Generally speaking if you have an algorithm to perform specific logical and mathematical operations on an input data, then you can assess its speed of operation by two methods:
You can run it on a specific platform, e.g. , a PC with a given specifications and count the execution time as you said.
The other method is to count the multiplication and addition operations performed by the algorithm in addition to the number of memory accessing if any. Since every operation consumes a specific number of clock cycles, then one can estimate the time in clock cycles.
Thank you very much my dear professor , are there good algorithms can do the job of counting the multiplication and addition operations performed by the algorithm in addition to the number of memory accessing if any? please tell me for any.
If you have the flow chart of the algorithm and the operations executed in the algorithm are defined, then one can calculate the operations manually for a specific input. This may be tedious, therefore, they can be counted automatically be adding counters in the program code. You can find more details in the link: http://www.cs.rpi.edu/~musser/gp/timing.html