# Bucket Sort vs. Radix Sort

## What's the Difference?

Bucket Sort and Radix Sort are both non-comparative sorting algorithms that operate on integers. However, they differ in their approach to sorting. Bucket Sort divides the input array into a number of buckets, each containing a subset of elements with similar values. These buckets are then sorted individually using another sorting algorithm or recursively applying Bucket Sort. On the other hand, Radix Sort sorts the input array by processing the digits of the elements from the least significant digit to the most significant digit. This process is repeated for each digit, resulting in a sorted array. While Bucket Sort is more suitable for sorting elements with a uniform distribution, Radix Sort is more efficient for sorting integers with a fixed number of digits.

## Comparison

Attribute | Bucket Sort | Radix Sort |
---|---|---|

Algorithm type | Comparison sort | Non-comparison sort |

Time complexity | O(n+k) | O(nk) |

Space complexity | O(n+k) | O(n+k) |

Stable sort | Yes | Yes |

Adaptive sort | No | No |

## Further Detail

### Introduction

Sorting algorithms are essential in computer science for organizing data in a specific order. Two popular sorting algorithms are Bucket Sort and Radix Sort. While both algorithms are used for sorting, they have distinct attributes that make them suitable for different scenarios. In this article, we will compare the attributes of Bucket Sort and Radix Sort to understand their strengths and weaknesses.

### Bucket Sort

Bucket Sort is a distribution sort algorithm that works by distributing elements into a number of buckets and then sorting the elements in each bucket. The algorithm divides the range of input values into a number of buckets, each containing a subset of the input elements. After distributing the elements into buckets, each bucket is sorted individually, either using a different sorting algorithm or recursively applying Bucket Sort. Finally, the sorted elements from all buckets are concatenated to produce the sorted output.

- Bucket Sort is efficient when the input is uniformly distributed over a range.
- It is easy to implement and can be parallelized for faster sorting.
- Bucket Sort has a linear time complexity O(n) when the elements are uniformly distributed.
- It is suitable for sorting floating-point numbers within a specific range.
- Bucket Sort is not suitable for sorting a large number of elements with a skewed distribution.

### Radix Sort

Radix Sort is a non-comparative integer sorting algorithm that sorts data with integer keys by grouping the keys by individual digits. The algorithm processes the digits of the keys from the least significant digit (LSD) to the most significant digit (MSD) or vice versa. Radix Sort can be implemented using different techniques such as LSD Radix Sort and MSD Radix Sort. In LSD Radix Sort, the algorithm starts sorting from the rightmost digit, while in MSD Radix Sort, it starts sorting from the leftmost digit.

- Radix Sort is efficient for sorting integers with a fixed number of digits.
- It has a time complexity of O(nk) where n is the number of elements and k is the number of digits in the input.
- Radix Sort is stable, meaning that the relative order of equal elements is preserved in the sorted output.
- It is suitable for sorting strings by considering each character as a digit.
- Radix Sort requires additional space for storing the buckets during sorting.

### Comparison

Both Bucket Sort and Radix Sort are linear time complexity sorting algorithms, making them efficient for sorting large datasets. However, they have different use cases and attributes that make them suitable for specific scenarios. Bucket Sort is ideal for sorting floating-point numbers within a specific range, while Radix Sort is better suited for sorting integers with a fixed number of digits. Bucket Sort is easy to implement and can be parallelized for faster sorting, whereas Radix Sort requires additional space for storing buckets during sorting.

While Bucket Sort is not suitable for sorting a large number of elements with a skewed distribution, Radix Sort is stable, preserving the relative order of equal elements in the sorted output. Radix Sort is also suitable for sorting strings by considering each character as a digit, making it versatile for different types of data. On the other hand, Bucket Sort is efficient when the input is uniformly distributed over a range, providing a linear time complexity of O(n) in such cases.

### Conclusion

In conclusion, both Bucket Sort and Radix Sort are efficient sorting algorithms with distinct attributes that make them suitable for different scenarios. Bucket Sort is ideal for sorting floating-point numbers within a specific range and when the input is uniformly distributed, while Radix Sort is better suited for sorting integers with a fixed number of digits and when stability is required in the sorted output. Understanding the strengths and weaknesses of each algorithm is essential for choosing the most appropriate sorting algorithm for a given dataset.

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