counting the number of objects having distinct key values (kind of hashing). Then doing some

arithmetic to calculate the position of each object in the output sequence.

Let us understand it with the help of an example.

For simplicity, consider the data in the range 0 to 9.

Input data: 1, 4, 1, 2, 7, 5, 2

a) Take a count array to store the count of each unique object.

Index: 0 1 2 3 4 5 6 7 8 9

Count: 0 2 2 0 1 1 0 1 0 0

b) Modify the count array such that each element at each index

stores the sum of previous counts.

Index: 0 1 2 3 4 5 6 7 8 9

Count: 0 2 4 4 5 6 6 7 7 7

The modified count array indicates the position of each object in the output sequence.

c) Output each object from the input sequence followed by decreasing its count by 1. Process

the input data: 1, 4, 1, 2, 7, 5, 2. Position of 1 is 2. Put data 1 at index 2 in output. Decrease

count by 1 to place next data 1 at an index 1 smaller than this index.