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Why is the number of primitive ops for sum += 1 equal to three?

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#1

should we be looking at only “basic” operation amounts or “primitive operation” when solving for an equation for time complexity with respect to n?

#2

Hello Eloy
The terms “basic” operations and “primitive” operations mean the same thing. Think of these as operations that can be performed by a hypothetical processor in one clock cycle, two clock cycles, or any constant number of clock cycles. Reading from a memory location into a processor register, writing to a memory location from a register and adding the values in two registers while saving the result in another register are all primitive operations.
So, sum += 1 involves:

  1. Reading the current value of the variable sum from memory to a register, say, register A

  2. Adding the constant 1 to the contents of register A, saving the result to register B

  3. Saving the contents of register B back to the memory location allocated for the variable sum

That is why we say that sum += 1 involves three primitive operations. I’m sure you are aware that, eventually, when we talk about asymptotic notation, the significance of the constants diminishes. So, even if you said sum += 1 involves two primitive operations, it would not be a serious mistake, in the long run. Please note that I have said “diminished” and not “vanished”. Leading constants are sometimes important even in asymptotic analysis, but that is an entirely different discussion.
Hope this helps.

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