## Introduction

ClickHouse uses a merge-sort algorithm to sort data internally. The merge-sort algorithm works by dividing the data into smaller blocks, sorting each block individually, and then merging the sorted blocks together to produce the final sorted output.

In ClickHouse, the sorting algorithm is implemented in a way that is optimized for performance and scalability. When sorting data, ClickHouse uses a multi-way merge-sort algorithm that can handle very large datasets by processing them in chunks.

The basic idea behind the multi-way merge-sort is to divide the data into smaller blocks, sort each block individually, and then merge the sorted blocks together in a way that minimizes the number of comparisons needed to produce the final output. ClickHouse uses a specialized data structure called a min-heap to efficiently select the next value to merge from each block.

To further improve performance, ClickHouse uses a variety of optimizations, such as sorting data in place whenever possible to minimize memory usage and avoiding unnecessary copies of data. The sorting algorithm is also designed to be parallelizable, so that sorting can be performed across multiple threads or nodes to further improve performance on large datasets.

Overall, the merge-sort algorithm used in ClickHouse is designed to provide fast and efficient sorting for large datasets while minimizing memory usage and taking advantage of parallel processing capabilities.

## How does the merge sort algorithm works?

The merge sort algorithm is a sorting algorithm that works by dividing the input data into smaller pieces, sorting each piece individually, and then merging the sorted pieces back together to produce the final sorted output. Here’s how the merge sort algorithm works:

- Divide the input data into smaller pieces: The first step in the merge sort algorithm is to divide the input data into smaller pieces. This is done by repeatedly dividing the data in half until each piece is only one element long.
- Sort each piece individually: Once the input data has been divided into smaller pieces, each piece is sorted individually using a simple sorting algorithm such as insertion sort or selection sort. Since the pieces are small, this sorting step is usually fast.
- Merge the sorted pieces together: After each piece has been sorted, they are merged back together in a way that ensures that the final output is sorted. This is done by repeatedly comparing the smallest elements from each of the sorted pieces and selecting the smallest element to add to the output. This process is repeated until all of the sorted pieces have been merged together to produce the final sorted output.

The merge sort algorithm is a divide-and-conquer algorithm that works by breaking down the problem into smaller subproblems, solving each subproblem independently, and then combining the solutions to produce the final result. Merge sort is known for its efficiency and is often used as a standard sorting algorithm in many applications. It has a worst-case time complexity of O(n log n), making it suitable for sorting large datasets efficiently.

## How multi-way merge-sort algorithm works?

The multi-way merge-sort algorithm is a variant of the merge-sort algorithm that can handle very large datasets by processing them in chunks. Instead of dividing the data into two pieces, as in the standard merge-sort algorithm, multi-way merge-sort divides the data into multiple smaller pieces, called runs. Here’s how the multi-way merge-sort algorithm works:

- Divide the input data into smaller runs: The first step in the multi-way merge-sort algorithm is to divide the input data into smaller runs, each of which is small enough to fit in memory. These runs are sorted using an efficient sorting algorithm, such as quicksort or heapsort.
- Merge the runs: Once the runs have been sorted, they are merged together to produce larger sorted runs. This is done by selecting the smallest element from each run and adding it to the output. The merging process continues until all of the runs have been merged together to produce a single sorted run.
- Repeat until the entire dataset is sorted: The merging process continues until the entire dataset has been sorted. If the dataset is too large to fit in memory, it is divided into smaller chunks and the process is repeated until the entire dataset has been sorted.

## Conclusion

The key advantage of the multi-way merge-sort algorithm is that it can handle very large datasets by processing them in smaller chunks. By dividing the dataset into smaller runs, multi-way merge-sort can sort data that is too large to fit in memory, and can take advantage of parallel processing to speed up the sorting process. Multi-way merge-sort is commonly used in external sorting applications, where the data is too large to fit in memory and must be sorted from external storage.

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