Counting Sort is a non-comparison sorting algorithm optimized for datasets where the range of values is close to the number of items. It achieves O(n+k) time complexity, making it ideal for large datasets with limited integer ranges. The algorithm's stability and practical implementation in various programming languages are also discussed, alongside its strengths and limitations.
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Counting Sort is a non-comparison sorting algorithm that counts the number of occurrences of each distinct value to determine the index at which each value should be placed in the output array
Time Complexity
Counting Sort has a time complexity of O(n+k), making it efficient for large datasets with a constrained range of integer values
Implementation
Counting Sort can be implemented in various programming languages, such as Python and Java, showcasing its versatility and efficiency
Counting Sort operates in three main phases: count accumulation, index calculation, and final placement
Counting Sort tallies the frequency of each value in the input array to create an auxiliary count array
The auxiliary count array is transformed into a cumulative count array, which maps to each element's index in the sorted output
The algorithm iterates through the original array, placing each element into the correct position in the output array based on the cumulative counts
Counting Sort offers a predictable linear time complexity, stability, and effectiveness for datasets with a narrow range of integer values
Performance
Counting Sort's performance is highly dependent on the nature of the input data, making it less efficient for datasets with a wide range of values
Memory Usage
Counting Sort requires additional memory proportional to the range of values, which can be prohibitive in memory-constrained environments
It is important to recognize that Counting Sort's efficiency is maintained only when the value range is not substantially larger than the number of elements to be sorted
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Counting Sort classification
Non-comparison sorting algorithm
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Counting Sort process
Counts occurrences of values, determines indices for output array placement
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Ideal conditions for Counting Sort efficiency
Large datasets with constrained range of integer values
