Question

1. Show how the Radix sort algorithm sorts the array: 36 14 27 40 31 17 5. Must show the operation of the algorithm in details.

Answer 1

Radix sort algorithm

Step 1:Starting Radix Sort. We will process digits from right to left. The first step will be to count occurances of digits from the input array.

  
Step 2: 36 has current digit 6. Add one to the 6 bin.   

  
Step 3: 14 has current digit 4. Add one to the 4 bin.

   
Step 4:   27 has current digit 7. Add one to the 7 bin.

  
Step 5: 40 has current digit 0. Add one to the 0 bin.

Step 6 : 31 has current digit 1. Add one to the 1 bin.

  

Step 7: 17 has current digit 7. Add one to the 7 bin.

Step 8: 5 has current digit 5. Add one to the 5 bin.

Step 9: Now we will do a rolling summation of the count array, to be used next as positions

But first we subtract 1 from the 0 position so that the resulting sums yield correct positions in the Auxilliary array.

Step 10: 0 + 1 is 1. Put that in position 1

  
  
Step 11: 1 + 0 is 1. Put that in position 2

Step 12: 1 + 0 is 1. Put that in position 3

  

  
Step 13: 1 + 1 is 2. Put that in position 4

  

  
Step 14: 2 + 1 is 3. Put that in position 5

  

  
Step 15: 3 + 1 is 4. Put that in position 6

Step 16 : 4 + 2 is 6. Put that in position 7

  

Step 17: 6 + 0 is 6. Put that in position 8

Step 18: 6 + 0 is 6. Put that in position 9

Step 19: Now use the Count array to decide where to move values into the Auxilliary array

5 has current digit 5. So we look in position 5 of the Count array, to see that we put it in position 3 of the Auxilliary array.

And we decrement the value of Count array position 5

Step 20:   17 has current digit 7. So we look in position 7 of the Count array, to see that we put it in position 6 of the Auxilliary array.

And we decrement the value of Count array position 7

Step 21: 31 has current digit 1. So we look in position 1 of the Count array, to see that we put it in position 1 of the Auxilliary array.

And we decrement the value of Count array position 1

  
Step 22: 40 has current digit 0. So we look in position 0 of the Count array, to see that we put it in position 0 of the Auxilliary array.   

And we decrement the value of Count array position 0

  
Step 23: 27 has current digit 7. So we look in position 7 of the Count array, to see that we put it in position 5 of the Auxilliary array.

And we decrement the value of Count array position 7

  

  
Step 24: 14 has current digit 4. So we look in position 4 of the Count array, to see that we put it in position 2 of the Auxilliary array.

And we decrement the value of Count array position 4

  

  
Step 25: 36 has current digit 6. So we look in position 6 of the Count array, to see that we put it in position 4 of the Auxilliary array.

And we decrement the value of Count array position 6

Done with this pass1.

Step 26 : Now we move the value back to the Input Array

40 has current digit 4. Add one to the 4 bin.

  

Step 27: 31 has current digit 3. Add one to the 3 bin.

Step 28: 14 has current digit 1. Add one to the 1 bin

Step 29:   5 has current digit 0. Add one to the 0 bin.

36 has current digit 3. Add one to the 3 bin.

Step 30: 36 has current digit 3. Add one to the 3 bin.

Step 31: 27 has current digit 2. Add one to the 2 bin.

Step 32: 17 has current digit 1. Add one to the 1 bin.

Step 33: Now we will do a rolling summation of the count array, to be used next as positions

But first we subtract 1 from the 0 position so that the resulting sums yield correct positions in the Auxilliary array.
Step 34: 0 + 2 is 2. Put that in position 1

Step 35: 2 + 1 is 3. Put that in position 2

3 + 2 is 5. Put that in position 3
Step 36:

3 + 2 is 5. Put that in position 3
Step 37:

5 + 1 is 6. Put that in position 4
Step 38:

5 + 1 is 6. Put that in position 4
Step 39:

6 + 0 is 6. Put that in position 5
Step 40:

6 + 0 is 6. Put that in position 6
Step 41:

6 + 0 is 6. Put that in position 7
Step 42:

6 + 0 is 6. Put that in position 8

Step 43:

6 + 0 is 6. Put that in position 9
Step 44:

Step 45: Now use the Count array to decide where to move values into the Auxilliary array

And we decrement the value of Count array position 1

Step 46: 27 has current digit 2. So we look in position 2 of the Count array, to see that we put it in position 3 of the Auxilliary array.

And we decrement the value of Count array position 2

Step 47: 36 has current digit 3. So we look in position 3 of the Count array, to see that we put it in position 5 of the Auxilliary array.

And we decrement the value of Count array position 3

Step 48: 5 has current digit 0. So we look in position 0 of the Count array, to see that we put it in position 0 of the Auxilliary array.

And we decrement the value of Count array position 0

Step 49: 14 has current digit 1. So we look in position 1 of the Count array, to see that we put it in position 1 of the Auxilliary array.

And we decrement the value of Count array position 1

Step 50: 31 has current digit 3. So we look in position 3 of the Count array, to see that we put it in position 4 of the Auxilliary array.

And we decrement the value of Count array position 3

Step 51: 40 has current digit 4. So we look in position 4 of the Count array, to see that we put it in position 6 of the Auxilliary array

And we decrement the value of Count array position 4

Done with this pass2.
Step 52: Now we move the value back to the Input Array

The array after Sorting is 5,14,17,27,31,36,40