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Efficient Algorithm Design
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We have noted that all comparison-based sorting algorithms have a lower-bound time complexity of
, which means no comparison-based algorithm can achieve better performance than
in the general case. However, there are sorting algorithms that do not depend on comparisons. These non-comparison-based algorithms leverage certain assumptions or information about the data to achieve better performance.
Unlike comparison-based algorithms, non-comparison-based algorithms can achieve a lower bound as efficiently as linear time. This remarkable efficiency is why they are sometimes referred to as linear-time sorting algorithms. By making use of specific properties of the data, such as a limited range of integer values or the distribution of digits, these algorithms can bypass the comparison limit and sort much faster under the right conditions. In this section, we will explore three well-known non-comparison-based sorting algorithms: counting sort, Radix sort,...