# Bucket Sort

1. Create m empty buckets (Or lists) in order.
2. Split the data into the m buckets
3. Sort each bucket internally using for example: quick sort or merge sort
4. Concatenate all sorted buckets

With the assumption that the data can be uniformly distributed into the buckets, the time complexity as below:

• step 2: O(n)
• step 3: O(m * (n/m) log (n/m)) ≈ O(n) when m is closed to n
• step 4: O(m)

So the total time complexity is O(n) When the data is too big to fit into the memory, we can use bucket sort to split the data into small file firstly.

bucket-sort

# Counting Sort

It is just a special case of bucket sort, which the number of bucket equal to the range of input data, so we don’t need to sort in each bucket.

1. Get/Change the data rang, suppose from 0 to k
2. Take a count array A to store the count of each unique object -> O(n)
3. Modify the count array A such that each element at each index stores the sum of previous counts -> O(k)
4. Output each object i from the input sequence based on the value of A[i] followed by decreasing A[i] by 1 -> O(n)

It can be used when k is not big, and the data range can be converted to non-negative integer.

counting-sort