I have organized the term 'complexity' in mathematics. Am I understanding correctly ?
- In common English 'complexity' means the degree of complicated-ness.
- But in mathematics, 'complexity' means something different. It can mean either 'time complexity' or 'space complexity'.
- When the term 'complexity' alone is used, it means 'time complexity'.
- The term 'time complexity' refers to the speed of an algorithm; how fast one can solve a problem using the algorithm.
- The term 'space complexity' refers to the amount of memory needed for solving the algorithm. "How many sheets of paper do I need to solve the problem."
- For evaluating space complexity, one can erase some texts on sheets when the texts are no longer needed. In this way you can save total needed sheets of paper.
- If there is no other specification, an integer input/output is usually considered "given as binary". If no other specification, Time complexity and Space complexity are evaluated, assuming given integer input/output is of a binary form.
- In fact the fact 7) is not that important, because almost all interesting algorithms need fairly big time complexity (take long time) compared to complexity of converting base of an integer (ex: binary to decimal or vice-versa). It is like for 100 seconds(main algorithm)+0.01 seconds(converting base), 0.01 seconds is negligible. I think it is similar for space complexity.
You can give opinions for each description 1.–8.