Bucket Sort

• If you believe that the key is uniformly distributed.
• You can find the max key in O(n) time.
• You can divide the range into k buckets
• Place each item into the correct bucket.

• 
  BUCKET_SORT(A, k) 
   Build an array of k empty lists.
   m  = FindMax(A)
   For i = 0 to A.size do
       Insert A[i] into Bucket[ ⌊ k*A[i].key/m⌋]
   EndFor
   Make A empty
   For i - 1 to k
       Sort Bucket[i] with a stable sort
       Insert Bucket[i] into A in order. 
   EndFor
   

• You usually use insertion sort to sort the buckets.
• But you could use any sort.
• Worst case: everything goes into one bucket
• The average case is outside the scope of this class.
• But evaluates to $O(n + \frac{n^2}{k} + k)$
• But if k ~ n, then this is O(n).