The Problem: The problem is a specification of valid input and the acceptable output for each valid input.
Input Instance: The inputs which fall in the set of valid inputs according to the problem.
Size of Input Instance: The memory/storage space needed to represent the input instance. e.g. In Euclidean GCD example, the size of input instance will not be just the representation of the numbers say m and n, but the total of m and n.
An Algorithm: An abstract computational procedure which takes some input/inputs and returns a certain output/outputs as per the input/inputs provided.
Will expand these in future…Please be patient.