Update Bucket-sort.md
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@ -14,68 +14,38 @@ Auxiliary space: O(n)
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## Steps
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The bucket sort algorithm works as follows.
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Bucket Sort for numbers having integer part:
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Algorithm :
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1.Find maximum element and minimum of the array
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2.Calculate the range of each bucket
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1. Assume the input array is:
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2.
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3. 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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range = (max - min) / n
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n is the number of buckets
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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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3.Create n buckets of calculated range
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4.Scatter the array elements to these buckets
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BucketIndex = ( arr[i] - min ) / range
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5.Now sort each bucket individually
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6.Gather the sorted elements from buckets to original array
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## Example
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arr[] = {10, 5, 2, 3}
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Input :
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Unsorted array: [ 9.8 , 0.6 , 10.1 , 1.9 , 3.07 , 3.04 , 5.0 , 8.0 , 4.8 , 7.68 ]
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No of buckets : 5
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index = 0 1 2 3
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Output :
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Sorted array: [ 0.6 , 1.9 , 3.04 , 3.07 , 4.8 , 5.0 , 7.68 , 8.0 , 9.8 , 10.1 ]
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cycle_start = 0
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![image](https://user-images.githubusercontent.com/98322627/194531206-9414d713-51df-44db-b51c-09b2b8307d78.png)
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Input :
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Unsorted array: [0.49 , 5.9 , 3.4 , 1.11 , 4.5 , 6.6 , 2.0]
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No of buckets: 3
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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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Output :
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Sorted array: [0.49 , 1.11 , 2.0 , 3.4 , 4.5 , 5.9 , 6.6]
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## Implementation
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