In computer science effectiveness of algorithm is exclusively depend on time factor for the execution of included statements within the block of code. Further the amount of memory it is being used for storing data also matters in calculating the space complexity of the program. The enumerate_elements_of_vector_for() procedure employs a for loop to iteratively access and count elements within the vector, while the enumerate_elements_of_vector_while() procedure employs a while loop for the same purpose. Our case study investigates their respective efficiency, taking into account time complexity and space complexity as key metrics. This manuscript specifically examines the time complexity and calculating the space complexity of the for and while functions. By shedding light on the nuances of time and space complexity in the context of enumeration, this case study strives to elucidate best practices for optimizing code and enhancing the overall efficiency of data processing algorithms..