recalculate it repeatedly (saving O(N^2) time).
Space Complexity: What it is and Why it Matters
Why do we trade space for time?
More FAQs in Space Complexity: What it is and Why it Matters
It is a measure of how much extra memory (RAM) an algorithm requires to execute, scaling relative to the input size.
Auxiliary space is the temporary, extra memory created by your algorithm to do its work, excluding the memory taken up by the raw input data itself.
If you store every element of the input into a Hash Map, it requires O(N) Linear Space, as the map grows proportionally with the data.
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