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Interchange Sort

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					                                  SORTING
                                ALGORITHMS


Sorting is an everyday activity in which the efficiency of the algorithm used is very
important. There are many sorting algorithms designed for use on computers and there
are computer packages available that enable us to compare the merits of the various
algorithms.




                                TYPES OF SORTING
                                  ALGORITHMS




INTERCHANGE
    SORT                                               SHUTTLE                     QUICK SORT
 ALGORITHMS                 BUBBLE                      SORT                       ALGORITHMS
                             SORT                    ALGORITHMS
                          ALGORITHMS
                    INTERCHANGE SORT
                             ALGORITHMS


In this algorithm, the smallest number in the list is found and interchanged with the first
number. Then the smallest excluding the first is found and interchanged with the second
number. Next the smallest numbers excluding the first two are found and interchange
with the third number. This process continues until the list is sorted.




           HOW TO SOLVE??



                     STEPS:
       7
                     1. List down the numbers such the figure besides.

       5             2. Swap 7 to 1 and 1 to 7.

                     3. Write the rest number.
       2
                     4. After that swap 5 to 2 and 2 to 5.

       4             5. Next, continue the process by comparing each number into the

                         correct order if necessary.
      10
                     6. Make sure all the numbers are sorted correctly.

       1             7. Total up the comparisons after the process had done.


       6
                                      ATTENTION!
                                             : These arrows
       3                              symbolized the swaps during
                                      the comparisons process.
           LET’S DO IT!


 7                 1          1          1          1          1          1          1

 5                 5          2          2          2          2          2          2

 2                 2          5          3          3          3          3          3

 4                 4          4          4          4          4          4          4

10               10         10         10         10           5          5          5

 1                 7          7          7          7          7          6          6

 6                 6          6          6          6          6          7          7

 3                 3          3          5          5        10         10         10
                          2nd pass
Original




                                     3rd pass



                                                4th pass




                                                           5th pass




                                                                      6th pass




                                                                                 7th pass
               1st pass
  list
NOTES:

Although no interchange take place on the 4th and 7th passes, this is a property of this
particular list and the passes must still be carried out to ensure that the list is correctly
sorted.

For the selection with interchange sort, we can see that:

The number of comparisons on the 1st pass=7, 2nd pass=6, 3rd pass=5, 4th pass=4,
5th pass=3, 6th pass=2, and 7th pass=1.

This gives a total of 7+6+5+4+3+2+1=28 comparisons.

The number of swaps will be at most one per pass.




            The idea of interchange sort method is to
             arrange the numbers from the smallest
              numbers on the top and the biggest
           numbers on the bottom. To do so, we need
           to swap the numbers if necessary until we
                   get exactly a correct order.
QUESTION 1


 6               2                  2              2            2            2             2

 5               5                  4              4            4            4             4

 9               9                  9              6            5            5             5

 4               4                  5              5            6            5             5

 5               5                  5              5            5            6             6

 2               6                  6              9            9            9             9
                                2nd pass
Original




                                               3rd pass




                                                            4th pass




                                                                         5th pass




                                                                                       6th pass
             1st pass
  list




                                               By following the steps before, let us see
 LET’S                                         whether the answer is correct or not.
 SEE!
                        1. Swap 6 to 2 and 2 to 6. Write the rest numbers.
                        2. After that swap 5 to 4 and 4 to 5. Write the rest numbers.
                        3. Continue swapping the numbers into a correct order.
                        4. Finally, swap 5 to 6 and 6 to 5. Now all the numbers have been
                           compared.
                        5. Write again the list to make sure all the numbers have been
                           sorted correctly.
                        6. Total up the number of comparisons.
QUESTION 2

Rearrange these numbers using the interchange sort algorithm. {11, 9, 3, 7, 2, 4}



        11                4            4             3            2            2

         9                9            2             2            3            3

         3                3            3             4            4            4

         7                7            7             7            7            7

         2                2            9             9            9            9

         4              11           11           11           11           11
                                   2nd pass
        Original




                      1st pass




                                                 3rd pass




                                                              4th pass




                                                                           5th pass
          list




Number of comparisons: 5+4+3+2+1=15 comparisons
QUESTION 3

Show the numbers below in the correct order by doing interchange sort. Total the
number of comparisons.



     18              18              15              11              11

     21              12              12              12              12

     11              11              11              15              15

     15              15              18              18              18

     12              21              21              21              21
                                    2nd pass
                    1st pass
    Original




                                                    3rd pass




                                                                    4th pass
      list




Number of comparisons: 4+3+2+1=10 comparisons
QUESTION 4

By following the steps, sort the numbers below correctly.


   8               8              8             5               2          2          2

   9               9              3             3               3          2          2

   2               2              2             2               2          3          3

   2               2              2             2               5          5          5

   5               5              5             8               8          8          8

   3               3              9             9               9          9          9

  11             10             10            10              10         10         10

  10             11             11            11              11         11         11
                              2nd pass
  Original




                                            3rd pass




                                                            4th pass




                                                                       5th pass




                                                                                  6th pass
               1st pass
    list




Number of comparisons: 6+5+4+3+2+1=21 comparisons
QUESTION 5

Arrange the number list below in the correct order and after that find the number of
comparisons.



       28              12                3               3               3

       28              28              28              12              12

       25              25              25              25              25

        3                3             12              28              28

       12              28              28              28              28
                                     2nd pass
       Original




                                                     3rd pass




                                                                     4th pass
                     1st pass
         list




Number of comparisons: 4+3+2+1=10 comparisons
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posted:8/13/2012
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