92 lines
2.3 KiB
Markdown
92 lines
2.3 KiB
Markdown
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# Bucket Sort
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Bucket sort, or bin sort, is a sorting algorithm that works by distributing the elements of an array into a number of buckets.
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Each bucket is then sorted individually, either using a different sorting algorithm, or by recursively applying the bucket sorting algorithm.
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Time Complexity : O(n)
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- Worst Case : O(n^2)
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- Average Case: O(n)
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- Best Case : O(n)
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Space complexity :
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The space complexity of the bucket sort is O(n+k).
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Auxiliary space: O(n)
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## Steps
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Suppose there is an array **arr** with **n** distinct elements. Given an element **A**, we can find its index by counting the number of elements smaller than **A**.
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1. If the element is at its correct position, simply leave it as it is.
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2. Else, we have to find the correct position of **A** by counting the number of elements smaller than it. Another element **B** is replaced to be moved to its correct position. This process continues until we get an element at the original position of **A**.
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The above-illustrated process constitutes a cycle. Repeat this cycle for every element of the list until the list is sorted.
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## Example
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arr[] = {10, 5, 2, 3}
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index = 0 1 2 3
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cycle_start = 0
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item = 10 = arr[0]
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Find position where we put the item
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pos = cycle_start
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i=pos+1
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while(i < n)
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if (arr[i] < item)
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pos++;
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We put 10 at arr[3] and change item to
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old value of arr[3].
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arr[] = {10, 5, 2, 10}
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item = 3
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Again rotate rest cycle that start with index '0'
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Find position where we put the item = 3
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we swap item with element at arr[1] now
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arr[] = {10, 3, 2, 10}
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item = 5
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Again rotate rest cycle that start with index '0' and item = 5
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we swap item with element at arr[2].
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arr[] = {10, 3, 5, 10 }
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item = 2
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Again rotate rest cycle that start with index '0' and item = 2
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arr[] = {2, 3, 5, 10}
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Above is one iteration for cycle_stat = 0.
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Repeat above steps for cycle_start = 1, 2, ..n-2
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## Implementation
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- [C++](https://www.tutorialspoint.com/cplusplus-program-to-implement-bucket-sort)
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- [Java](https://www.codespeedy.com/bucket-sort-in-java/)
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- [Python](https://stackabuse.com/bucket-sort-in-python/)
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## Video URL
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[Youtube Video about Bucket Sort](https://www.youtube.com/watch?v=JMlYkE8hGJM&feature=share&utm_source=EJGixIgBCJiu2KjB4oSJEQ)
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## Other
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[Wikipedia](https://en.wikipedia.org/wiki/Bucket_sort)
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