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 Cup_Sort() algorithm is a unique approach that sorts elements of an array by classifying them based on their digit length before arranging them in increasing order. This classification helps in reducing unnecessary comparisons and makes the sorting process more structured. This manuscript focuses on the implementation of the Cup_Sort() function and studies its performance in terms of time complexity and space complexity. It also presents a case study to evaluate the efficiency and effectiveness of this algorithm when compared to traditional sorting methods.