Final answer:
The focus of measurement in complexity theory should be on algorithm complexity, which includes both time complexity and space complexity. These measure how runtime and memory requirements of an algorithm scale with input size.
Step-by-step explanation:
According to the complexity theory, the focus of measurement should be on algorithm complexity. Algorithm complexity encompasses both time complexity, which is how the execution time of an algorithm increases with the size of the input data, and space complexity, which is the amount of memory space required by the algorithm as the size of the input data grows. Both of these aspects are critical for understanding the efficiency and feasibility of algorithms, especially in large-scale problems where resources are limited.
Time complexity is often represented using Big O notation, which gives an upper bound on the growth rate of the runtime of an algorithm. Space complexity, on the other hand, deals with how much physical memory an algorithm requires and is similarly important in scenarios where memory is a constraint.