The answer
It is a measure of how much extra memory (RAM) an algorithm requires to execute, scaling relative to the input size.
Space Complexity: What it is and Why it Matters
What is Space Complexity?
More FAQs in Space Complexity: What it is and Why it Matters
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.
Yes, drastically. Every recursive call adds a frame to the Call Stack. A recursion depth of N requires O(N) auxiliary space, which can cause Stack Overflow errors.
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