Bubble Sort

Sorting  Computers only use numeric values for sorting  Does this mean you cannot sort a file by a character field (such as last name or state)?  No, it doesn’t. The computer converts all characters into a series of 0’s and 1’s. It’s the 0’s and 1’s that the computer uses to compare fields for sorting.  You can sort a file by  ascending order (lowest to highest)  descending order (highest to lowest)

Bubble Sort Logic  Let’s look at the logic to sort 5 test scores in a file  The mainline logic will consist of 3 subroutines  Housekeeping  Sort-Scores  Finish-Up

Starting the Sort-Scores Routine  When Housekeeping is done, the five scores from the In-Score file are in the Score array.  Let’s assume the scores are: Score(1) = 90 Score(2) = 85 Score(3) = 65 Score(4) = 95 Score(5) = 75 The next slide shows the start of the routine

Swapping Scores  To start the sort, the first two values in the array are compared. Score(1) = 90 Score(2) = 85 Score(3) = 65 Score(4) = 95 Score(5) = 75 If they are out of ascending order, switch (or swap) their positions in the array Score(1) = 85 Score(2) = 90 Score(3) = 65 Score(4) = 95 Score(5) = 75 The order is a little better than before

Swapping Dilemma  Here is our original score array  If we move the value 90 from Score(1) to Score(2),  both array elements would contain the value 90  the value 85 would be lost  If you move 85 to Score(1), then the value 90 would be lost  How can we solve this problem? Score(1) = 90 Score(2) = 85 Score(3) = 65 Score(4) = 95 Score(5) = 75

Swapping Solution  The solution: create a temporary variable to hold one of the scores  The solution work like this:  Move 85 - in Score(2) - to Temp –Move 90 - in Score(1) - to Score(2) –Move 85 - in Temp - the Score(1) Now Score(1) equals 85 and Score(2) equals 90

More on Swapping  The previous routine is written only to switch elements 1 and 2  Here is a more universal routine that can be used with any two adjacent elements to be swapped  Variable X represents the position of the first element  Value X+1 represents the position of the second element

Sorting Logic  The decision - Score(X) > Score(X+1) has to be executed four times.  Why not five times since there are five elements?  5 is the last element, so there is no element after it to compare

Following the Swapping Logic - Step 1  The original array Score(1) = 85 Score(2) = 90 Score(3) = 65 Score(4) = 95 Score(5) = 75 Score(1) = 90 Score(2) = 85 Score(3) = 65 Score(4) = 95 Score(5) = 75 The logic: –Set X to 1 –X < 5, so the loop is entered –Compare Score(X) = 90 to Score(X+1) = 85. They are out of order so swap them The result is:

Following the Swapping Logic - Step 2  Step 2 logic:  Add 1 to X; X now equals 2  X < 5, so the loop is entered  Compare Score(X) = 90 to Score(X+1) = 65. They are out of order so swap them  The result is: Score(1) = 85 Score(2) = 90 Score(3) = 65 Score(4) = 95 Score(5) = 75 Score(1) = 85 Score(2) = 65 Score(3) = 90 Score(4) = 95 Score(5) = 75

Following the Swapping Logic - Step 3  Step 3 logic:  Add 1 to X; X now equals 3  X < 5, so the loop is entered  Compare Score(X) = 90 to Score(X+1) = 95. They are in order. No swap is made  The result is: Score(1) = 85 Score(2) = 65 Score(3) = 90 Score(4) = 95 Score(5) = 75 Score(1) = 85 Score(2) = 65 Score(3) = 90 Score(4) = 95 Score(5) = 75

Following the Swapping Logic - Step 4  Step 4 logic:  Add 1 to X; X now equals 4  X < 5, so the loop is entered  Compare Score(X) = 95 to Score(X+1) = 75. They are out of order so swap them  The result is: Score(1) = 85 Score(2) = 65 Score(3) = 90 Score(4) = 95 Score(5) = 75 Score(1) = 85 Score(2) = 65 Score(3) = 90 Score(4) = 75 Score(5) = 95

Following the Swapping Logic - Step 5  Step 5 logic:  Add 1 to X; X now equals 5  X = 5, so the loop is not entered and the swapping logic is completed  Every element has been compared to the one adjacent to it Score(1) = 85 Score(2) = 65 Score(3) = 90 Score(4) = 75 Score(5) = 95 The largest amount (95) has sunk to the bottom of the list

Continuing the Swapping Logic  Although the list is in a better ascending order, it is still not in order  The five steps need to be performed again so the following values will swap places  85 and 65  90 and 75 Score(1) = 85 Score(2) = 65 Score(3) = 90 Score(4) = 75 Score(5) = 95 Score(1) = 65 Score(2) = 85 Score(3) = 75 Score(4) = 90 Score(5) = 95

Continuing the Swapping Logic  The five steps will need to be performed one more time to swap 85 and 75  The final result Score(1) = 65 Score(2) = 85 Score(3) = 75 Score(4) = 90 Score(5) = 95 Score(1) = 65 Score(2) = 75 Score(3) = 85 Score(4) = 90 Score(5) = 95

If the list were in the worst possible order....  The five steps would have to be performed four time to get the list in correct ascending order Score(1) = 95 Score(2) = 90 Score(3) = 85 Score(4) = 75 Score(5) = 65 Score(1) = 65 Score(2) = 75 Score(3) = 85 Score(4) = 90 Score(5) = 95 To go from this list to this list Have to pass through the loop 4 times

Complete Sort Logic  X is used to determine that all elements in the list have been compared for swapping Y is used to determine if there have been enough passes through the list to sort the list correctly

More on Bubble Sorts  Using a variable for the array size  Previously, a constant (5) was used to determine the end of loop processing  Using a variable means the code doesn’t change if the size of the array changes

Rules for Sorting  The greatest number of pair comparisons needed to be made during each loop is one fewer than the number of elements is the array  The pair comparison loop needs to be processed one time fewer than the number of elements in the array

Reducing Unnecessary Comparisons  In a bubble sort, the first pass through the list guarantees the last item on the list will be at the bottom  For second pass, the second to the last item will be in the correct position  Each pass will correctly place an item towards the bottom of the list  When performing each pass, why continue to compare items known to be correct?

Reducing Comparisons Logic  Pairs-To-Compare is set to X-1 the first time through the list Comparisons are done Pairs-To-Compare times 1 is subtracted from Pairs- To-Compare, so next comparison processing will pass one less time

Eliminating Unnecessary Passes Logic  To eliminate unneeded passes -  Set a flag (Switch-Occurred) to “No” before starting –When a switch occurs, set the flag to “Yes” –If a pass has no switches, the flag remains set to “No” –If the flag is “No” when exiting the loop, the sort is finished