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In the study of Design and Analysis of Algorithms, the running time of an algorithm plays a crucial role in determining its efficiency and practicality. Two important categories of time complexity are quadratic-time algorithms and exponential-time algorithms. These two classes differ significantly in terms of growth rate, scalability, and suitability for large input sizes. A quadratic-time algorithm is one whose running time grows proportionally to the square of the input size. It is usually expressed using Big-O notation as O(n²), where n represents the size of the input. This means that if the input size doubles, the running time increases by approximately four times. Quadratic-time complexity often arises in algorithms that use nested loops, where each loop runs n times. Although such algorithms are manageable for small to medium-sized inputs, their performance degrades noticeably as input size increases. A common example of a quadratic-time algorithm is the Bubble Sort algorithm. In Bubble Sort, each element in the _________ ____ ______ _________ ____ _______ ___ _______ __________ _____ ____.
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